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Long Division Calculator

Division is one of the basic arithmetic operations, the others being multiplication (the inverse of division), addition, and subtraction. The arithmetic operations are ways that numbers can be combined in order to make new numbers. Division can be thought of as the number of times a given number goes into another number. For example, 2 goes into 8 4 times, so 8 divided by 4 equals 2.

Division can be denoted in a few different ways. Using the example above:

8 ÷ 4 = 2

In order to more effectively discuss division, it is important to understand the different parts of a division problem.

Components of division

Generally, a division problem has three main parts: the dividend, divisor, and quotient. The number being divided is the dividend, the number that divides the dividend is the divisor, and the quotient is the result:

One way to think of the dividend is that it is the total number of objects available. The divisor is the desired number of groups of objects, and the quotient is the number of objects within each group. Thus, assuming that there are 8 people and the intent is to divide them into 4 groups, division indicates that each group would consist of 2 people. In this case, the number of people can be divided evenly between each group, but this is not always the case. There are two ways to divide numbers when the result won't be even. One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an integer, and the leftover number is a remainder. For example, 9 cannot be evenly divided by 4. Instead, knowing that 8 ÷ 4 = 2, this can be used to determine that 9 ÷ 4 = 2 R1. In other words, 9 divided by 4 equals 2, with a remainder of 1. Long division can be used either to find a quotient with a remainder, or to find an exact decimal value.

components of division

How to perform long division?

To perform long division, first identify the dividend and divisor. To divide 100 by 7, where 100 is the dividend and 7 is the divisor, set up the long division problem by writing the dividend under a radicand, with the divisor to the left (divisorvdividend), then use the steps described below:

long division step 1

This is the stopping point if the goal is to find a quotient with a remainder. In this case, the quotient is 014 or 14, and the remainder is 2. Thus, the solution to the division problem is:

100 ÷ 7 = 14 R2

To continue the long division problem to find an exact value, continue the same process above, adding a decimal point after the quotient, and adding 0s to form new dividends until an exact solution is found, or until the quotient to a desired number of decimal places is determined.

long division step 6

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Long Division Calculator – with Steps to Solve

Enter the divisor and dividend below to calculate the quotient and remainder using long division. The results and steps to solve it are shown below.

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How to Do Long Division with Remainders

Parts of a long division problem, steps to calculate a long division problem, how to get the quotient and remainder as a decimal, how to do long division without division, frequently asked questions.

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Learning long division is a crucial milestone in understanding essential math skills and a rite of passage to completing elementary school. It strikes fear in elementary school students and parents alike.

A recent study found that the understanding of long division and fractions in elementary school is directly linked to the student’s ability to learn and understand algebra later in school. [1]

Have no fear!

Learning long division can be easy, and in just a few easy steps, you can solve any long division problem. Follow along as we break it down, but first, we need to cover the anatomy of a long division problem.

diagram showing the parts of a long division math problem

There are a few parts to a long division problem, as shown in the image above.

The dividend is the number being divided and appears to the right and under the division line.

The divisor is the number being divided by and appears to the left of the division line.

The quotient is the solution and is shown above the dividend over the division line. Often in long division, the quotient is referred to as just the whole number part of the solution.

The remainder is the remaining part of the solution, or what’s leftover, that doesn’t fit evenly into the quotient.

There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process.

Step One: Set up the Expression

The first step in solving a long division problem is to draw the equation that needs to be solved. If the problem is already in long division form, then skip along to step two.

If it’s not, this is how to draw the long division problem.

Start by drawing a vertical bar to separate the divisor and dividend and an overbar to separate the dividend and quotient.

Place the dividend to the right of the vertical bar and under the overbar. Place the divisor to the left of the vertical bar.

For example , to divide 75 by 4, the long division problem should look like this:

diagram showing how to write a long division proble

Step Two: Divide

With the long division problem drawn, start by dividing the first digit in the dividend by the divisor.

You can also think about this as counting the number of times the divisor will evenly fit into this digit in the dividend.

If the divisor does not fit into the first digit an even number of times, drop the remainder or decimal portion of the result and write the whole number portion of the result in the quotient above the overline directly above the digit in the dividend.

For example , the divisor “4” goes evenly into the first digit of the dividend “7” one time, so a “1” can be added to the quotient above the 7.

diagram illustrating how to divide the first digit of the dividend by the divisor to solve the first digit of the quotient

Step Three: Multiply

The next step is to multiply the divisor by the digit just added to the quotient. Write the result below the digit in the dividend.

This step forms the part of the expression for the next step.

Continuing with our example, multiplying the divisor “4” by “1”, which we found in the previous step, equals “4”. So, add a “4” below the first digit in the dividend.

diagram illustrating how to multiply the divisor by the first digit of the quotient in the solution of a long division problem

Step Four: Subtract

Now, add a minus sign “-” before the number added in the previous step and draw a line below it to form a subtraction expression.

Continuing the example above, add a “-” before the “4” and a subtraction line below it.

diagram illustrating where to add the minus sign and subtraction line in a long division problem

Now that you have created a subtraction problem, it’s time to solve it.

To solve, subtract “7” minus “4”, which equals “3”, so write a “3” below the subtraction line.

diagram showing how to solve the subtraction portion of the long division problem where 7 minus 4 equals 3

Note: if the resulting value of the subtraction problem is greater than the divisor, then you made a mistake in step 2 and should double-check your work.

If the long division problem has a dividend that is a single digit, then hooray, you’re done! The remaining number that is the result of the subtraction problem is the remainder , and the number above the dividend is the whole number quotient.

If more digits are remaining in the dividend, then proceed to the next step.

Step Five: Pull Down the Next Number

At this point in the process, it’s time to operate on the next number in the dividend. To do this, pull down the next digit in the dividend and place it directly to the right of the result from the subtraction problem above.

The next digit in the dividend is “5”. So, pull “5” down and write it next to the “3” found in the previous step.

diagram showing how to pull down the next digit in the dividend in a long division problem

Step Six: Repeat

At this point, you might be wondering where to go from here. Repeat steps two to five until all the digits in the dividend have been pulled down, divided, multiplied, and subtracted.

When dividing, use the result of the subtraction problem combined with the pulled-down digit as the dividend and divide the divisor into it.

Continuing the examples above, divide the result of the subtraction problem and the pulled-down digit by the divisor. Thus, the next step is to divide 35 by 4. The result is “8”, so add “8” to the quotient.

diagram showing how to divide 35 by 4 to find the next digit in the quotient

Next, multiply the quotient digit “8” by the divisor “4”, which equals 32. Add “32” to the long division problem and place a negative sign in front of it.

diagram showing how to multiply 8 by 4 equalling 32

Next, repeat the subtraction process, subtracting 32 from 35, which equals 3. Add a “3” below the subtraction line. Since there are no longer any remaining digits in the dividend, this is the remainder portion of the solution.

diagram showing how to subtract 32 from 35 to find the remainder in the long division problem

Therefore, 75 divided by 4 is 18 with a remainder of 3. As you practice these steps, use the calculator above to confirm your answer and validate your steps solving long division problems.

If you’ve gotten this far, then you should have a good idea of how to solve a long division problem, but you might be stuck if you need to get the quotient as a decimal rather than a whole number with a remainder.

To calculate the quotient in decimal form, follow the steps above the get the whole number and remainder.

Next, divide the remainder by the divisor to get the remainder as a decimal. Finally, add the decimal to the quotient to get the quotient in decimal form.

For example , 75 ÷ 4 is 18 with a remainder of 3.

Divide 3 by 4 to get the decimal 0.75. 3 ÷ 4 = 0.75

Then, add 0.75 to 18 to get the quotient as a decimal. 0.75 + 18 = 18.75

Thus, the decimal form of 75 ÷ 4 equals 18.75.

While it defeats the purpose of actually learning how to do long division, there is technically a way to perform long division without actually doing any division. The way to do this is as follows.

Set up the long division expression the exact same way as you would normally.

Graphic showing the first step of setting up the expression for the subtraction method of doing long division

Step Two: Repeatedly Subtract the Divisor

Now, subtract the divisor from the dividend. Afterward, subtract the divisor again from the remaining value. Do this repeatedly until the remaining value is less than the divisor.

Graphic showing the second step of repeatedly subtracting for the subtraction method of doing long division

Step Three: Count the Number of Subtractions

Finally, to find the quotient, simply count the number of times you subtracted the divisor. This is the whole number portion of the quotient, and the final remaining value is the remainder.

Graphic showing the final step of calculating the quotient and remainder for the subtraction method of doing long division

Note: While this method of solving long division problems may seem easier, it is often very impractical to do so. For example, in the above example of 75 divided by 4, you would need to repeat the subtraction 18 times!

Therefore, traditional long division is the vastly superior method.

Why is long division important?

Long division is important not just because it is a tool that allows us to solve difficult division problems, but because it helps to teach logical thinking that will prepare students to excel in solving future mathematical problems.

Why do we still teach long division?

We still teach long division because it teaches students how to think logically, a valuable skill that is shown not just to improve future understanding of algebraic concepts, but also to help solve problems in all aspects of their lives.

How do you check a long division answer?

Just like subtraction is the opposite of addition, multiplication is the opposite of division. Therefore, to check a long division answer, multiply the quotient by the divisor, and if it equals the dividend, then the answer is correct!

Can you do long division on a calculator?

While a calculator can solve division problems, it will not list out the steps used in evaluating a long division problem, and will therefore not improve your understanding of how to perform long division.

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How to Solve Division Problems and Find the Right Answer

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Finding the right answer when you're dividing can be tricky. Keep reading to learn some tips and tricks for getting the correct solution to your division problems!

Getting Division Problems Right

Know how to solve.

The first step in getting division problems right is using the correct process to solve them. When you're working with long division problems, it's important to have the basic division facts memorized. Use flashcards to master all of the division facts within 100.

It also helps to know that division is the inverse of multiplication. This means you can multiply the quotient of a division problem (the answer) by the divisor (number you're dividing by) to get the dividend (number being divided). For instance, in the problem 12 ÷ 3 = 4, 12 is the dividend, 3 is the divisor and 4 is the quotient, so 4 x 3 = 12.

Once you've mastered your basic division facts, the next step is to get a handle on long division. One of the most challenging aspects of dividing larger numbers is estimating each digit of the answer. For instance, when you're dividing 645 by 9, you'll start by estimating how many times 9 goes into 64. Below are several techniques you can use to help you estimate:

Checking Your Answer

Even if you've followed the correct procedure to solve your division problem, it's still possible that you made a small mathematical error somewhere along the line. Fortunately, there's a very effective way to check that your answer is correct. Follow these steps:

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Division can be confusing, especially when working with larger numbers. Read on to learn how to help your fifth grader remember how to divide many different lengths of numbers.

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Division is splitting into equal parts or groups.

It is the result of "fair sharing"., example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates.

Answer: 12 divided by 3 is 4. They get 4 each.

We use the ÷ symbol, or sometimes the / symbol to mean divide:

Let's use both symbols here so we get used to them.

More Examples

Here are some more examples:

Opposite of Multiplying

Division is the opposite of multiplying . When we know a multiplication fact we can find a division fact:

Example: 3 × 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Why? Well, think of the numbers in rows and columns like in this illustration:

So there are four related facts :

Knowing your Multiplication Tables can help you with division!

Example: What is 28 ÷ 7 ?

Searching around the multiplication table we find that 28 is 4 × 7, so 28 divided by 7 must be 4.

Answer: 28 ÷ 7 = 4

There are special names for each number in a division:

dividend ÷ divisor = quotient

Example: in 12 ÷ 3 = 4:

  • 12 is the dividend
  • 3 is the divisor
  • 4 is the quotient

But Sometimes It Does Not Work Perfectly!

Sometimes we cannot divide things up exactly ... there may be something left over.

Example: There are 7 bones to share with 2 pups.

But 7 cannot be divided exactly into 2 groups, so each pup gets 3 bones, but there will be 1 left over :

We call that the Remainder .

Read more about this at Division and Remainders

Try these division worksheets .

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How to Do Long Division

Last Updated: November 29, 2023 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 3,846,897 times.

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals . This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life. [1] X Research source

Step 1 Set up the equation.

  • The quotient (answer) will eventually go on top, right above the dividend.
  • Leave yourself plenty of space below the equation to carry out multiple subtraction operations.
  • Here's an example: if there are six mushrooms in a 250-gram pack, how much does each mushroom weigh on average? In this case, we must divide 250 by 6. The 6 goes on the outside, and the 250 on the inside.

Step 2 Divide the first digit.

  • In our example, you'd want to determine how many times 6 goes into 2. Since six is larger than two, the answer is zero. If you wish, may write a 0 directly above the 2 as a place-holder, and erase it later. Alternatively, you can leave that space blank and move on to the next step.

Step 3 Divide the first...

  • If your answer to the previous step was 0, as in the example, expand the number by one digit. In this case, we'd ask how many times 6 can go into 25.
  • If your divisor has more than two digits, you'll have to expand out even further, to the third or maybe even fourth digit of the dividend in order to get a number that the divisor goes into.
  • Work in terms of whole numbers . If you use a calculator , you'll discover that 6 goes into 25 a total of 4.167 times. In long division, you always round down to the nearest whole number, so in this case, our answer would be 4.

Step 4 Enter the first digit of the quotient.

  • It is important in long division to make sure the columns of numbers remain correctly aligned. Work carefully, otherwise you may make an error that leads you to the wrong answer.
  • In the example, you would place a 4 above the 5, since we're putting 6 into 25.

Multiplying

Step 1 Multiply...

  • In the example, 6 times 4 is 24. After you've written a 4 in the quotient, write the number 24 beneath the 25, again being careful to keep the numbers aligned.

Step 3 Draw a line.

Subtracting

Step 1 Subtract...

  • In the example, we'll subtract 24 from 25, getting 1.
  • Do not subtract from the complete dividend, but only those digits you worked with in Parts One and Two. In the example, you should not subtract 24 from 250.

Step 2 Bring down the next digit.

  • In the example, because 6 can't go into 1 without exceeding it, you need to bring down another digit. In this case, you'll grab the 0 from 250 and place it after the 1, making it 10, which 6 can go into.

Step 3 Repeat the whole process.

  • In the example, determine how many times 6 can go into 10. Write that number (1) into the quotient above the dividend. Then multiply 6 by 1, and subtract the result from 10. You should end up with 4.
  • If your dividend has more than three digits, keep repeating this process until you've worked through all of them. For example, if we we had started with 2,506 grams (88.4 oz) of mushrooms, we'd pull the 6 down next and place it next to the four.

Remainders and Decimals

Step 1 Record the remainder.

  • In the example, the remainder would be 4, because 6 cannot go into four, and there are no more digits to bring down.
  • Place your remainder after the quotient with a letter "r" before it. In the example, the answer would be expressed as "41 r4."
  • You would stop here if you were trying to calculate something that would not make sense to express in partial units , for example, if you were trying to determine how many cars were needed to move a certain number of people. In a case such as this, it would not be useful think about things in terms of partial cars or partial people.
  • If you plan to calculate a decimal, you can skip this step.

Step 2 Add a decimal point.

  • In the example, since 250 is a whole number, every digit after the decimal will be 0, making it 250.000.

Step 3 Keep repeating.

  • In the example, determine how many times 6 can go into 40. Add that number (6) to the quotient above the dividend and after the decimal point. Then multiply 6 by 6, and subtract the result from 40. You should end up with 4 again.

Step 4 Stop and round.

  • In the example, you could keep getting 4 out of 40-36 forever, and add 6's to your quotient indefinitely. Instead of doing this, stop the problem and round the quotient. Because 6 is greater than (or equal to) 5, you would round up to 41.67.
  • Alternatively, you can indicate a repeating decimal by placing a small horizontal line over the repeating digit. In the example, this would make the quotient 41.6, with a line over the 6. [15] X Research source

Step 5 Add the unit back to your answer.

  • If you added a zero as a place-holder at the beginning, you should erase that now as well.
  • In the example, because you asked how much each mushroom in a 250-gram pack of 6 weighs, you'll need to put your answer into grams. Therefore, your final answer is 41.67 grams.

Practice Problems and Answers

how do you solve this division problem

Community Q&A

wikiHow Staff Editor

Video . By using this service, some information may be shared with YouTube.

  • If you have time, it's a good idea to do calculations on paper first, then check with a calculator or computer. Remember that machines sometimes get the answers wrong for various reasons. If there is an error, you can do a third check using logarithms . Doing division by hand rather than relying on machines is good for your mathematical skills and conceptual understanding. [16] X Research source Thanks Helpful 2 Not Helpful 0
  • Start by using simple calculations. This will give you the confidence and develop the necessary skills to move to more advanced ones. Thanks Helpful 11 Not Helpful 7
  • Look for practical examples from everyday life. This will help learn the process because you can see how it is useful in the real world. Thanks Helpful 1 Not Helpful 1

Tips from our Readers

  • To remember the steps, use the mnemonic "Does McDonalds Sell Cheese Burgers Rare?" The D stands for "divide", M for "multiply", S for "subtract", C for "check" your work, B for "bring down" more digits, and R for "repeat" the whole process if needed. This little memory device covers all the key parts of long division.
  • Be sure you have multiplication facts mastered before attempting long division. It will be painfully slow if you must stop to figure out what 7 x 7 is each time. Quick recall of times tables is essential. Consider practicing flash cards or math games to improve.
  • To divide any number by a power of 10, simply move the decimal point leftward by the exponent on the 10. For example, to divide 20 by 1000 (which is 10^3), think "what times 20 equals 1000?" and move the decimal in 20 three places left to get 0.02.
  • Long division works very similarly to dividing fractions. Set up the equation just like a fraction, with the number being divided (dividend) on top and divisor on bottom. Then divide the numerator by denominator using the long division process.
  • Don't worry if you make mistakes at first! Long division takes practice. Check each step carefully as you work problems. Over time, you will get faster and more confident. Be patient with yourself and celebrate small successes along the way.

how do you solve this division problem

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  • ↑ https://www.csun.edu/~vcmth00m/longdivision.pdf
  • ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut36_longdiv.htm
  • ↑ https://www.calculatorsoup.com/calculators/math/longdivision.php
  • ↑ https://www.mathsisfun.com/long_division.html
  • ↑ https://www.bbc.co.uk/bitesize/guides/z3kmpbk/revision/4
  • ↑ https://flexbooks.ck12.org/cbook/ck-12-fifth-grade-math-resource-flexlet/section/1.1/primary/lesson/long-division-without-remainders/
  • ↑ https://www.mathsisfun.com/long_division2.html
  • ↑ https://www.calculatorsoup.com/calculators/math/longdivisiondecimals.php
  • ↑ https://www.mathsisfun.com/definitions/recurring-decimal.html

About This Article

Grace Imson, MA

To do long division, follow these seven steps: Step 1. Calculate how many times the number outside the division bar goes into the first number inside the bar. Step 2. Put the answer on top of the bar. Step 3. Multiply the number outside the division bar by the number at the top of the bar. Step 4. Write the answer below the number inside the division bar, so the first digits of both numbers are lined up. Step 5. Subtract the two numbers inside the division bar and write the answer below the two numbers. If there are any remaining digits inside the division bar, bring them down to the new answer. Step 6. Repeat the division process with the new number. Step 7: If you get to a point where the number outside the division bar can’t fit into the remaining number, write that number, also known as the remainder, next to your answer with an “r” in front of it. Did this summary help you? Yes No

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Long Division

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too. Let us learn how to divide using the long division method , along with long division examples with answers, which include the long division steps in this article.

What is Long Division Method?

Long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division . Observe the following long division method to see how to divide step by step and check the divisor, the dividend, the quotient, and the remainder.

Long Division Method - Long division step by step

The above example also showed us how to do 2 digit by 1 digit division.

Parts of Long Division

While performing long division, we need to know the important parts of long division. The basic parts of long division can be listed as follows:

The following table describes the parts of long division with reference to the example shown above.

How to do Long Division?

Division is one of the four basic mathematical operations, the other three being addition , subtraction , and multiplication . In arithmetic, long division is a standard division algorithm for dividing large numbers, breaking down a division problem into a series of easier steps. Let us learn about the steps that are followed in long division.

Long Division Steps

In order to perform division, we need to understand a few steps. The divisor is separated from the dividend by a right parenthesis 〈)〉 or vertical bar 〈|〉 and the dividend is separated from the quotient by a vinculum (an overbar). Now, let us follow the long division steps given below to understand the process.

  • Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
  • Step 2: Then divide it by the divisor and write the answer on top as the quotient.
  • Step 3: Subtract the result from the digit and write the difference below.
  • Step 4: Bring down the next digit of the dividend (if present).
  • Step 5: Repeat the same process.

Let us have a look at the examples given below for a better understanding of the concept. While performing long division, we may come across problems when there is no remainder, while some questions have remainders. So, first, let us learn division in which we get remainders.

Division with Remainders

Case 1: When the first digit of the dividend is equal to or greater than the divisor.

Example: Divide 435 ÷ 4

Solution: The steps of this long division are given below:

  • Step 1: Here, the first digit of the dividend is 4 and it is equal to the divisor. So, 4 ÷ 4 = 1. So, 1 is written on top as the first digit of the quotient.
  • Step 2: Subtract 4 - 4 = 0. Bring the second digit of the dividend down and place it beside 0.
  • Step 3: Now, 3 < 4. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it beside 3.
  • Step 4: So, we have 35 as the new dividend. We can see that 35 > 4 but 35 is not divisible by 4, so we look for the number just less than 35 in the table of 4 . We know that 4 × 8 = 32 which is less than 35 so, we go for it.
  • Step 5: Write 8 in the quotient. Subtract: 35 - 32 = 3.
  • Step 6: Now, 3 < 4. Thus, 3 is the remainder and 108 is the quotient.

Long Division steps

Case 2: When the first digit of the dividend is less than the divisor.

Example: Divide 735 ÷ 9

Solution: Let us divide this using the following steps.

  • Step 1: Since the first digit of the dividend is less than the divisor, put zero as the quotient and bring down the next digit of the dividend. Now consider the first 2 digits to proceed with the division.
  • Step 2: 73 is not divisible by 9 but we know that 9 × 8 = 72 so, we go for it.
  • Step 3: Write 8 in the quotient and subtract 73 - 72 = 1.
  • Step 4: Bring down 5. The number to be considered now is 15.
  • Step 5: Since 15 is not divisible by 9 but we know that 9 × 1 = 9, so, we take 9.
  • Step 6: Subtract: 15 - 9 = 6. Write 1 in the quotient.
  • Step 7: Now, 6 < 9. Thus, remainder = 6 and quotient = 81.

Divide 735 by 9 using long division method

Case 3: This is a case of long division without a remainder.

Division without Remainder

Example: Divide 900 ÷ 5

Solution: Let us see how to divide step by step.

Long Division without Remainder

  • Step 1: We will consider the first digit of the dividend and divide it by 5. Here it will be 9 ÷ 5.
  • Step 2: Now, 9 is not divisible by 5 but 5 × 1 = 5, so, write 1 as the first digit in the quotient.
  • Step 3: Write 5 below 9 and subtract 9 - 5 = 4.
  • Step 4: Since 4 < 5, we will bring down 0 from the dividend to make it 40.
  • Step 5: 40 is divisible by 5 and we know that 5 × 8 = 40, so, write 8 in the quotient.
  • Step 6: Write 40 below 40 and subtract 40 - 40 = 0.
  • Step 7: Bring down the next 0 from the dividend. Since 5 × 0 = 0, we write 0 as the remaining quotient.
  • Step 9: Therefore, the quotient = 180 and there is no remainder left after the division, that is, remainder = 0.

Long division problems also include problems related to long division by a 2 digit number, long division polynomials and long division with decimals. Let us get an an idea about these in the following sections.

Long Division by a 2 Digit Number

Long division by a 2 digit number means dividing a number by a 2-digit number . For long division by a 2 digit number , we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend.

For example, if we need to divide 7248 by 24, we can do it using the long division steps. Let us see how to divide step by step.

  • Step 1: Since it is a long division by a 2 digit number, we will check for the divisibility of the first two digits of the dividend. The first 2 digits of the dividend are 72 and it is greater than the divisor, so, we will proceed with the division.
  • Step 2: Using the multiplication table of 24, we know that 24 × 3 = 72. So we write 3 in the quotient and 72 below the dividend to subtract these. Subtract 72 - 72 = 0.
  • Step 3: Bring down the next number from the dividend, that is, 4. The number to be considered now is 4.
  • Step 4: Since 4 is smaller than 24, we will put 0 as the next quotient, since 24 × 0 = 0 and write 0 below 4 to subtract 4 - 0 = 4
  • Step 5: Bring down the next number from the dividend, that is, 8 and place it next to this 4. The number to be considered now is 48.
  • Step 6: Using the multiplication table of 24, we know that 24 × 2 = 48. So we write 2 in the quotient and 48 below the dividend to subtract these. Subtract 48 - 48 = 0. Thus, remainder = 0 and quotient = 302. This means, 7248 ÷ 24 = 302.
  • Long Division of Polynomials

When there are no common factors between the numerator and the denominator , or if you can't find the factors, you can use the long division process to simplify the expression. For more details about long division polynomials, visit the Dividing Polynomials page.

Long Division with Decimals

Long division with decimals can be easily done just like the normal division. We just need to keep in mind the decimals and keep copying them as they come. For more details about long division with decimals, visit the Dividing Decimals page.

How to Divide Decimals by Whole Numbers?

When we need to divide decimals by whole numbers, we follow the same procedure of long division and place the decimal in the quotient whenever it comes. Let us understand this with the help of an example.

Example: Divide 36.9 ÷ 3

  • Step 1: Here, the first digit of the dividend is 3 and it is equal to the divisor. So, 3 ÷ 3 = 1. So, 1 is written on top as the first digit of the quotient and we write the product 3 below the dividend 3.
  • Step 2: Subtract 3 - 3 = 0. Bring the second digit of the dividend down and place it beside 0, that is, 6
  • Step 3: Using the multiplication table of 3, we know that 3 × 2 = 6. So we write 2 in the quotient and 6 below the dividend to subtract these. Subtract 6 - 6 = 0.
  • Step 4 : Now comes the decimal point in the dividend. So, place a decimal in the quotient after 12 and continue with the normal division.
  • Step 5: Bring down the next number from the dividend, that is, 9. The number to be considered now is 9.
  • Step 6: Using the multiplication table of 3, we know that 3 × 3 = 9. So we write 3 in the quotient and 9 below the dividend to subtract these. Subtract 9 - 9 = 0. Thus, remainder = 0 and quotient = 12.3. This means, 36.9 ÷ 3 = 12.3

Long Division Tips and Tricks:

Given below are a few important tips and tricks that would help you while working with long division:

  • The remainder is always smaller than the divisor.
  • For division, the divisor cannot be 0.
  • The division is repeated subtraction, so we can check our quotient by repeated subtractions as well.
  • We can verify the quotient and the remainder of the division using the division formula : Dividend = (Divisor × Quotient) + Remainder.
  • If the remainder is 0, then we can check our quotient by multiplying it with the divisor. If the product is equal to the dividend, then the quotient is correct.

☛ Related Articles

  • Long Division Formula
  • Long Division with Remainders Worksheets
  • Long Division Without Remainders Worksheets
  • Long Division with 2-digit Divisors Worksheets
  • Long Division Calculator

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Long Division Examples with Answers

Example 1: Ron planted 75 trees equally in 3 rows. Use long division to find out how many trees did he plant in each row?

The total number of trees planted by Ron = 75. The number of rows = 3. To find the number of trees in each row, we need to divide 75 by 3 because there is an equal number of trees in each of the three rows. Let us also observe how to do 2 digit by 1 digit division here.

Long Division steps for dividing 75 by 3

Therefore, the number of trees in each row = 25 trees.

Example 2: $4000 needs to be distributed among 25 men for the work completed by them at a construction site. Calculate the amount given to each man.

The total amount is $4000. The number of men at work = 25. We need to calculate the amount given to each man. To do so, we have to divide 4000 by 25 using the long division method. Let us see how to work with long division by a 2 digit number and also see how to do long division step by step.

Long Division example

Each man will be given $160. Therefore, $160 is the amount given to each man.

Example 3: State true or false with respect to long division.

a.) In the case of long division of numbers, the remainder is always smaller than the divisor.

b.) We can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.

a.) True, in the case of long division of numbers, the remainder is always smaller than the divisor.

b.) True, we can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.

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Practice Questions on Long Division

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FAQs on Long Division

What is long division in math.

Long division is a process to divide large numbers in a convenient way. The number which is divided into smaller groups is known as a dividend, the number by which we divide it is called the divisor, the value received after doing the division is the quotient, and the number left after the division is called the remainder.

The following steps explain the process of long division. This procedure is explained with examples above on this page.

  • Write the dividend and the divisor in their respective positions.
  • Take the first digit of the dividend from the left.
  • If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top as the quotient.
  • Write the product below the dividend and subtract the result from the dividend to get the difference. If this difference is less than the divisor, and there are no numbers left in the dividend, then this is considered to be the remainder and the division is done. However, if there are more digits in the dividend to be carried down, we continue with the same process until there are no more digits left in the dividend.

What are the Steps of Long Division?

Given below are the 5 main steps of long division. For example, let us see how we divide 52 by 2.

  • Step 1: Consider the first digit of the dividend which is 5 in this example. Here, 5 > 2. We know that 5 is not divisible by 2.
  • Step 2: We know that 2 × 2 = 4, so, we write 2 as the quotient.
  • Step 3: 5 - 4 = 1 and 1 < 2 (After writing the product 4 below the dividend, we subtract them).
  • Step 4: 1 < 2, so we bring down 2 from the dividend and we get 12 as the new dividend now.
  • Step 5: Repeat the process till the time you get a remainder less than the divisor. 12 is divisible by 2 as 2 × 6 = 12, so we write 6 in the quotient, and 12 - 12 = 0 (remainder).

Therefore, the quotient is 26 and the remainder is 0.

How to do Long Division with 2 Digits?

For long division with 2 digits, we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend. If the first 2 digits of the dividend are less than the divisor, then consider the first three digits of the dividend. Proceed with the division in the same way as we divide regular numbers. This procedure is explained with examples above on this page under the heading of 'Long Division by a 2 Digit Number'.

What is the Long Division of Polynomials?

In algebra , the long division of polynomials is an algorithm to divide a polynomial by another polynomial of the same or the lower degree. For example, (4x 2 - 5x - 21) is a polynomial that can be divided by (x - 3) following some defined rules, which will result in 4x + 7 as the quotient.

How to do Long Division with Decimals?

The long division with decimals is performed in the same way as the normal division. This procedure is explained with examples above on this page under the heading of 'How to Divide Decimals by Whole Numbers'? For more details, visit the page about dividing decimals . The basic steps of long division with decimals are given below.

  • Write the division in the standard form.
  • Start by dividing the whole number part by the divisor.
  • Place the decimal point in the quotient above the decimal point of the dividend.
  • Bring down the digits on the tenths place, i.e., the digit after the decimal.
  • Divide and bring down the other digit in sequence.
  • Divide until all the digits of the dividend are over and a number less than the divisor or 0 is obtained in the remainder.

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Mathematics LibreTexts

1.3.2: Dividing Whole Numbers and Applications

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  • Page ID 60897

  • The NROC Project

Learning Objectives

  • Use three different ways to represent division.
  • Divide whole numbers.
  • Perform long division.
  • Divide whole numbers by a power of 10.
  • Recognize that division by 0 is not defined.
  • Solve application problems using division.

Introduction

Some people think about division as “fair sharing” because when you divide a number you are trying to create equal parts. Division is also the inverse operation of multiplication because it “undoes” multiplication. In multiplication, you combine equal sets to create a total. In division, you separate a whole group into sets that have the same amount. For example, you could use division to determine how to share 40 empanadas among 12 guests at a party.

What is Division?

Division is splitting into equal parts or groups. For example, one might use division to determine how to share a plate of cookies evenly among a group. If there are 15 cookies to be shared among five people, you could divide 15 by 5 to find the “fair share” that each person would get. Consider the picture below.

Screen Shot 2021-04-12 at 3.49.51 PM.png

15 cookies split evenly across 5 plates results in 3 cookies on each plate. You could represent this situation with the equation:

\(\ 15 \div 5=3\)

You could also use a number line to model this division. Just as you can think of multiplication as repeated addition, you can think of division as repeated subtraction. Consider how many jumps you take by 5s as you move from 15 back to 0 on the number line.

Screen Shot 2021-04-12 at 3.51.46 PM.png

Notice that there are 3 jumps that you make when you skip count by 5 from 15 back to 0 on the number line. This is like subtracting 5 from 15 three times. This repeated subtraction can be represented by the equation: \(\ 15 \div 5=3\).

Finally, consider how an area model can show this division. Ask yourself, if you were to make a rectangle that contained 15 squares with 5 squares in a row, how many rows would there be in the rectangle? Start by making one row of 5 squares:

Screen Shot 2021-04-12 at 3.56.19 PM.png

Then add two more rows of 5 squares so you have 15 squares.

Screen Shot 2021-04-12 at 3.57.02 PM.png

The number of rows is 3. So, 15 divided by 5 is equal to 3.

Find \(\ 24 \div 3\) using a set model and a number line model.

Screen Shot 2021-04-12 at 3.58.43 PM.png

Number line model:

Screen Shot 2021-04-12 at 3.59.12 PM.png

\(\ 24 \div 3=8\)

Ways to Represent Division

As with multiplication, division can be written using a few different symbols. We showed this division written as \(\ 15 \div 5=3\), but it can also be written two other ways:

\(\ \begin{array}{r} 3\\ 5 \longdiv { 1 5 } \end{array}\)

\(\ \frac{15}{5}=3\)

Each part of a division problem has a name. The number that is being divided up, that is the total, is called the dividend . In the work in this topic, this number will be the larger number, but that is not always true in mathematics. The number that is dividing the dividend is called the divisor . The answer to a division problem is called the quotient .

The blue box below summarizes the terminology and common ways to represent division.

Three Ways to Represent Division

\(\ 12 \div 3=4\) ( with a division symbol ; this equation is read "12 divided by 3 equals 4."

\(\ \begin{array}{r} 4\\ 3 \longdiv { 1 2 } \end{array}\) ( with a division or long division symbol ; this expression is read "12 divided by 3 equals 4." Notice here, though, that you have to start with what is underneath the symbol. This may take some getting used to since you are reading from right to left and bottom to top!)

\(\ \frac{12}{3}=4\) ( with a fraction bar ; this expression can also be read "12 divided by 3 equals 4." In this format, you read from top to bottom.)

In the examples above, 12 is the dividend , 3 is the divisor and 4 is the quotient.

\(\ \text { Dividend } \div \text { Divisor }=\text { Quotient }\)

\(\ \begin{array}{r} \text{Quotient}\\ \text{Divisor}\longdiv{\text{Dividend}} \end{array}\)

\(\ \frac{\text { Dividend }}{\text { Divisor }}=\text { Quotient }\)

Which of the following expressions represent dividing $56 equally among 7 people?

#1: \(\ \frac{7}{56}\)

#2: \(\ 56 \div 7\)

#3: \(\ 56\longdiv {7}\)

  • #2 represents the situation.
  • All three expressions represent the situation.
  • #1 represents the situation.
  • #3 represents the situation.
  • Correct. #2 is the only expression that represents 56 divided by 7.
  • Incorrect. #1 and #3 represent 7 divided by 56, not 56 divided by 7. The correct answer is #2 is the only expression that represents the situation.
  • Incorrect. This expression represents 7 divided by 56, not 56 divided by 7. The correct answer is #2 is the only expression that represents the situation.

Dividing Whole Numbers

Once you understand how division is written, you are on your way to solving simple division problems. You will need your multiplication facts to perform division. If you do not have them memorized, you can guess and check or use a calculator.

Consider the following problems:

\(\ 10 \div 5=?\)

\(\ 48 \div 2=?\)

\(\ 30 \div 5=?\)

In the first problem, \(\ 10 \div 5\), you could ask yourself, “how many fives are there in ten?” You can probably answer this easily. Another way to think of this is to consider breaking up 10 into 5 groups and picturing how many would be in each group.

\(\ 10 \div 5=2\)

To solve \(\ 48 \div 2\), you might realize that dividing by 2 is like splitting into two groups or splitting the total in half. What number could you double to get 48?

\(\ 48 \div 2=24\)

To figure out \(\ 30 \div 5\), you could ask yourself, how many times do you have to skip count by 5 to get from 0 to 30? 5, 10, 15, 20, 25, 30. You have to skip count 6 times to get to 30.

\(\ 30 \div 5=6\)

Compute \(\ 35 \div 5\).

Compute \(\ 32 \div 4\).

Sometimes when you are dividing, you cannot easily share the number equally. Think about the division problem \(\ 9 \div 2\). You could think of this problem as 9 pieces of chocolate being split between 2 people. You could make two groups of 4 chocolates, and you would have one chocolate left over.

Screen Shot 2021-04-14 at 12.57.15 PM.png

In mathematics, this left over part is called the remainder . It is the part that remains after performing the division. In the example above, the remainder is 1. We can write this as:

\(\ 9 \div 2=4\quad \mathrm{R} 1\)

We read this equation: “Nine divided by two equals four with a remainder of 1."

You might be thinking you could split that extra piece of chocolate in parts to share it. This is great thinking! If you split the chocolate in half, you could give each person another half of a piece of chocolate. They would each get \(\ 4 \frac{1}{2}\) pieces of chocolate. We are not going to worry about expressing remainders as fractions or decimals right now. We are going to use the remainder notation with the letter R. Here’s an example:

\(\ 45 \div 6\)

\(\ 45 \div 6=7\quad \mathrm{R} 3\)

Since multiplication is the inverse of division, you can check your answer to a division problem with multiplication. To check the answer 7 R3, first multiply 6 by 7 and then add 3.

\(\ 6 \cdot 7=42\)

\(\ 42+3=45\), so the quotient 7 R3 is correct.

Compute \(\ 67 \div 7\).

  • Incorrect. \(\ 9 \cdot 7=63\). There is a remainder of 4. The correct answer is 9 R4.
  • Correct. \(\ 9 \cdot 7=63\) and there are 4 left over.
  • Incorrect. This is a division, not subtraction, problem. The correct answer is 9 R4.
  • Incorrect. \(\ 70 \div 7=10\), so the answer to \(\ 67 \div 7\) cannot be; \(\ 9 \cdot 7=63\) and there are 4 left over. The correct answer is 9 R4.

Performing Long Division

Long division is a method that is helpful when you are performing division that you cannot do easily in your head, such as division involving larger numbers. Below is an example of a way to write out the division steps.

\(\ 68 \div 4\)

\(\ 68 \div 4=17\)

\(\ 6,707 \div 233\)

\(\ 6,707 \div 233=28 \quad\mathrm{R} 183\)

Compute \(\ 417 \div 34\).

  • Incorrect. This is a division problem, not an addition problem. The correct answer is 12 R9.
  • Incorrect. \(\ 12 \cdot 34=408\). The correct answer is 12 R9.
  • Correct. \(\ 12 \cdot 34=408\) and \(\ 408+9=417\)
  • Incorrect. \(\ 13 \cdot 34=442\). The correct answer is 12 R9.

Dividing Whole Numbers by a Power of 10

Just as multiplication by powers of 10 results in a pattern, there is a pattern with division by powers of 10. Consider three quotients: \(\ 20 \div 10 ; 200 \div 10 ; 2,000 \div 10\).

Think about \(\ 20 \div 10\). There are 2 tens in twenty, so \(\ 20 \div 10=2\). The computations for \(\ 200 \div 10\) and \(\ 2,000 \div 10\) are shown below.

\(\ 200 \div 10\)

\(\ 200 \div 10=20\)

\(\ 2000 \div 10\)

\(\ 2,000 \div 10=200\)

Examine the results of these three problems to try to determine a pattern in division by 10.

\(\ \begin{aligned} 20 \div 10 &=2 \\ 200 \div 10 &=20 \\ 2,000 \div 10 &=200 \end{aligned}\)

Notice that the number of zeros in the quotient decreases when a dividend is divided by 10: 20 becomes 2; 200 becomes 20 and 2,000 become 200. In each of the examples above, you can see that there is one fewer 0 in the quotient than there was in the dividend.

Continue another example of division by a power of 10.

\(\ 2,000 \div 100\)

\(\ 2,000 \div 100=20\)

Consider this set of examples of division by powers of 10. What pattern do you see?

\(\ \begin{array}{rl} 20 &\div &10=2 \\ 200 &\div &10=20 \\ 2,000 &\div &10=200 \\ 2,000 &\div &100=20 \\ 2,000 &\div &1,000=2 \end{array}\)

Notice that when you divide a number by a power of 10, the quotient has fewer zeros. This is because division by a power of 10 has an effect on the place value. For example, when you perform the division \(\ 18,000 \div 100=180\), the quotient, 180, has two fewer zeros than the dividend, 18,000. This is because the power of 10 divisor, 100, has two zeros.

Compute \(\ 135,000 \div 100\).

  • Incorrect. This answer is too large. \(\ 13,500 \cdot 100=1,350,000\). The correct answer is 1,350.
  • Incorrect. This is a division, not a subtraction, problem. The correct answer is 1,350.
  • Incorrect. This is a division, not a multiplication, problem. The correct answer is 1,350.
  • Correct. 1,350 \cdot 100=135,000.

Division by Zero

You know what it means to divide by 2 or divide by 10, but what does it mean to divide a quantity by 0? Is this even possible? Can you divide 0 by a number? Consider the two problems written below.

\(\ \frac{0}{8} \text { and } \frac{8}{0}\)

We can read the first expression, “zero divided by eight” and the second expression, “eight divided by zero.” Since multiplication is the inverse of division, we could rewrite these as multiplication problems.

\(\ 0 \div 8=?\)

\(\ ? \cdot 8=0\)

The quotient must be 0 because \(\ 0 \cdot 8=0\).

\(\ \frac{0}{8}=0\)

Now let’s consider \(\ \frac{8}{0}\).

\(\ 8 \div 0=?\)

\(\ ? \cdot 0=8\)

This is not possible. There is no number that you could multiply by zero and get eight. Any number multiplied by zero is always zero. There is no quotient for \(\ \frac{8}{0}\). There is no quotient for any number when it is divided by zero.

Division by zero is an operation for which you cannot find an answer, so it is not allowed. We say that division by 0 is undefined.

Using Division in Problem Solving

Division is used in solving many types of problems. Below are three examples from real life that use division in their solutions.

Luana made 40 empanadas for a party. If the empanadas are divided equally among 12 guests, how many will each guest have? Will there be any leftover empanadas?

Each guest will have 3 empanadas. There will be 4 empanadas left over.

A case of floor tiles has 12 boxes in it. The case costs $384. How much does one box cost?

Each box of tiles costs $32

A banana grower is shipping 4,644 bananas. There are 86 crates, each containing the same number of bananas. How many bananas are in each crate?

Each crate contains 54 bananas.

A theater has 1,440 seats. The theater has 30 rows of seats. How many seats are in each row?

  • Incorrect. This answer is too large. Use division, \(\ 1440 \div 30\), not subtraction for this problem. The correct answer is 48.
  • Correct. \(\ 1440 \div 30=48\).
  • Incorrect. The answer is too large. Use division, \(\ 1440 \div 30\), not multiplication, for this problem. The correct answer is 48.
  • Incorrect. There is a place-value error. The correct answer is 48.

Division is the inverse operation of multiplication, and can be used to determine how to evenly share a quantity among a group. Division can be written in three different ways: using a fraction bar, using a division symbol, and using long division. Division can be represented as splitting a total quantity into sets of equal quantities, as skip subtracting on the number line, and as a dimension with an area model. Remainders may result when performing division and they can be represented with the letter R, followed by the number remaining. Since division is the inverse operation of multiplication, you need to know your multiplication facts in order to do division. For larger numbers, you can use long division to find the quotient.

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Step by Step Guide for Long Division

What is long division.

Long division is a way to solve division problems with large numbers. Basically, these are division problems you cannot do in your head.

Getting started

One of the problems students have with long division problems is remembering all the steps. Here’s a trick to mastering long division. Use the acronym DMSB , which stands for:

D = Divide M = Multiply S = Subtract B = Bring down

This sequence of letters can be hard to remember, so think of the acronym in the context of a family:  

Dad, Mother, Sister, Brother .

Write D M S B in the corner of your worksheet to remember the sequence you’re about to use.

How to write it down

First, you have to write down the problem in long division format. A typical division problem looks like this:

Dividend ÷ Divisor = Quotient

To write this down in long division format it looks like this:

Let’s try a fairly simple example:

Now, let’s write that problem down in the long division format:

We’re ready to start using the acronym: D M S B

Step 1: D for Divide

How many times will 5 go into 65? That’s too hard to work out in your head, so let’s break it down into smaller steps.

The first problem you’ll work out in this equation is how many times can you divide 5 into 6. The answer is 1. So you put 1 on the quotient line.

Step 2: M for Multiply

You multiply your answer from step 1 and your divisor: 1 x 5 = 5. You write 5 under the 6.

Step 3: S for Subtract

Next you subtract. In this case it will be 6 – 5 = 1.

Step 4: B for Bring down

The last step in the sequence is to bring down the next number from the dividend, which in this case is 5. You write the 5 next to the 1, making the number 15.

Now you start all over again:

How many times can you divide 5 into 15. The answer is 3. So you put 3 on the quotient line.

You multiply your answer from step 1 and your divisor: 3 x 5 = 15. Write this underneath the 15.

Now we subtract 15 from 15. 15 – 15 = 0.

There is no need for step 4. We have finished the problem.

Once you have the answer, do the problem in reverse using multiplication (5 x 13 = 65) to make sure your answer is correct.

K5 Learning has a number of free long division worksheets for grade 4 , grade 5 and grade 6 . Check them out in our math worksheet center .

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Order of Operations Worksheets - Addition, Subtraction, Multiplication & Division

Related Topics & Worksheets: Order Of Operations Order Of Operations Worksheet

Objective: I know how to perform mixed operations with addition, subtraction, multiplication and division. If the calculations involve a combination of addition, subtraction, multiplication and division then

Step 1: First, perform the multiplication and division from left to right.

Step 2: Then, perform addition and subtraction from left to right. Example: Calculate 9 × 2 – 10 ÷ 5 + 1 =

Solution: 9 × 2 – 10 ÷ 5 + 1 (perform multiplication)

= 18 – 10 ÷ 5 + 1 (perform division)

= 18 – 2 + 1 (perform subtraction)

= 16 + 1 (perform addition)

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1 Trending: Our Most Serious National Security Threat Isn’t Russian Nukes In Space, It’s Intelligence Agencies In Washington

2 trending: elizabeth warren wants to file your taxes, 3 trending: did our intelligence agencies suggest the russia hoax to hillary clinton’s campaign, 4 trending: president joe biden’s border invasion victimizes young and old americans everywhere, with biden in mental decline, how do you solve a problem like kamala harris.

how do you solve this division problem

With Biden’s mental acuity becoming an undeniable problem, Democrats will have to figure out what to do with a vice president who’s even more unpopular than him.

Author Mark Hemingway profile

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With yesterday’s special counsel report providing independent confirmation that Joe Biden is probably senile , we need to do something very painful that the Biden campaign and our compliant political press don’t want to do: Have a forthright conversation about Kamala Harris.

Last weekend, NBC News put out a poll that set off klaxons among Democrats. Trump is leading Biden by five points in NBC’s poll, and, more generally, the 2024 general election polls thus far show Trump consistently winning . This is a marked reversal from 2020, where the polls showed Biden with a 7-point lead heading into an election he barely edged out an electoral college victory by 40,000 or so votes.

Now, there are a number of obvious reasons why Biden is flailing this time around. The NBC poll notes Trump has a 20-point advantage on the economy, a 30-point advantage on immigration and border security, and a 16-point advantage on “being competent and effective.” (Democrats are probably pretty despondent to consider he’s being walloped on that last metric by President Covfefe.)

But when you look at Biden’s approval rating in the poll, something else jumps out. Biden’s approval rating – 36 percent approve, 54 percent disapprove of the job he’s doing as president – is absolutely terrible for an incumbent president during an election year. But the NBC poll offers up the approval ratings of all the major candidates, and it turns out Biden doesn’t have the lowest approval rating in the White House. That belongs to Kamala Harris, who is at 28 percent approval, 53 percent disapproval. WOOF.

Now, obviously, given the major issues dragging Biden down, it would hardly seem like Kamala Harris would be the singular thing that sinks Biden, even if her approval rating is comparable to that of venereal disease. However, Biden needs all the help he can get, and given his unique problems, an energetic and engaged vice president would go a long way toward counteracting the negative perception of him.

Obviously, there’s the issue of Biden’s age and cognitive decline. Especially after yesterday’s news, Democrats are not going to get through another election cycle berating reporters that Biden’s confusion is a result of a heroic lifelong struggle to overcome a childhood stutter. Biden is speaking in the present tense about world leaders who died when grunge was still popular , and that’s when he’s capable of speaking at all . Voters can clearly see that mentally, the wheel may be turning, but the hamster is deceased.

As a result, the Biden campaign’s goal is to minimize his public presence during the election, which can only hurt him. They did this to a large extent in 2020, but Covid was a convenient excuse. Now, what’s the reason why Biden is turning down an audience of 20 million people to conduct an interview on Super Bowl Sunday? CNN assures us that turning down such a huge audience is part of a “larger media strategy” where Biden’s advisers “give the already fatigued public a break from politics during the big game.” The reality as we know it is that they simply don’t want to have another viral clip where he’s asked a tough question about Gaza and he responds by nodding off on camera and dribbling cerebral spinal fluid out of the corner of his mouth.

In fact, an AP story from earlier this week, “ Biden is going small to try to win big in November. That means stops for boba tea, burgers and beer ,” does indeed confirm that the Biden strategy for the coming election is, to the extent he’s going to campaign at all, he’s going to do it in intimate, easily controlled settings. They’re scared to let voters interact with him and see him up close.

Now, given that’s the case, just imagine Biden had an energetic, well-liked vice president out on the trail. Voters could at least tell themselves that if they vote for Biden and we have to confront the all-too-likely possibility Biden goes face down in a bowl of Chunky Monkey in the Oval and never wakes up, at least there’s a commanding presence in the wings waiting to step-up.

Instead, we have Kamala Harris, who seems to defy the laws of political physics by existing in two categories at the same time — she’s both actively disliked by voters and an almost complete nonentity when it comes to exerting any influence on policy or politics. I mean, what has she done of note as vice president? Anything at all? During his first year in office, Biden tasked her with overseeing diplomatic efforts allegedly aimed at stopping the mass influx of illegal immigrants across the southern border. How’s that going? Let’s check the spin at CNN :

Since being tasked with tackling root causes, Harris has only occasionally talked about the effort as the situation along the US-Mexico border became a political vulnerability for Biden. … A senior administration official recognized the attention on the US-Mexico border but maintained that Harris’ work is not intended to solve the immediate issues on the ground there.

In other words, Kamala is trying to distance herself from her own responsibilities on an issue that is now voters’ number one concern. “Not intended to solve the immediate issues on the ground there”? What an awe-inspiring display of leadership.

Then there’s the issue of Kamala herself; Biden’s age-related senility means that his verbal stumbles at least induce some measure of pity along with the embarrassment. Kamala’s furor loquendi, on the other hand, well, what the hell are we supposed to make of the fact that even The New York Times concedes , “the vice president’s critics have not exactly fabricated, ex nihilo, the notion that she chops language into what they call ‘word salads.’” Frankly, that’s a polite read on authentic California self-actualized airhead gibberish such as, “I think it’s very important, as you have heard from so many incredible leaders, for us, at every moment in time, and certainly this one, to see the moment in time in which we exist and are present, and to be able to contextualize it, to understand where we exist in the history and in the moment, as it relates not only to the past but the future.”

Then, something must be said about Kamala Harris’ truly bizarre and omnipresent laugh, which is less an expression of amusement and more like a frantic attempt to hide her obvious discomfort. If you think I’m being unfair, apparently, the vice president’s braying is an international incident. Last March, Daily Telegraph columnist Tim Blair went on Australian TV and was asked about her weird propensity to laugh at the drop of a hat.

“Here’s the thing about Kamala Harris, if she were able somehow if she were a genius who could solve every problem on Earth and bring the Middle East together and solve every energy crisis, it wouldn’t matter,” Blair said . “Because the laugh kills it anyway; the laugh is the biggest, destructive, negative force probably ever unleashed in American politics. No one’s voting for the laugh.”

In sum, not only has Kamala Harris not accomplished anything meaningful as vice president, but her physical presence seems to cause people to intensely dislike her, even if that’s irrational to some degree. Not only is Kamala Harris incapable of helping push Biden over the finish line, but the smart political move would be to cut the dead weight and add someone to the ticket who is moderately capable and not actively disliked by over half of voters.

And while there’s been a lot of chatter about Dems finding a way to replace Biden — which is intensifying rapidly after yesterday’s revelations — there’s been almost no talk about the Kamala problem. Historically, swapping out a VP on the ticket due to scandal or perceived political advantage has plenty of precedents. But that’s not going to happen here, no matter how helpful it would be, because cementing the narrative that Harris was chosen for her sex and skin color, not her qualifications, is not something a political party that has fully committed to identity politics could get away with.

Given the political headwinds facing Biden, a decent vice presidential candidate who’s able to vigorously campaign could be the difference between Biden’s reelection and Trump: The Revenging. Democrats insist the latter possibility would be the end of American self-governance, but apparently, they don’t believe that, or they would insist at least one person on the Democratic ticket be able to speak an intelligible sentence.

Regardless, the emerging questions about Biden’s mental fitness mean that Kamala Harris is likely going to face a lot of scrutiny that Democrats, and even Harris herself, hoped to avoid. So far, whenever there’s even been a small focus on her role as vice president, voters haven’t liked what they’ve seen.

  • 2024 campaign
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  • Kamala Harris
  • vice president

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How to diagnose and fix DNS problems

Dead websites, page loading issues, web not working as it should? Here's what to do next.

A laptop screen displaying a Page Not Found - Error 404 message

Browsing the web is so easy, simple and straightforward that it feels almost automatic. Sure, you know there's a lot of low-level tech making this happen, but who cares when it just works?

That only makes it more frustrating when you suddenly get major page loading issues, though, dead websites everywhere, and all kinds of other web-based complications.

Internet connectivity problems across multiple websites can look like something you'll never fix yourself, but that's not always true – they're often related to DNS (Domain Name System) problems. In this article we'll look at how to identify these, and then get your system working again.

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What is DNS?

Accessing a new website looks simple, at least from user's point of view. Enter the URL in a browser, wait a few seconds, website appears, that's about it. Peek under the hood, though, and there's a lot more going on.

Your browser can't access a web server from a domain name like techradar.com, for instance. It can only find and download websites when it has a server IP address , such as 199.232.198.114.

A device normally handles this by asking your ISP's DNS server to translate the domain name into an IP address. Easy.

But what if DNS fails, and the server doesn't always return the IP address you need? Then you'll see major web problems.

What does a DNS issue look like?

If your DNS fails entirely then it's likely you'll see timeouts, DNS or other errors with all your internet apps. It might look like your entire internet is dead.

Other DNS failures are partial, though, affecting some websites only. Maybe you'll access sites a, b and c as usual, but x, y and z all seem to be down.

Partial failures can also cause odd-looking page loading issues. What if DNS allows you to access bigsite.com, but not the domain where it hosts its images, scripts or contact forms? 

You might see image placeholders, empty spaces where content used to be, or buttons and other site features not working as they should. It's this mix of problems across multiple sites that's one of the tell-tale signs of a DNS problem.

Diagnosing a DNS issue

The simplest DNS problem to diagnose is an issue with your current server. Try the same websites on a connection using another DNS server, and if they're now accessible and work correctly, it looks like you have a DNS issue.

If you've problems on a mobile device connected to your home Wi-Fi, for example, switching to your mobile network allows you to test a site with new DNS servers. 

Or if you're on the move and already using your mobile network, look for a free hotspot you can try. (Just for a quick connectivity test, though – free Wi-Fi can be a security risk causing more problems than it solves, and you should always use at least a cheap VPN to stay safe on these networks.)

No other connections available? Try the virtual online browser Browserling . If you can reach it, choose Chrome as your preferred browser, enter the URL in the address box and click Test Now! Browserling uses its own DNS to connect to the site, so if it gets you access and your own connection doesn't, it could be a DNS issue.

Test your DNS server

A more advanced test is to manually ask your DNS server for the IP address of the domain you're trying to access. If the server can't find the IP or displays an error, that points to a DNS difficulty.

To try this on Windows, click Start , type CMD and open Command Prompt , then type NSLOOKUP and press Enter. ( NSLOOKUP is often available on Macs and Linux – try opening it from your terminal window.) 

NSLOOKUP launches and displays the name and IP address of your current DNS server (or 192.168.* if devices get their DNS via your router's connection.)

Now type the name of any domain you can't currently access, press Enter, and NSLOOKUP queries your DNS server.

If NSLOOKUP displays the site IP address, it looks like DNS is working correctly.

But if NSLOOKUP displays an error like ' can't find Google .com: Non-existent domain ', that's pretty conclusive evidence that something is screwed up at the DNS level. Although there is one more quick trick you should try.

Try another DNS server

You've proved that your DNS server can't find an IP address for a domain, but will other DNS servers do any better? NSLOOKUP makes it really, really easy to find out.

Type SERVER 1.1.1.1 , press Enter , and NSLOOKUP changes its default DNS server to the IP address 1.1.1.1. (That's Cloudflare. If you know you were using Cloudflare before and that's the DNS with the problem, switch to Google's 8.8.8.8 , instead.)

Now enter whatever domain you couldn't reach earlier, and NSLOOKUP sends its DNS query to Cloudflare (or Google), instead.

If NSLOOKUP failed earlier but successfully gets an IP with Cloudflare, that looks like a problem affecting your DNS server only.

Test this by entering the IP address in your browser, instead of the regular domain. Use 142.250.179.238 for Google, for instance. If you can't access the website when you enter a domain, but it at least begins to load with the IP address, that confirms your DNS issues.

How to fix DNS problems

If it looks like your ISP's DNS isn't working, the quickest and most effective solution is to switch to a free public DNS server . Google and Cloudflare offer fast and reliable services which anyone can use, no registration required.

Changing DNS servers normally involves tweaking your device network settings. The Cloudflare support site has guides on setting up Cloudflare DNS for Windows, Mac, Android, iOS, routers, gaming consoles, Linux and more. These are sometimes very basic ('install app X to do it for you'), but Google's equivalent page has more detailed advice if you need it.

Whatever changes you make, be sure to note down your original settings first, just in case you need to switch them back later.

Reboot your device when you're done,  and it should now be using your (hopefully) problem-free new DNS server.

If you still have internet connectivity problems, though, it's time to ask your ISPs support team for help. Tell them what you've tried, and that should help them diagnose the issue and get your connection running smoothly again.

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Mike is a lead security reviewer at Future, where he stress-tests VPNs , antivirus and more to find out which services are sure to keep you safe, and which are best avoided. Mike began his career as a lead software developer in the engineering world, where his creations were used by big-name companies from Rolls Royce to British Nuclear Fuels and British Aerospace. The early PC viruses caught Mike's attention, and he developed an interest in analyzing malware, and learning the low-level technical details of how Windows and network security work under the hood.

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IMAGES

  1. Long Division Calculator

    how do you solve this division problem

  2. 👍 Solve long division problems. How to teach long division: a step. 2019-01-06

    how do you solve this division problem

  3. How do you do division problems

    how do you solve this division problem

  4. What Is The Answer To A Division Problem Called

    how do you solve this division problem

  5. Problem Solving on Division

    how do you solve this division problem

  6. Problem Solving

    how do you solve this division problem

VIDEO

  1. Division ➗ Word Problems|| Maths Division|| Learn basic Division || Mathematics

  2. A Nice Power Division Problem

  3. Common division method

  4. How to sove division problem

  5. A Nice Power Division Problem

  6. 2.9 Division: Problem Solving (Drawing a Diagram)

COMMENTS

  1. Long Division Calculator with Remainders

    Step-by-Step Set up the division problem with the long division symbol or the long division bracket. Put 487, the dividend, on the inside of the bracket. The dividend is the number you're dividing. Put 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.

  2. Microsoft Math Solver

    Get math help in your language Works in Spanish, Hindi, German, and more Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.

  3. 6 Ways to Do Division

    1 Write out the problem using a long division bar. The division bar ( 厂 ) looks like an ending parentheses attached to a horizontal line that goes over the string of numbers beneath the bar.

  4. Long Division Calculator

    One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an integer, and the leftover number is a remainder. For example, 9 cannot be evenly divided by 4. Instead, knowing that 8 ÷ 4 = 2, this can be used to determine that 9 ÷ 4 = 2 R1.

  5. Solve

    QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ...

  6. Parts of a Division Problem: Dividend, Divisor, Quotient ...

    Welcome to Parts of a Division Problem: Dividend, Divisor, Quotient, & Remainder with Mr. J! Need help with division vocabulary? You're in the right place!Wh...

  7. Long Division Calculator

    There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process. Step One: Set up the Expression The first step in solving a long division problem is to draw the equation that needs to be solved.

  8. How to Solve Division Problems and Find the Right Answer

    1. Round the divisor and the dividend. For instance, you could round 9 up to 10 and 64 down to 60. Since 60 ÷ 10 = 6, and 9 is less than 10, this means 9 can go into 64 more than 6 times. 2. Use your division facts to estimate. For this problem, you know that 9 x 6 = 54 and 9 x 7 = 63, so 7 is likely to be the best fit. 3. Guess and check.

  9. Division

    Division Division is splitting into equal parts or groups. It is the result of "fair sharing". Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates? 12 Chocolates 12 Chocolates Divided by 3 Answer: 12 divided by 3 is 4. They get 4 each. Symbols ÷ /

  10. Intro to division (article)

    Problem 1A There are a total of gumballs that will be divided evenly into groups. Problem 1B Which expression can we use to show 16 gumballs divided into 4 equal-size groups? Choose 1 answer: 4 ÷ 16 A 4 ÷ 16 16 ÷ 4 B 16 ÷ 4 16 × 4 C 16 × 4

  11. How to Solve Division Problems

    Solving simple division problems is closely linked to multiplication. In fact, to check your work, you'll have to multiply the quotient by the divisor to see if it equals the dividend. If it doesn't, you've solved incorrectly. Let's try solving one simple division problem. For example: 12 ÷ 2 =

  12. Math Antics

    Learn More at mathantics.comVisit http://www.mathantics.com for more Free math videos and additional subscription based content!

  13. How to Do Long Division: 15 Steps (with Pictures)

    A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals.

  14. Division Problems: Different Models and Examples

    1. Division Problems: Repetition. This is the first type of division problem you are going to learn to do. For example: In my living room, there are 120 books in total, placed on 6 shelves. Knowing that each shelf has the same number of books, calculate how many books there are on each shelf. A total number of objects: there are 120 books in total.

  15. Long Division Calculator

    Please enter your division problem below and press "Divide": ÷ Long Division Worksheets We recommend that you use the Long Division Calculator above in conjunction with our printable Long Division Worksheets. Long Division Workbook Since practice makes perfect, you may also be interested in a long division workbook from Amazon.

  16. Practice Solving Division Problems

    In this post, we are going to learn to analyze, think about, and solve problems that require division: division problems. At Smartick, we want to emphasize the fact that you have to know how to solve any kind of math problem accurately. As a result, we are going to give you a variety of problems that require division to solve. Division problems ...

  17. Solving Math Problems : How to Solve Division Problems

    In math division problems, there are a number of formats for determining how many times one number will go into another. Solve division problems with tips fr...

  18. Ways to Divide & Types of Division

    The three ways to divide are tally marks, place value, and multiplication. Tally marks and place value create groups and portion out the tally marks or value equally among the groups....

  19. Long Division

    Long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.Observe the following long division method to see how to divide step by step and check the divisor, the dividend, the quotient, and the remainder.

  20. 1.3.2: Dividing Whole Numbers and Applications

    45 − 42 = 3 45 − 42 = 3. 3 is not enough for another 6. So, 3 is the remainder. 45 ÷ 6 = 7 R3 45 ÷ 6 = 7 R 3. Since multiplication is the inverse of division, you can check your answer to a division problem with multiplication. To check the answer 7 R3, first multiply 6 by 7 and then add 3. 6 ⋅ 7 = 42 6 ⋅ 7 = 42.

  21. Step by Step Guide for Long Division

    Step 3: S for Subtract. Now we subtract 15 from 15. 15 - 15 = 0. There is no need for step 4. We have finished the problem. Once you have the answer, do the problem in reverse using multiplication (5 x 13 = 65) to make sure your answer is correct. K5 Learning has a number of free long division worksheets for grade 4, grade 5 and grade 6.

  22. Order of Operations (addition, subtraction, multiplication, division)

    Step 1: First, perform the multiplication and division from left to right. Step 2: Then, perform addition and subtraction from left to right. Example: Calculate 9 × 2 - 10 ÷ 5 + 1 = Solution: 9 × 2 - 10 ÷ 5 + 1 (perform multiplication) = 18 - 10 ÷ 5 + 1 (perform division) = 18 - 2 + 1 (perform subtraction) = 16 + 1 (perform addition) = 17

  23. With Biden In Mental Decline, How Do You Solve A Problem Like Kamala

    "Here's the thing about Kamala Harris, if she were able somehow if she were a genius who could solve every problem on Earth and bring the Middle East together and solve every energy crisis, it ...

  24. How to diagnose and fix DNS problems

    (Image credit: Microsoft) How to fix DNS problems. If it looks like your ISP's DNS isn't working, the quickest and most effective solution is to switch to a free public DNS server.Google and ...

  25. Long Division Made Easy

    This long division math youtube video tutorial explains how to divide big numbers the easy way. It explains how to perform long division with 2-digit diviso...

  26. Listen: How do you solve a problem like Barnaby?

    Add articles to your saved list and come back to them any time. Samantha Selinger-Morris: Before we get into how this is all sort of exploded, I guess in political circles, can you briefly tell me ...

  27. State announces it is processing 2023 income tax returns

    LAKEWOOD, Monday, February 12, 2024 — Taxpayers can now file income tax returns for 2023 and the Colorado Department of Revenue, Taxation Division has a few tips to make the process easier and help Coloradans receive their returns as quickly as possible.