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Unit 12: Add and subtract decimals

Adding decimals intro.

  • Estimating decimal addition (Opens a modal)
  • Adding decimals (Opens a modal)
  • Add decimals visually Get 5 of 7 questions to level up!

Adding decimals (tenths and hundredths)

  • Introduction to adding decimals: tenths (Opens a modal)
  • Adding decimals with ones and tenths parts (Opens a modal)
  • Adding decimals with ones, tenths and hundredths (Opens a modal)
  • Adding decimals with hundredths (Opens a modal)
  • Adding decimals (tenths) Get 3 of 4 questions to level up!
  • Adding decimals (hundredths) Get 3 of 4 questions to level up!

Subtracting decimals intro

  • Estimating decimal subtraction (Opens a modal)
  • Subtracting decimals (Opens a modal)
  • Subtract decimals visually Get 5 of 7 questions to level up!

Subtracting decimals (tenths and hundredths)

  • Strategies for subtracting basic decimals (Opens a modal)
  • Strategies for subtracting more complex decimals with tenths (Opens a modal)
  • Subtraction strategies with hundredths (Opens a modal)
  • More advanced subtraction strategies with hundredths (Opens a modal)
  • Subtracting decimals (tenths) Get 3 of 4 questions to level up!
  • Subtract decimals (hundredths) Get 3 of 4 questions to level up!

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Mathematics LibreTexts

6.4: Addition and Subtraction of Decimals

  • Last updated
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  • Page ID 48867

  • Denny Burzynski & Wade Ellis, Jr.
  • College of Southern Nevada via OpenStax CNX

Learning Objectives

  • understand the method used for adding and subtracting decimals
  • be able to add and subtract decimals
  • be able to use the calculator to add and subtract decimals

The Logic Behind the Method

Consider the sum of 4.37 and 3.22. Changing each decimal to a fraction, we have

\(4 \dfrac{37}{100} + 3 \dfrac{22}{100}\) Performing the addition, we get

\(\begin{array} {rcl} {4.37 + 3.22 = 4 \dfrac{37}{100} + 3 \dfrac{22}{100}} & = & {\dfrac{4 \cdot 100 + 37}{100} + \dfrac{3 \cdot 100 + 22}{100}} \\ {} & = & {\dfrac{437}{100} + \dfrac{322}{100}} \\ {} & = & {\dfrac{437 + 322}{100}} \\ {} & = & {\dfrac{759}{100}} \\ {} & = & {7 \dfrac{59}{100}} \\ {} & = & {\text{seven and fifty-nine hundredths}} \\ {} & = & {7.59} \end{array}\)

Thus, \(4.37 + 3.22 = 7.59\).

The Method of Adding and Subtracting Decimals

When writing the previous addition, we could have written the numbers in col­umns.

\(\begin{array} {r} {4.37} \\ {\underline{+3.22}} \\ {7.59} \end{array}\)

This agrees with our previous result. From this observation, we can suggest a method for adding and subtracting decimal numbers.

Method of Adding and Subtracting Decimals To add or subtract decimals:

Align the numbers vertically so that the decimal points line up under each other and the corresponding decimal positions are in the same column. Add or subtract the numbers as if they were whole numbers. Place a decimal point in the resulting sum or difference directly under the other decimal points.

Sample Set A

Find the following sums and differences.

\(9.813 + 2.140\)

\(\begin{array} {r} {9.813} \\ {\underline{+2.140}} \\ {11.953} \end{array}\) The decimal points are aligned in the same column.

\(841.0056 + 47.016 + 19.058\)

\(\begin{array} {r} {841.0056} \\ {47.016\ \ } \\ {\underline{+19.058\ \ }} \end{array}\)

To insure that the columns align properly, we can write a 0 in the position at the end of the numbers 47.016 and 19.058 without changing their values.

Vertical addition. 841.0056 plus 47.0160 plus 19.0580 equals 907.0796. A 1 needed to be carried in the hundredths, the tens, and the hundreds columns.

\(1.314 - 0.58\)

\(\begin{array} {r} {1.314} \\ {\underline{-0.58\ \ }} \end{array}\) Write a 0 in the thousandths position.

Vertical subtraction. 1.314 minus 0.580 equals 0.734. The ones, and hundredths digits need to be borrowed from once, and the tenths needs to be borrowed from twice to perform the subtraction.

\(16.01 - 7.053\)

\(\begin{array} {r} {16.01\ \ } \\ {\underline{-7.053}} \end{array}\) Write a 0 in the thousandths position.

Vertical subtraction. 16.101 minus 7.053 equals 8.957. The ones, tenths, hundredths, and thousandths digits need to be borrowed from once to perform the subtraction.

Find the sum of 6.88106 and 3.5219 and round it to three decimal places.

\(\begin{array} {r} {6.88106} \\ {\underline{+3.5219\ \ }} \end{array}\) Write a 0 in the ten thousandths position.

Vertical addition. 6.88106 plus 3.52190 equals 10.40296. A 1 needs to be carried over the tenths and ones digits to perform the addition.

We need to round the sum to the thousandths position. Since the digit in the position immediately to the right is 9, and 9>5, we get

Wendy has $643.12 in her checking account. She writes a check for $16.92. How much is her new account balance?

To find the new account balance, we need to find the difference between 643.12 and 16.92. We will subtract 16.92 from 643.12.

Vertical subtraction. 643.12 minus 16.92 equals 626.20.

After writing a check for $16.92, Wendy now has a balance of $626.20 in her checking account.

Pracitce Set A

\(3.187 + 2.992\)

\(14.987 - 5.341\)

\(0.5261 + 1.0783\)

\(1.06 - 1.0535\)

\(16,521.07 + 9,256.15\)

Find the sum of 11.6128 and 14.07353, and round it to two decimal places.

Calculators

The calculator can be useful for finding sums and differences of decimal numbers. However, calculators with an eight-digit display cannot be used when working with decimal numbers that contain more than eight digits, or when the sum results in more than eight digits. In practice, an eight-place decimal will seldom be encoun­tered. There are some inexpensive calculators that can handle 13 decimal places.

Sample Set B

Use a calculator to find each sum or difference.

42.0638 + 126.551

The sum is 168.6148.

Find the difference between 305.0627 and 14.29667.

The difference is 290.76603

51.07 + 3,891.001786

Since 3,891.001786 contains more than eight digits, we will be unable to use an eight-digit display calculator to perform this addition. We can, however, find the sum by hand.

\(\begin{array} {r} {51.070000} \\ {\underline{3891.001786}} \\ {3942.071786} \end{array}\)

The sum is 3,942.071786.

Practice Set B

Use a calculator to perform each operation.

\(4.286 + 8.97\)

\(452.0092 - 392.558\)

Find the sum of 0.095 and 0.001862

Find the difference between 0.5 and 0.025

Find the sum of 2,776.00019 and 2,009.00012.

Since each number contains more than eight digits, using some calculators may not be helpful. Adding these by “hand technology,” we get 4,785.00031

For the following 15 problems, perform each addition or subtraction. Use a calculator to check each result.

Exercise \(\PageIndex{1}\)

\(1.84 + 7.11\)

Exercise \(\PageIndex{2}\)

\(15.015 - 6.527\)

Exercise \(\PageIndex{3}\)

\(11.842 + 28.004\)

Exercise \(\PageIndex{4}\)

\(3.16 - 2.52\)

Exercise \(\PageIndex{5}\)

\(3.55267 + 8.19664\)

Exercise \(\PageIndex{6}\)

\(0.9162 - 0.0872\)

Exercise \(\PageIndex{7}\)

\(65.512 - 8.3005\)

Exercise \(\PageIndex{8}\)

\(761.0808 - 53.198\)

Exercise \(\PageIndex{9}\)

\(4.305 + 2.119 - 3.817\)

Exercise \(\PageIndex{10}\)

\(19.1161 + 27.8014 + 39.3161\)

Exercise \(\PageIndex{11}\)

\(0.41276 - 0.0018 - 0.00011\)

Exercise \(\PageIndex{12}\)

\(2.181 + 6.05 + 1.167 + 8.101\)

Exercise \(\PageIndex{13}\)

\(1.0031 + 6.013106 + 0.00018 + 0.0092 + 2.11\)

Exercise \(\PageIndex{14}\)

\(27 + 42 + 9.16 - 0.1761 + 81.6\)

Exercise \(\PageIndex{15}\)

\(10.28 + 11.111 + 0.86 + 5.1\)

For the following 10 problems, solve as directed. A calculator may be useful.

Exercise \(\PageIndex{16}\)

Add 6.1121 and 4.916 and round to 2 decimal places.

Exercise \(\PageIndex{17}\)

Add 21.66418 and 18.00184 and round to 4 decimal places.

Exercise \(\PageIndex{18}\)

Subtract 5.2121 from 9.6341 and round to 1 decimal place.

Exercise \(\PageIndex{19}\)

Subtract 0.918 from 12.006 and round to 2 decimal places.

Exercise \(\PageIndex{20}\)

Subtract 7.01884 from the sum of 13.11848 and 2.108 and round to 4 decimal places.

Exercise \(\PageIndex{21}\)

A checking account has a balance of $42.51. A check is written for $19.28. What is the new balance?

Exercise \(\PageIndex{22}\)

A checking account has a balance of $82.97. One check is written for $6.49 and another for $39.95. What is the new balance?

Exercise \(\PageIndex{23}\)

A person buys $4.29 worth of hamburger and pays for it with a $10 bill. How much change does this person get?

Exercise \(\PageIndex{24}\)

A man buys $6.43 worth of stationary and pays for it with a $20 bill. After receiving his change, he realizes he forgot to buy a pen. If the total price of the pen is $2.12, and he buys it, how much of the $20 bill is left?

Exercise \(\PageIndex{25}\)

A woman starts recording a movie on her video cassette recorder with the tape counter set at 21.93. The movie runs 847.44 tape counter units. What is the final tape counter reading?

Exercises for Review

Exercise \(\PageIndex{26}\)

Find the difference between 11,206 and 10,884.

Exercise \(\PageIndex{27}\)

Find the product, \(820 \cdot 10,000\).

Exercise \(\PageIndex{28}\)

Find the value of \(\sqrt{121} - \sqrt{25} + 8^2 + 16 \div 2^2\).

Exercise \(\PageIndex{29}\)

Find the value of \(8 \dfrac{1}{3} \cdot \dfrac{36}{75} \div 2 \dfrac{2}{5}\).

\(\dfrac{20}{9} = \dfrac{5}{3}\) or \(2 \dfrac{2}{9}\)

Exercise \(\PageIndex{30}\)

Round 1.08196 to the nearest hundredth.

Adding and Subtracting Decimals

Adding decimals is easy when you keep your work neat

To add decimals, follow these steps:

  • Write down the numbers, one under the other, with the decimal points lined up
  • Put in zeros so the numbers have the same length ( see below for why that is OK)
  • Then add , using column addition , remembering to put the decimal point in the answer

Example: Add 1.452 to 1.3

Example: add 3.25, 0.075 and 5.

That's all there is to it: line up the decimal points, pad with zeros, then add normally.

Subtracting

To subtract, follow the same method: line up the decimal points, then subtract .

Example: What is 7.368 − 1.15 ?

To check we can add the answer to the number subtracted:

Example: Check that 7.368 minus 1.15 equals 6.218

Let us try adding 6.218 to 1.15

It matches the number we started with, so it checks out.

Putting In Zeros

Why can we put in extra zeros?

A zero is really saying "there is no value at this decimal place".

  • In a number like 10, the zero is saying "no ones"
  • In a number like 2.50 the zero is saying "no hundredths"

So it is safe to take a number like 2.5 and make it 2.50 or 2.500 etc

But DON'T take 2.5 and make it 20.5, that is plain wrong.

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Decimals  - Adding and Subtracting Decimals

Decimals  -, adding and subtracting decimals, decimals adding and subtracting decimals.

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Decimals: Adding and Subtracting Decimals

Lesson 2: adding and subtracting decimals.

/en/decimals/introduction-to-decimals/content/

Adding and subtracting with decimals

Adding and subtracting decimals happens a lot in real life. You may find that you need to add up the cost of your groceries to see if you have enough money to pay for them. Or perhaps you need to subtract the cost of a bill from your bank account.

When you're adding or subtracting decimal numbers, it's important to set up the expression correctly . The numbers need to be in a certain place, and so do the decimals .

Click through the slideshow below to learn how to set up these expressions.

addition and subtraction of decimals problem solving

First, let's set up an addition expression: 21.4 plus 6.82 .

addition and subtraction of decimals problem solving

Just like with any addition example, we're going to stack one number on top of the other.

addition and subtraction of decimals problem solving

But instead of lining our numbers up on the right...

But instead of lining our numbers up on the right...we're going to line up the decimal points .

addition and subtraction of decimals problem solving

No matter how many numbers are on either side of the decimal point, we'll always line up the decimal points before adding.

Once we have the decimal points lined up, our decimals are ready to be added.

addition and subtraction of decimals problem solving

When we subtract decimals, we'll set up the decimals in the same way. Let's set up this example.

addition and subtraction of decimals problem solving

Instead of lining up our two numbers on the right, we'll line up the two decimal points.

And now our decimals are ready to be subtracted.

addition and subtraction of decimals problem solving

Adding decimal numbers

Now that we know how to set up problems with decimals, let's practice by solving a few. First, we'll work on adding . If you feel comfortable adding larger numbers , you're ready to add decimal numbers.

Click through the slideshow to learn how to add decimals.

addition and subtraction of decimals problem solving

Let's try solving this problem: 1.9 + 2.15 .

addition and subtraction of decimals problem solving

First, we'll make sure the decimals are lined up.

addition and subtraction of decimals problem solving

We'll start by adding the digits farthest to the right . In this case, we have nothing on top and 5 on the bottom.

addition and subtraction of decimals problem solving

Nothing plus 5 equals 5 . We'll write 5 beneath the line.

addition and subtraction of decimals problem solving

Now we'll add the next set of digits to the left : 9 and 1 .

addition and subtraction of decimals problem solving

9 + 1 equals 10 , but there's no room to write both digits in 10 underneath the 9 and 1 . We'll have to carry .

We learned how to carry numbers in the lesson on Adding Two- and Three-Digit Numbers .

addition and subtraction of decimals problem solving

We'll write the right digit, 0 , under the line...

addition and subtraction of decimals problem solving

We'll write the right digit, 0 , under the line...then we'll carry the left digit, 1 , up to the next set of digits in the problem.

addition and subtraction of decimals problem solving

Now we'll write the decimal point. We'll place it directly beneath the other two decimal points.

addition and subtraction of decimals problem solving

Next, we'll move left to add the next set of digits: 1 and 2 . Since we carried the 1 , we'll add it too.

addition and subtraction of decimals problem solving

1 + 1 + 2 equals 4 . We'll write 4 below the line.

addition and subtraction of decimals problem solving

We're done. 1.9 + 2.15 = 4.05 . We can read this answer as four and five-hundredths .

addition and subtraction of decimals problem solving

Let's try it with a money problem: $51.99 + $25.32 .

addition and subtraction of decimals problem solving

We'll make sure our decimal points are lined up properly.

addition and subtraction of decimals problem solving

As always, we'll start by adding the digits on the right. Here, that's 9 and 2 .

addition and subtraction of decimals problem solving

9 + 2 equals 11 , so it looks like we'll have to carry .

addition and subtraction of decimals problem solving

The 1 on the right stays underneath the 9 and the 2 .

addition and subtraction of decimals problem solving

We'll carry the 1 on the left and place it above the next set of digits to the left.

addition and subtraction of decimals problem solving

Now we'll move left to add the next set of digits. Since we carried the 1 , we'll add it too.

addition and subtraction of decimals problem solving

1 + 9 + 3 = 13 .

addition and subtraction of decimals problem solving

We'll put the 3 under the digits we added.

addition and subtraction of decimals problem solving

We'll carry the 1 and place it above the next column to the left.

addition and subtraction of decimals problem solving

Now it's time to write the decimal point. Remember to place it directly beneath the other two decimal points.

addition and subtraction of decimals problem solving

Next, we'll move left and add the next set of digits. We'll make sure to add the 1 we carried.

addition and subtraction of decimals problem solving

1 + 1 + 5 = 7 . We'll write 7 beneath the line.

addition and subtraction of decimals problem solving

To finish, we'll add the next column to the left: 5 and 2 .

addition and subtraction of decimals problem solving

5 + 2 equals 7 . We'll write 7 underneath the 2 .

addition and subtraction of decimals problem solving

We'll finish by writing the dollar sign ( $ ).

addition and subtraction of decimals problem solving

We're done. $51.99 + $25.32 = $77.31 . We can read this answer as seventy-seven dollars and thirty-one cents .

Try solving these problems to practice adding decimal numbers.

Subtracting Decimal Numbers

On the previous page, you saw that adding numbers with decimals is a lot like adding other numbers. The same is true for subtracting numbers with decimals. If you can subtract large numbers , you can subtract numbers with decimals too!

Click through the slideshow to learn how to subtract decimals.

addition and subtraction of decimals problem solving

Let's try to solve this problem: 41.2 - 3.09 .

addition and subtraction of decimals problem solving

First, we'll make sure the expression is set up correctly. Here, 41.2 is the larger number, so we'll put it on top.

addition and subtraction of decimals problem solving

The decimal points are lined up.

addition and subtraction of decimals problem solving

As always, we’ll begin with the digits farthest to the right . Here, we have nothing on top and 9 on the bottom.

We can’t take 9 away from nothing . We'll need to place a digit after 41.2 so we can subtract from it.

addition and subtraction of decimals problem solving

The value of our number won't change if we use the digit that means nothing: 0 . We'll place a 0 after 41.2 .

addition and subtraction of decimals problem solving

Now we can subtract the digits on the right. 0 is smaller than 9 , so we’ll need to borrow to make 0 larger.

We learned how to borrow in the lesson on Subtracting Two- and Three-Digit Numbers .

addition and subtraction of decimals problem solving

We'll borrow from the digit to the left of 0 . Here, it's 2 . We'll take 1 from it.

addition and subtraction of decimals problem solving

2 - 1 = 1 . To help us remember we subtracted 1, we'll cross out the 2 and write 1 above it.

addition and subtraction of decimals problem solving

Then we'll place the 1 we took next to the 0 .

addition and subtraction of decimals problem solving

0 becomes 10 .

addition and subtraction of decimals problem solving

10 is larger than 9 , which means we can subtract. We'll solve for 10 - 9 .

addition and subtraction of decimals problem solving

10 - 9 = 1 . We'll write 1 beneath the line.

addition and subtraction of decimals problem solving

Now we'll move left to subtract the next set of digits: 1 - 0 .

addition and subtraction of decimals problem solving

1 - 0 = 1 . We'll write 1 beneath the line.

addition and subtraction of decimals problem solving

Now it's time to write the decimal point . We'll place it directly beneath the other two decimal points.

addition and subtraction of decimals problem solving

Now we'll find the difference of the next set of digits to the left: 1 - 3 .

Because 1 is smaller than 3, it looks like we'll need to borrow again. We need to make the 1 larger.

addition and subtraction of decimals problem solving

We'll borrow from the digit to the left of 1 . Here, we'll borrow 1 from the 4 .

addition and subtraction of decimals problem solving

4 - 1 = 3 . We'll write 3 above the 4 .

addition and subtraction of decimals problem solving

Then we'll place the 1 we took next to the 1 .

addition and subtraction of decimals problem solving

1 becomes 11 .

addition and subtraction of decimals problem solving

11 is larger than 3 , which means we can subtract. We'll solve for 11 - 3 .

addition and subtraction of decimals problem solving

11 - 3 = 8 . We'll write 8 beneath the line.

addition and subtraction of decimals problem solving

Finally, we'll move to the left to subtract the last set of digits. The top digit is 3 , but there's nothing beneath it.

addition and subtraction of decimals problem solving

3 minus nothing equals 3 , so we'll write 3 beneath the line.

addition and subtraction of decimals problem solving

41.2 - 3.09 = 38.11 . We can read this as thirty-eight and eleven-hundredths .

addition and subtraction of decimals problem solving

Let's try subtracting money. Let's see if we can solve $14.76 - $3.86 .

First, let's make sure the expression is set up correctly. The larger number is on top , and the decimal points are lined up .

addition and subtraction of decimals problem solving

As always, let's start by finding the difference of the digits on the right. Here, that's 6 - 6 .

addition and subtraction of decimals problem solving

6 - 6 = 0 . We'll write 0 beneath the line.

addition and subtraction of decimals problem solving

We'll move left to the next set of digits: 7 and 8 . 7 is smaller than 8 , so we'll borrow to make 7 larger.

addition and subtraction of decimals problem solving

Let's look at the digit to the left of 7 . Here, it's 4 . We'll take 1 from it.

addition and subtraction of decimals problem solving

4 - 1 = 3 . We'll cross out the 4 and write 3 above it.

addition and subtraction of decimals problem solving

Then we'll place the 1 we took next to the 7 .

addition and subtraction of decimals problem solving

7 becomes 17 .

addition and subtraction of decimals problem solving

Now it's time to subtract. We'll solve for 17 - 8 .

addition and subtraction of decimals problem solving

17 - 8 = 9 . We'll write 9 beneath the line.

addition and subtraction of decimals problem solving

We'll put a decimal point directly beneath the other two decimal points.

addition and subtraction of decimals problem solving

Next, we'll move left to find the difference of the next set of digits. Here, that's 3 - 3 .

addition and subtraction of decimals problem solving

3 - 3 = 0 . We'll write 0 below the line.

addition and subtraction of decimals problem solving

Finally, we'll move left to subtract the last set of digits. The top digit is 1 , but there's nothing beneath it.

addition and subtraction of decimals problem solving

1 minus nothing equals 1 . We'll write 1 beneath the line.

addition and subtraction of decimals problem solving

Next, we'll write a dollar sign ( $ ) to the left of the 1 .

addition and subtraction of decimals problem solving

$14.76 - $3.86 = $10.90 . We can read this as ten dollars and ninety cents .

Try solving these problems to practice subtracting decimal numbers.

previous

/en/decimals/multiplying-and-dividing-decimals/content/

Adding and Subtracting Decimals

Adding and subtracting decimals is the same as the addition and subtraction of whole numbers keeping in mind that the decimal point needs to be in place. The length of the decimal numbers can be adjusted by adding or removing zeros from the decimal part. Let us learn more about the addition and subtraction of decimals in this article.

What is Addition and Subtraction of Decimals?

The addition and subtraction of decimals involves the usual addition and subtraction rules. The only points to be taken care of are the decimal places after the decimal point. The numbers need to be written in columns according to their place values before and after the decimal point. The decimal place value chart shows that the place values before the decimal point start from ones tens, hundreds, and so on; whereas, the place values after the decimal point start from tenths, followed by hundredths, and so on. Let us understand this with the help of the addition of the decimal numbers explained in the following section.

Addition of Decimals

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column. For example, let us add 12.5 + 14.9 using the following steps.

addition of Decimals

  • Step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.
  • Step 2: Now add the decimal numbers to get the sum. In this case, 12.5 + 14.9 = 27.4

Now let us understand the subtraction of decimals in the following section.

Subtraction of Decimals

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values. Let us understand this with the help of the example given below.

Example: Subtract the given decimals: 15.8 - 2.7

Solution: Let us subtract these decimals using the following steps.

Subtraction of Decimals

  • Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.
  • Step 2: Now subtract the decimal numbers starting from the tenths column, moving on to the ones column, and then the tens column. Copy the decimal as it comes. In this case, 15.8 - 2.7 = 13.1

Adding and Subtracting Unlike Decimals

'Unlike decimals' are those decimal numbers that do not have the same number of digits after the decimal point. For example, 3.45 and 7.831 are 'unlike decimals' because 3.45 has two numbers after the decimal point and 7.831 has three numbers after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these unlike decimals. We just need to convert the 'unlike decimals' to 'like decimals' by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers becomes equal and it is easier to add or subtract the numbers. Let us understand this with the help of the following example.

Example: Add the decimal numbers 24, 32.1, 0.08, 0.5, and 4.003

Solution: Let us add these numbers using the following steps.

Adding and Subtracting Unlike Decimals

  • Step 1: Here, each of the numbers needs to have an equal number of decimal digits.
  • Step 2: For this, we rewrite the numbers as follows: 24.000, 32.100, 0.080, 0.500, and 4.003. Therefore, the sum of the given decimal numbers is 60.683

How to Add and Subtract Decimals with Whole Numbers?

For adding or subtracting a decimal and a whole number , the whole number is changed into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeros after the decimal point. For example, the whole number 5 is written in the decimal form as 5.0. Let us understand this with the help of the following examples.

Addition or Subtraction of Decimals and Whole Numbers

Example: Add 15 + 12.56

  • Step 1: Refer to the figure given above and place a decimal after 15 and write two zeros after it so that both the numbers become like decimals.
  • Step 2: Now add the decimal numbers and find the sum using the usual rules of addition. Therefore, the 15 + 12.56 = 27.56

Let us understand this using subtraction.

Example: Subtract 6 - 2.25

  • Step 1: Refer to the figure given above and place a decimal after 6 and write two zeros after it so that both the numbers become like decimals.
  • Step 2: Now subtract the decimal numbers and find the difference using the usual rules of subtraction. Therefore, 6 - 2.25 = 3.75

Important Points on Addition and Subtraction of Decimals

  • The value of a decimal does not change on placing a zero after the decimal digits. For example, 5 can be written as 5.00
  • Even though the time and angle measure is represented in decimal format, they cannot be added or subtracted as decimals.

☛ Related Topics

  • Adding and Subtracting Decimals Worksheets
  • Adding and Subtracting Decimals Worksheets 6th grade
  • Adding and Subtracting Decimals Worksheets 5th grade
  • Dividing Decimals
  • Multiplying Decimals

Examples on Decimal Addition and Subtraction

Example 1: Add 0.2 + 0.22 + 0.222 + 0.2222 using the rules of decimal addition and subtraction.

The given decimals will be converted to like decimals by placing the required number of zeros after the decimals, such that each number has an equal number of decimals. These can be written as follows.

Solved Examples on Addition and Subtraction of Decimals

∴ The sum of the given decimals is 0.8642

Example 2: Find the difference between 7847 and 78.47 using the concept of adding and subtracting decimals.

The number 7847 is written in the decimal form as 7847.00. Now the subtraction can be performed in the following way.

Solved Examples on Addition and Subtraction of Decimals

Therefore, 7847 - 78.47 = 7768.53

Example 3: Write true or false with respect to decimal addition and subtraction.

a.) 20 + 12.17 = 32.17

a.) 10 + 69.32 = 69.42

a.) True, 20 + 12.17 = 32.17

a.) False, 10 + 69.32 = 79.32

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addition and subtraction of decimals problem solving

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Practice Questions on Addition and Subtraction of Decimals

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FAQs on Decimal Addition and Subtraction

How to add and subtract decimals.

The addition and subtraction of decimals is done using the usual addition and subtraction rules. The only thing to be kept in mind is the number of digits after the decimal point and that the decimal point needs to be placed appropriately in the sum or the difference. The numbers need to be written in columns according to their place values before and after the decimal point and then they are added or subtracted.

What is the Rule for Adding and Subtracting Decimals?

The rule for adding and subtracting decimals is related to the decimal point. For example, in order to add 56.12 + 10.14, we need to align these numbers one below the other such that the decimal point falls in place and all the numbers are written according to the place values. This will result in 66.26. In case if they are unlike decimals, we need to convert them to like decimals by writing the appropriate number of zeros after the decimal so that the decimal places become equal. For example, 34.25 + 12.986 can be written as 34.250 + 12.986 and the sum will be 34.250 + 12.986 = 47.236

In order to add and subtract decimals with whole numbers, we need to change the whole number into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeros after the decimal point. For example, if we need to add 8 + 4.321, then we can write the whole number 8 in the decimal form as 8.000 and then add it to 4.321. After this, the numbers can be added and written as, 8.000 + 4.321 = 12.321

How to Add Decimal Numbers?

For adding any two decimal numbers, we use the following steps. Let us understand this using an example. For example, let us add 23.12 + 4.23

  • Step 2: Now add the decimal numbers to get the sum. In this case, it will be 23.12 + 4.23 = 27.35

How to Subtract Decimal Numbers?

In order to subtract any two decimal numbers, we use the following steps. Let us understand this using an example. For example, let us subtract 44.32 - 3.6

  • Step 2: Now subtract the decimal numbers to get the difference. In this case, it will be 44.32 - 03.60 = 40.72

How to Add a Decimal Number and a Whole Number?

In order to add a decimal number to a whole number, the whole number needs to be changed to a decimal. For example, let us add 5 and 3.236. Here, we change 5 to 5.000 and we have 5.000 + 3.326 = 8.326

How to Multiply Two Decimals?

The multiplication of decimals with whole numbers is similar to the multiplication of whole numbers. The only difference is in the placement of the decimal point. The following steps can be followed to multiply decimals with whole numbers:

  • Step 1: Initially, ignore the decimal point and multiply the two numbers normally.
  • Step 2: After multiplication, count the number of decimal places in the given decimal numbers. Suppose the multiplicand has 2 numbers after the decimal point and the multiplier has 1 number after the decimal point, then we will add these 2 + 1 = 3. So, we will place the decimal in the product after 3 places from the right. For example, 0.04 × 0.2 = 0.008

How to Divide a Decimal by Another Decimal?

In order to divide a decimal number by a decimal number, we need to convert the divisor into a whole number and then continue the division . For example, if we need to divide 13.8 ÷ 0.6, we will use the following steps.

  • Step 1: The dividend is 13.8 and the divisor is 0.6. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 0.6 × 10 = 6
  • Step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 13.8 × 10 = 138. In other words, we need to move both the decimal points to the right until the divisor becomes a whole number. Therefore, 138 ÷ 6 = 23.

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Decimal Word Problem Worksheets

Extensive decimal word problems are presented in these sets of worksheets, which require the learner to perform addition, subtraction, multiplication, and division operations. This batch of printable decimal word problem worksheets is curated for students of grade 3 through grade 7. Free worksheets are included.

Adding Decimals Word Problems

Adding Decimals Word Problems

Decimal word problems presented here help the children learn decimal addition based on money, measurement and other real-life units.

  • Download the set

Subtracting Decimals Word Problems

Subtracting Decimals Word Problems

These decimal word problem worksheets reinforce the real-life subtraction skills such as tender the exact change, compare the height, the difference between the quantities and more.

Decimals: Addition and Subtraction

Decimals: Addition and Subtraction

It's review time for grade 4 and grade 5 students. Take these printable worksheets that help you reinforce the knowledge in adding and subtracting decimals. There are five word problems in each pdf worksheet.

Multiplying Decimals Whole Numbers

Multiplying Decimals Whole Numbers

Reduce the chaos and improve clarity in your decimal multiplication skill using this collection of no-prep, printable worksheets. A must-have resource for young learners looking to ace their class!

Decimal Division Whole Numbers

Decimal Division Whole Numbers

Revive your decimal division skills with a host of interesting lifelike word problems involving whole numbers. Keep up with consistent practice and you’ll fly high in the topic in no time!

Multiplying Decimals Word Problems

Multiplying Decimals Word Problems

Each decimal word problem involves multiplication of a whole number with a decimal number. 5th grade students are expected to find the product and check their answer using the answer key provided in the second page.

Dividing Decimals Word Problems

Dividing Decimals Word Problems

These division word problems require children to divide the decimals with the whole numbers. Ask the 6th graders to perform the division to find the quotient by applying long division method. Avoid calculator.

Decimals: Multiplication and Division

Decimals: Multiplication and Division

These decimal worksheets emphasize decimal multiplication and division. The perfect blend of word problems makes the grade 6 and grade 7 children stronger in performing the multiplication and division operation.

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Decimal Addition & Subtraction Worksheets

Add and subtract decimals with tenths, hundredths, and thousandths place values.

Decimal Addition and Subtraction Worksheets

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Worksheets for introducing decimal concepts, comparing decimals, and ordering decimals.

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Decimals Addition and Subtraction

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Worksheet on Word Problems on Addition and Subtraction of Decimals

Practice the questions given in the worksheet on word problems on addition and subtraction of decimals. Read the questions carefully to add or subtract the decimals as required.

1. Tania bought a book for $152.75, a pen for $45.25 and a chocolate for $28.75. What amount did she spend?

2. Nancy bought biscuits for $51.25. She gave a $100 note to the shopkeeper. How much dis she get back from the shopkeeper?

3. Mary had $305.80 in her bank account. She deposited $250.25 more and then withdrew $317.50 from her account. What is the balance now in her account?

4. Mike wants to buy a Physics book costing $600. He has $475.25 only in his purse. How much more money does he need to purchase the book?

5. Ron purchased a bag for $134.60, a book for $328.23 and a tie for $80.55. How much is left with him if he had $600 in all?

6. The difference of two decimals are 68.09. The smaller one is 353.48. Find the other one.

7. The sum of three decimals are 938.629. Two of them are 456.54 and 392.69. Find the third one.

8. Rachel had $739.68. She gave $235.09 to Jessica, $345.45 to Rebecca and the remaining money to Sara. How much did she give to Sara?

9. Jaclyn weighs 27.14 kg, Mary weighs 31.37 kg and Jenny weighs 28.38 kg. What is their total weight?

10. Kate travelled 320.25 km and Maya travelled 236.38 km. Who travelled more and by what distance?

11. Jack has lost $145.50 in a market. He is now left with $95.75. How much did he have?

12. Noor had $350.50. She bought jeans for $264.50 and a shirt for $65.75. How much did she have after pay?

13. Sam bought a pair of shirts for $205.75, a pant for $225.25 and a coat for $1225.20. What was the total cost of all the three items?

14. The sum of two decimals are 138.28. One of them is $68.42. Find the other one.

15. Jenifer had $178.50 with her. She has spent $138.85. How much money does she have now?

Answers for the worksheet on word problems on addition and subtraction of decimals are given below.

8. $ 159.14

9. 86.89 kg

10. Kate 83.87 km

11. $241.25

13. $1656.50

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Word Problems on Addition and Subtraction of Decimals | Adding and Subtracting Decimals Word Problems

See your kids excel in mathematics taking the help of the free and extensive problems available on decimal addition and subtraction. Use the interactive exercise Word Problems on Addition and Subtraction and develop personalized learning among your kids. This Worksheet on Adding and Subtracting Decimals has an extensive collection of frequently asked problems in your exams. Assess your strengths and weaknesses using the problems over here regarding decimal addition and subtraction and get a good grip on the concept.

Do Read Similar Articles:

  • Worksheet on Concept of Decimal
  • Simplify Decimals Involving Addition and Subtraction Decimals
  • Adding Decimals
  • Subtracting Decimals

Word Problems Involving Addition and Subtraction of Decimals

Example 1. There are 8.50 liters of milk in the pan. Raju added 5 g of sugar and 1.25 liters of water to the pan. Find how many liters of milk and water are there in the pan? Solution: No. of liters of milk in the pan = 8.50 No.of liters of water in the pan = 1.25 No. of liters of milk and water in the pan is 8.50 + 1.25 = 9.75 Hence, There are 9.75 liters of milk and water are there in the pan.

Example 2. Raju has 14.50 acres of agricultural land. He decided to give his first son Sai 6.50 acres of land and the second son Sudheer 5.50 acres of land. Find how much land does Raju has after distributing his sons? Solution: Raju has the agricultural land = 14.50 Raju gave the land for the first son = 6.50 Raju gave the land for the second son = 5.50 No. of acres of land Raju distributed for his sons = 6.50 + 5.50 =12.00 No. of acres of land Raju has after distributing his sons =14.50-12.00 = 2.50 Therefore, Raju has 2.50 acres of agricultural land after distribution.

Example 3. The price of the sugar last month is Rs 42.50. This month the price of sugar is increased by Rs 2.50. Find out what is the price of the sugar this month? Solution: The price of the sugar last month = 42.50 The price of the sugar this month is increased by =  2.50 The price of the sugar this month = 42.50 + 2.50 = 45.00 Hence, the price of the sugar this month is Rs 45.

Example 4. Karthik wants to go to the temple which is 150.50 km. Karthik stops driving the car after driving 65.80 km, because of the traffic jam. How much distance he has to travel for going to the temple? Solution: Karthik wants to go to the temple at a distance = 150.50 Karthik traveled by car up to the distance = 65.80 The distance Karthik has to travel for going to the temple = 150.50-65.80 = 84.70 Therefore, Karthik has to travel 84.70 km for going to the temple.

Example 5. Praveen wants to buy a house in Banglore. He went to choose the houses. In the first house, the rooms were 28.50 square feet longer. The second house was 2.7 square feet shorter. The third house was 5.6 square feet longer than the first house. What is the difference in feet between the second and third house rooms? Solution:  The size of the rooms in the first house was = 28.50 The size of the rooms in the second house was shorter by = 2.7 The size of the rooms in the second house was = 28.50 – 2.7 = 25.8 The size of the rooms in the third house was longer than the first house by = 5.6 The size of the rooms in the third house was = 28.50 +5.6 = 34.1 The difference in feet for the second and third house was = 34.1-25.8 = 8.3 Hence, The difference in feet for the second and third houses was 8.3 square feet.

Example 6. Varsha had money Rs 750.80. She bought a dress for Rs 530.20. How much money left with Varsha? Solution: Varsha had money = 750.80 She bought a dress = 530.20 Money left with Varsha = 750.80-530.20 = 220.60 Hence, Money left with Varsha = 220.60

Example 7. Pavan went to a store. He bought 2.25 kg of cashews and almonds. If pavan bought 1.25 kg of almonds, how many kg of cashews? Solution: Total no. of kg of cashews and almonds = 2.25 kg Pavan bought almonds = 1.25 kg No. of kg of cashews = 2.25-1.25 = 1 kg Hence, the total no. of kg of cashews is 1 kg.

Example 8. Sindhu purchased a book for Rs 50.50, a pen for Rs 25.50. How much amount did Sindhu spend? Solution: Sindhu purchased a book = 50.50 Sindhu purchased a pen = 25.50 The amount Sindhu spend = 50.50 +25.50 = 76 Hence, the amount Sindhu spends is Rs 76.

Example 9. Harish has some money. He bought a gift for his friend in the amount of Rs 500.50. Harish is left with the amount of Rs 300. Find the amount of money Harish has before spending the money? Solution: Harish bought a gift for his friend = 500.50 Harish has left with the money = 300 The amount of money Harish has before spending the money = 500.50+300 = 800.50 Therefore, Harish has 800.50 before spending the money.

Example 10. In a juice shop, there are 10.25 liters of orange juice and 12.50 liters of grape juice. How many liters of juices are needed to fill an order of 30 liters of juice? Solution: No. of liters of Orange juice = 10.25 No.of liters of grape juice = 12.50 Total no. of liters of juices in the shop = 10.25+12.50 = 22.75 No. of liters of juices required to fill an order of 30 liters of juice = 30-22.75 = 7.25 Hence, no. of liters of juice required to fill an order is 7.25 liters.

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addition and subtraction of decimals problem solving

Home / United States / Math Classes / 6th Grade Math / Addition and Subtraction of Decimals

Addition and Subtraction of Decimals

We use decimal numbers as an alternate method to represent fractional numbers. We can perform math operations like addit ion and subtraction on decimal numbers by using the place value system. Check out the steps involved in the addition and subtraction operations with the help of some examples. ...Read More Read Less

Table of Contents

addition and subtraction of decimals problem solving

Place value charts

What are decimal places, steps for adding and subtracting decimals, how do we solve problems involving both the addition and subtraction of decimals.

  • Solved Examples
  • Frequently Asked Questions

A place value chart ensures that the digits are in their proper places. It helps with the comparison, addition, and subtraction of numbers. The place value of each digit can be easily shown through a place value chart. The value of a place is 10 times the value of the place to its right. Also, the value of each place is one-tenth \(\left(\frac{1}{10} \right)\) the value of the place to its left.

dec_add_sub1

The places to the right of the decimal point are called the decimal places . Tenths, hundredths, thousandths, and so on, are decimal places.

For example, in 3.2, 3 is in the ones place and 2 is in the tenths place.

We have to follow some basic steps to add decimal numbers , and the steps are as follows:

Step 1: Align the decimal numbers according to their place values first, such that their decimal points are lined up.

Step 2: If necessary, convert decimals to like decimals.

Step 3: Add or subtract the numbers and place the decimal point in the sum or difference according to the numbers added or subtracted, such that all the decimal points are aligned.

Example: Add: 55.23 + 12.41

Solution: First, let us line up the like place values, which leads to the lining up of the decimal places.

           55.23

         + 12.41

Now, we will begin adding from the extreme right.

        —————

           67.64

The answer is 67.64.

Example: Subtract: 77.14 – 8.62

Solution: Let us first line up like place values and line up the decimal places.

–  8.62

Now, we will begin the subtraction from the extreme right.

dec_add_sub2

The answer is 68.52.

In case a problem involves both operations simultaneously, some rules need to be followed: Step 1: Always perform the operation in the parentheses first. Step 2: Once the above step is completed, then proceed with the addition of decimals.

Step 3: Finally, proceed with subtraction.

Solved Addition and Subtraction of Decimals Examples

Example 1: Add: 25.23 + 2.41

Solution: First, let us line up the like place values to line up the decimal points.

             2 5.23

          + 2.41

          +   2.41

      —————

             27.64

The answer is 27.64.

Example 2: Subtract: 17.14 – 8.62

Solution: Let us first line up like place values to line up the decimal points.

dec_add_sub3

The answer is 8.52.

Example 3: John has $100, with which he intends to buy various games. He first buys a game based on dice for $8.99 and then bowling pins for $33.50. His mother gave him an additional $20 so he could buy an archery target, but he got one for $16.50. How much money does he have remaining in total?

add_sub_eg0003

Initial money that John has = $100

The cost of the game based on dice = $8.99

The cost of bowling pins = $33.50

Money remaining = 100 – (33.50 + 8.99)

Money given by John’s mother = $20

The cost of the archery target = $16.50

Money remaining in total (R) = 100 – (33.50 + 8.99) + 20 – 16.50

Step 1: Operation in parentheses

dec_add_sub5

R =100 – 42.49 +  20 – 16.50  

Step 2: Add

dec_add_sub6

R =120 – 42.49 – 16.50

R =120 – (42.49 + 16.50)

dec_add_sub6

Step 3: Subtract

dec_add_sub11

So, John is left with a total of $61.01.

What is a decimal point?

A decimal number is the combination of an integral part and a decimal part. The decimal point is a point or dot used to separate the integral and the decimal part of a number.

What happens when we do not line up the decimal points while adding or subtracting?

When we do not line up the decimal points while adding or subtracting, it makes the addition or subtraction a bit difficult to solve and get the answer. It is essential that the decimals are aligned according to their place values before addition or subtraction, and if not, the answer may be incorrect.

What are like decimals? How do we convert to like decimals?

Like decimals are decimals that have the same number of decimal places. 

When the decimals are not like decimals, we add the required number of zeros to the right of the decimal to convert it to like decimals. This is done to make the addition or subtraction process easier.

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addition and subtraction of decimals problem solving

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Decimal Subtraction Worksheets

Up to 3 decimal places.

Welcome to our Decimal Subtraction Worksheets. Here you will find our range of Fifth Grade Column Subtraction Worksheets involving decimal numbers, which will help you to learn to subtract decimals with up to 3 decimal places.

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  • subtract decimals with up to 3 decimal places;
  • set out decimal subtractions correctly.

Decimal Column Subtraction Sheets

  • Decimal Column Subtraction 1
  • Sheet 1 Answers
  • PDF version
  • Decimal Column Subtraction 2
  • Sheet 2 Answers
  • Decimal Column Subtraction 3
  • Sheet 3 Answers
  • Decimal Column Subtraction 4
  • Sheet 4 Answers
  • Decimal Column Subtraction 5
  • Sheet 5 Answers
  • Decimal Column Subtraction 6
  • Sheet 6 Answers

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More Fifth Grade Subtraction Worksheets

Here you will find a range of Free Printable 5th Grade Subtraction Worksheets.

The following worksheets involve using subtraction at a 5th grade level.

Using these sheets will help your child to:

  • subtract decimals including tenths and hundredths mentally;
  • subtract multi-digit numbers, including decimals using column subtraction.
  • 5th Grade Subtraction Worksheets up to Billions (columns)
  • Subtracting Decimals Worksheets (mental)
  • Free Subtraction Worksheets (randomly generated)
  • Money Worksheets (randomly generated)

5th Grade Decimal Column Addition Sheets

Here you will find a selection of decimal column addition sheets for 5th grade.

  • add two or more numbers with up to 3 decimal places;
  • set out decimal addition sums correctly.
  • Decimal Column Addition Worksheets

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

All the free 5th Grade Math Worksheets in this section follow the Elementary Math Benchmarks for Grade 5.

  • Math Games 5th Grade
  • 5th Grade Math Puzzles

Here you will find a range of printable 5th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

  • learn and practice their addition facts, including decimals;
  • practice their subtraction facts, including decimals;
  • practice and apply multiplication and division facts;
  • develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 5th grade.

  • 5th Grade Math Problems

Here you will find our selection of free 5th grade math word problems.

Each sheet is availabel in both standard and metric units (where applicable).

Each sheet comes complete with a separate answer sheet.

All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.

Using these sheet will help your child to:

  • apply their addition, subtraction, multiplication and division skills;
  • apply their knowledge of rounding and place value;
  • solve a range of problems including "real life" problems and ratio problems.

All the worksheets help to support Elementary math benchmarks.

These sheets involve solving one or two more challenging longer problems.

These sheets involve solving many 'real-life' problems involving data.

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These sheets involve solving a range of ratio problems.

  • Multiplication Word Problems 5th Grade

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Solving Problems that Include Fractions and Decimals

Introduction.

There are four important operations that you will encounter when solving problems in mathematics. The figures below indicate some of the actions in a problem that lead to different operations.

Addition and subtraction are related operations. Addition typically means to combine two or more numbers, and subtraction involves the difference , or removal, of one number from another.

Combining things, Accumulations, and Amounts of increase all pointing to Addition

Multiplication and division are also related operations. Both operations involve grouping and rates.

Combining several groups with the same size, Scaling a quantity, and Calculating Area all pointing at Multiplication

You have explored how to tell when to use which operation. Now, you will focus on identifying the operation from a word problem, and then use procedures to actually perform the operation and determine a solution to the problem.

Working with Signed Numbers

Signed numbers include integers and other rational numbers that have either a positive or a negative sign.

elevation markers

Source: Badwater Elevation Sign, Complex01 and Elevation Benchmark, Jeff Kramer, Wikimedia Commons

Use the diagram below to review standard procedures for adding, subtracting, multiplying, and dividing integers.

A description of how to perform Subtraction, Addition, Division, and Multiplication

Adding and Subtracting Decimals

You have applied the rules of integers to solve word problems. Now, you will review ways to add and subtract decimals, and then use what you learn to solve problems relating to addition and subtraction of positive and negative decimals.

Click on the image below to open a base-ten model interactive in a new web browser tab or window. The interactive represents the two addends in an addition problem, or the minuend  and subtrahend in a subtraction problem. Use the manipulative to work through at least 3 problems.

  • Click on a block and drag it on top of its opposite block to remove zero pairs.
  • Click on a block and drag it to the next column to regroup.
  • Click “Next Problem” to move to the next problem when you are ready.

addition and subtraction of decimals problem solving

Need additional help for addition?

Need additional help for subtraction?

Use what you noticed in the interactive to answer the following questions.

In the original problem, 4.3 – 1.5, when you dragged a ones rod into the tenths column, it split into 10 tenths. How does that relate to the regrouping that was recorded symbolically in the image shown below?

addition and subtraction of decimals problem solving

In an addition problem, such as 6.4 + 4.8, when you regroup 10 tenths into 1 one and drag the ones rod into the ones place, how did that action appear in the regrouping that was recorded symbolically such as the regrouping shown in the image below?

addition and subtraction of decimals problem solving

Pause and Reflect

1. Why is it important to line up the decimal point when adding or subtracting decimal numbers?

2. When regrouping 1 one and 3 tenths into 13 tenths, why do you cross out the original 3 in the tenths place and replace it with 13? 

Adding and Subtracting Fractions

You have used models and algorithms to add and subtract decimals, paying special attention to the regrouping that was necessary to perform the computations. Now, you will extend the idea of regrouping to models and procedures used to add and subtract fractions, including mixed numbers.

Consider the following problem.

apples

The example below shows how Marley used fraction strips to solve this problem.

Click the image below to view additional examples, including a video with a worked-out example for you to follow.

addition and subtraction of decimals problem solving

1. How is regrouping when subtracting mixed numbers similar to regrouping when subtracting decimals?

2. When adding decimals, you regroup when the sum of the two digits in a place value that is greater than 10. When would you need to regroup as you add mixed numbers?

Multiplying and Dividing Decimals

Now that you’ve investigated addition and subtraction with decimals and fractions, let’s take a closer look at multiplication and division. You will start in this section with decimals, and then use a similar model to multiply and divide fractions and mixed numbers in the next section.

addition and subtraction of decimals problem solving

  • Write an expression that you can use to determine the amount of oil that Rachel started with.
  • How would you represent 2.2 and 2.5 as improper fractions with denominators of 10?

The interactive below uses blocks to multiply decimals. When the blocks are combined, they will form a rectangle; the area of the rectangle is the product of the two decimals or the answer to Rachel’s problem.

addition and subtraction of decimals problem solving

  • In the first activity, the first decimal is the length of the rectangle, and the second decimal is the width. Represent each decimal by dragging the appropriate blocks and moving them to the area for each decimal.
  • In the second activity, use the information from the decimals and drag the blocks to the open area to create a rectangle. You will use the green blocks to fill in the missing pieces of the rectangle.
  • Is the answer the same as what we found earlier in Anu's solution?
  • Adjust the numerators to create and represent two more multiplication problems. Record those problems on a piece of paper.

Based on what you saw in the interactive, why do you think that the product has the same number of digits to the right of the decimal as the total number of digits to the right of the decimal in the two factors ?

Multiplying and Dividing Fractions

In this section, you will look at models to represent multiplying and dividing fractions.

Multiplying Fractions

running shoes

Use the interactive below to represent the problem and graphically illustrate the product. Use the Numerator and Denominator sliders to create each fraction or mixed number. You may also need to use the Zoom in/out sliders to see the entire model.

addition and subtraction of decimals problem solving

Need additional directions?

Use the interactive to answer the following questions:

  • What are the dimensions of the shaded rectangle in the solution? Check Your Answer
  • The solid lines represent the boundaries of a rectangle with an area of 1 square unit. The dashed lines represent the boundaries of a number of equal-sized regions within this area. What fraction of 1 does each smaller rectangle represent? Check Your Answer

addition and subtraction of decimals problem solving

  • What mixed number does this rearranged figure represent? How does this compare with the product of 3 4 and 6 1 2 ? Check Your Answer

Dividing Fractions

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To solve this problem, Barbara used a fraction strip generator, which gave her the following diagram.

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  • Barbara knew this was a division problem, not a multiplication problem. How did she know that? Check Your Answer
  • Use the diagram to explain why the quotient of 6 1 2 ÷ 1 2 is 13. Check Your Answer

Use the same fraction strip generator that Barbara used to solve the problem below.

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Click the image below to open the fraction strip generator in a new web browser tab or window. Enter the key information from the problem, including the dividend and the divisor , and then use the results to answer the questions that follow.

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In the fraction diagrams, both 5 3 4 and 3 8 are marked off into eighths. Why do you think that is the case? Check Your Answer

To divide 5 3 4 by 3 8 , the number sentence beneath the diagrams shows multiplication of 5 3 4 by 8 3 , which is the reciprocal of 3 8 . Multiplying by 8 3 is the same as multiplying by 8 , and then dividing by 3 . Why do you need to multiply 5 3 4 by 8 , which is the numerator of the reciprocal? Check Your Answer

The next step in the number sentence divides the product of 5 3 4 and 8 by 3 (multiplies 5 3 4 by the fraction 8 3 ) . Why do you need to divide by 3 at this point? Check Your Answer

See the completed fraction diagram for Patrice's ornament problem.

Completed fraction diagram

1. How does the multiplication algorithm connect to the area model that you used in the first interactive?

2. How does the division algorithm connect to the fraction strip model that you used in the interactive?

You studied models that represent operations on rational numbers (fractions and decimals). You also connected those models to the standard algorithms for performing the operations.

The graphic below summarizes procedures to add, subtract, multiply, and divide decimals.

addition and subtraction of decimals problem solving

The graphic below summarizes procedures to add, subtract, multiply, or divide fractions, including mixed numbers.

addition and subtraction of decimals problem solving

Copy and paste the link code above.

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COMMENTS

  1. Decimals word problem worksheets

    These grade 4 math worksheets have word problems involving the addition and subtraction of one-digit decimals. Some questions may i) have 3 terms, ii) involve comparisons or iii) require conversions of fractions with a denominator of 10 or 100. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4 Worksheet #5 Worksheet #6 Similar:

  2. Adding & subtracting decimals word problems

    Adding and subtracting decimals word problems Adding & subtracting decimals word problems Google Classroom Rosa is building a guitar. The second fret is 33.641 mm from the first fret. The third fret is 31.749 mm from the second fret. How far is the third fret from the first fret? mm Stuck? Review related articles/videos or use a hint.

  3. Add and subtract decimals

    Unit 1 Intro to multiplication Unit 2 1-digit multiplication Unit 3 Intro to division Unit 4 Understand fractions Unit 5 Place value through 1,000,000 Unit 6 Add and subtract through 1,000,000 Unit 7 Multiply 1- and 2-digit numbers Unit 8 Divide with remainders Unit 9 Add and subtract fraction (like denominators) Unit 10 Multiply fractions

  4. Addition and Subtraction of Decimals with Steps and Examples

    Step 1: The numbers are first padded with zero depending upon the maximum digits present after the decimal for any of the numbers. For example, while adding 3.456 to 7.1, since the number 3.456 has the number of digits after the decimal, the padding is done according to 3.456. Since 3.456 has 3 digits after the decimal, we pad two zeros after 1.

  5. 6.4: Addition and Subtraction of Decimals

    Add or subtract the numbers as if they were whole numbers. Place a decimal point in the resulting sum or difference directly under the other decimal points. Sample Set A. Find the following sums and differences. 9.813 + 2.140. Solution. 9.813 +2.140- ------11.953 The decimal points are aligned in the same column.

  6. Adding and Subtracting Decimals

    To add decimals, follow these steps: Write down the numbers, one under the other, with the decimal points lined up Put in zeros so the numbers have the same length ( see below for why that is OK) Then add, using column addition, remembering to put the decimal point in the answer Example: Add 1.452 to 1.3 Example: Add 3.25, 0.075 and 5

  7. Decimals: Adding and Subtracting Decimals

    Learn all about adding decimals and subtracting decimals in this free basic math lesson. Learn all about adding decimals and subtracting decimals in this free basic math lesson. ... Just like with any addition example, ... Try solving these problems to practice subtracting decimal numbers. 5.85 - 2.73 = 84.50 - 2.30 = 99.90 - 67.40 =

  8. Adding and Subtracting Decimals

    Get Started Adding and Subtracting Decimals Adding and subtracting decimals is the same as the addition and subtraction of whole numbers keeping in mind that the decimal point needs to be in place. The length of the decimal numbers can be adjusted by adding or removing zeros from the decimal part.

  9. Word Problems on Addition and Subtraction of Decimals

    We know we need to add or subtract the decimals as we add or subtract ordinary numbers. Let us consider some of the following examples. 1. Kate had $ 368.29. Her mother gave her $ 253.46 and her sister gave her $ 57.39. How much money does she has now? Money Kate had = $ 368.29 Money gave her mother = $ 253.46 Money gave her sister = + $ 57.39

  10. Solving problems with decimals using addition and subtraction

    Worksheet Transcript Calculating with whole numbers and decimals: Representing Decimals Multiplying and dividing decimals by 10,100,1000 Deriving decimal addition and subtraction facts Adding decimals Subtracting decimals Applying mental calculation strategies to adding and subtracting decimals

  11. Decimals Addition & Subtraction for Grade 5

    Our grade 5 addition and subtraction of decimals worksheets provide practice exercises in adding and subtracting numbers with up to 3 decimal digits. Sample Grade 5 Decimal Subtraction Worksheet More decimals worksheets Find all of our decimals worksheets, from converting fractions to decimals to long division of multi-digit decimal numbers.

  12. Decimal Word Problems Worksheets

    Decimals: Addition and Subtraction It's review time for grade 4 and grade 5 students. Take these printable worksheets that help you reinforce the knowledge in adding and subtracting decimals. There are five word problems in each pdf worksheet. Download the set Multiplying Decimals Whole Numbers

  13. Decimal Addition and Subtraction

    This printable includes a mix of addition and subtraction problems for students to solve. Each problem needs to be re-written vertically and students must line up the columns properly. 5th Grade. ... Rewrite each decimal addition or subtraction problem vertically on the graph paper, then solve. The grid paper will help students line up columns ...

  14. Worksheet on Word Problems on Addition and Subtraction of Decimals

    Practice the questions given in the worksheet on word problems on addition and subtraction of decimals. Read the questions carefully to add or subtract the decimals as required. 1. Tania bought a book for $152.75, a pen for $45.25 and a chocolate for $28.75. What amount did she spend? 2. Nancy bought biscuits for $51.25.

  15. Adding & Subtracting Decimals

    Lesson Transcript Author Brigette Banaszak View bio Instructor Yuanxin (Amy) Yang Alcocer View bio Understand adding and subtracting decimals. Practice by solving examples and decimal word...

  16. Word Problems on Addition and Subtraction of Decimals

    Solution: No. of liters of milk in the pan = 8.50 No.of liters of water in the pan = 1.25 No. of liters of milk and water in the pan is 8.50 + 1.25 = 9.75 Hence, There are 9.75 liters of milk and water are there in the pan. Example 2. Raju has 14.50 acres of agricultural land.

  17. Solving problems with decimals using addition and subtraction

    Start Lesson In this lesson, we will solve addition and subtraction problems with decimals and generate our own word problems to suit equations. We will develop our understanding of decimal problem-solving through bar models and a variety of real life contexts.

  18. Addition and Subtraction of Decimals

    How do we solve problems involving both the addition and subtraction of decimals? Solved Examples Frequently Asked Questions Place value charts A place value chart ensures that the digits are in their proper places. It helps with the comparison, addition, and subtraction of numbers.

  19. Adding/Subtracting Decimals Practice Questions

    addition, subtraction, subtracting. Practice Questions. Previous: Data Handling Cycle Practice Questions. Next: Multiplying/Dividing by Decimals Practice Questions. The Corbettmaths Practice Questions on Adding or Subtracting Decimals.

  20. How to Solve Word Problems Involving Addition & Subtraction of Decimals

    Steps to Solve Word Problems Involving Addition and Subtraction of Decimals. Step 1: Identify the important numbers and key words in the problem that will indicate the operation (s) you will ...

  21. Mixed decimals word problems for grade 5

    Add, subtract and multiply decimals These grade 5 math word problems involve the addition, subtraction and multiplication of decimal numbers with one or two decimal digits. Some problems may have more than 2 terms, include superfluous data or require the conversion of fractions with denominators of 10 or 100.

  22. Decimal Subtraction Worksheets

    Decimal Subtraction Worksheets. Here you will find a range of Printable Decimal Subtraction Worksheets set out in columns. The sheets are arranged in order of difficulty with the easiest sheets first. Using these sheets will help your child to: subtract decimals with up to 3 decimal places; set out decimal subtractions correctly.

  23. Solving Problems that Include Fractions and Decimals

    The graphic below summarizes procedures to add, subtract, multiply, or divide fractions, including mixed numbers. Given problem situations, the student will use addition, subtraction, multiplication, and division to solve problems involving positive and negative fractions and decimals.

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