Free Printable Fraction Word Problems Worksheets for 6th Grade

Fraction Word Problems: Discover a collection of free printable Math worksheets for Grade 6 students, focusing on solving real-life scenarios involving fractions. Enhance learning and problem-solving skills with Quizizz's resources.

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Explore printable Fraction Word Problems worksheets for 6th Grade

Fraction Word Problems worksheets for Grade 6 are an essential resource for teachers looking to help their students master the challenging world of fractions in math. These worksheets provide a variety of math word problems that incorporate fractions, allowing students to practice their skills in a fun and engaging way. Teachers can use these worksheets to supplement their lesson plans, provide extra practice for struggling students, or even as a form of assessment to gauge their students' understanding of the material. With a wide range of topics covered, from addition and subtraction of fractions to more complex problems involving ratios and proportions, these Grade 6 worksheets are a valuable tool for any math teacher looking to enhance their students' learning experience.

In addition to Fraction Word Problems worksheets for Grade 6, teachers can also utilize Quizizz, an interactive platform that offers a variety of educational resources, including quizzes, games, and other engaging activities. Quizizz allows teachers to create custom quizzes and games based on the content they are teaching, making it a perfect complement to the worksheets they are already using in their classroom. With Quizizz, students can practice their math skills in a more interactive and enjoyable way, helping to solidify their understanding of the material. Furthermore, Quizizz provides teachers with valuable data and insights into their students' progress, allowing them to identify areas where additional support may be needed. By incorporating both Fraction Word Problems worksheets for Grade 6 and Quizizz into their lesson plans, teachers can provide a well-rounded and effective learning experience for their students.

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

  • Download the set

Represent and Simplify the Fractions: Type 2

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

Related Worksheets

» Decimal Word Problems

» Ratio Word Problems

» Division Word Problems

» Math Word Problems

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Fraction Word Problems Worksheets

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Traverse through our printable fraction word problems worksheets for a wide range of real-world scenarios that involve identifying fractions and equivalent fractions and performing four operations with proper fractions, improper fractions, and mixed numbers. With exclusive theme-based word problems on adding, subtracting, multiplying, and dividing fractions, our free worksheets will see the young beginners and skilled learners practice with relish!

These pdf worksheets are most recommended for students in grade 3 through grade 7.

Identifying Fractions | Worksheet #1

Savor a potpourri of everyday circumstances that have fractions in place. Read the scenarios carefully and pinpoint the fractions that take part in them to solve this free identifying fractions worksheet.

Identifying Fractions 1

Identifying Fractions | Worksheet #2

Children in 3rd grade and 4th grade need to pore over the fraction word problems, identify the numerators as parts and denominators as whole, and solve them.

Identifying Fractions 2

Equivalent Fractions Word Problems

Here's an exclusive set that hands out well-researched word problems on equivalent fractions, so compelling that you would instantly want to add it to your repertoire! Grab these printable practice worksheets now!

Equivalent Fractions Word Problems

Adding Fractions Word Problems

Casting around for story problems on fraction addition? Watch kitchen ingredients, handicrafts, and many other familiar objects contribute their bits toward the cause of fractions for addition.

Adding Fractions Word Problems

Subtracting Fractions Word Problems

Plug into this bunch of pdf worksheets with interesting word problems on fraction subtraction for grade 3, grade 4, grade 5, and grade 6, and steal the limelight!

Subtracting Fractions Word Problems

Multiplying Fractions Word Problems

Unleash your hidden skills at fraction multiplication through our fraction word problems worksheets, where it's raining relatable situations. Children will discover a whole new way of embracing fractions in their daily lives.

Multiplying Fractions Word Problems

Dividing Fractions Word Problems

A free, must-have resource for 5th grade, 6th grade, and 7th grade students. Tap into the student’s inner genius and watch them perform fraction division with renewed passion!

Dividing Fractions Word Problems

Related Printable Worksheets

▶ Adding Fractions

▶ Subtracting Fractions

▶ Multiplying Fractions

▶ Dividing Fractions

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Fraction Word Problems Worksheets

The fraction word problems worksheet helps the students uncover fraction concepts and their usage in real-life situations. Fractions mean a part of the whole and they find their place everywhere making it an important topic to learn.

Benefits of Fraction Word Problems Worksheets

These worksheets are thoughtfully curated for the students to put their knowledge of fractions into use. The benefit of fraction word problem worksheets is that the young minds get to explore the vastness of usage of fractions in mathematics and real life.

The students will learn a lot using their basic knowledge of addition subtraction multiplication and division in dealing with word problems including fractions, mixed fractions, and ratios.

Download Fraction Word Problems Worksheet PDFs

These math worksheets are free to download and easy to proceed with, as the questions are arranged in increasing order of difficulty. The interactive and engaging question problems help the students explore a wide range of fraction usage and their applicability in real life scenarios.

☛ Check Grade wise Fraction Word Problems Worksheets

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6th Grade Fraction Worksheets

Created: October 12, 2022

Last updated: June 6, 2023

The use of the fraction worksheets 6th grade is a seamless way to make your sixth graders master the concepts of fractions. These worksheets comprise questions on various forms of fractions, fraction conversion, and fraction word problems. The worksheets have lots of benefits for students, tutors, and parents.

Simplifying Fractions Worksheet 6th Grade

Simplifying Fractions Worksheet 6th Grade

6th Grade Simplifying Fractions Worksheet

6th Grade Simplifying Fractions Worksheet

6th Grade Fraction To Percent Worksheet

6th Grade Fraction To Percent Worksheet

6th Grade Math Worksheets Fractions

6th Grade Math Worksheets Fractions

Reducing Fractions Worksheet 6th Grade

Reducing Fractions Worksheet 6th Grade

Fractions Worksheets Grade 6

Fractions Worksheets Grade 6

Brighterly’s fraction word problems worksheets 6th grade

By learning with the fractions worksheets, students will master mathematical concepts like ratios, proportions, percentages, etc. Top experts with years of experience tutoring kids in mathematics design worksheets. Thus, the sheets are tailored to meet the demands of kids and make learning seamless for them.

Brighterly’s 6th grade fraction to decimal worksheet is suitable for all grade six students, irrespective of their learning capability. The worksheets are deliberately designed to make learning an enjoyable and interactive experience.

Math for Kids

Furthermore, the questions on the worksheets are arranged according to varying difficulty levels. That is, kids proceed from less complicated to more challenging tasks.

Printable 6th grade fractions worksheets

Printable fractions worksheets for sixth graders make it easier for parents to make their kids study. Since the tools are in paper format, kids would be able to study regularly. Also, the questions on the worksheets come with answers so kids can check the answers by themselves.

6th Grade Fraction Worksheets PDF

Fraction Worksheets 6th Grade

Fraction Word Problems Worksheets 6th Grade

6th Grade Fractions Worksheets

6th Grade Fraction To Decimal Worksheet

Fractions Worksheets

  • Improper Fractions To Mixed Numbers Worksheets
  • Simplifying Fractions Worksheets
  • Reducing Fractions Worksheets
  • Improper Fractions Worksheets
  • Fraction Worksheets for Grade 3

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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Grade 6 Math Word Problems: Tips, Tricks, and Answers

Do you want to stimulate your 6 th grader’s creative thinking skills? Then, enjoy this brilliant math article. In this comprehensive guide, we will provide you with a treasure trove of fun solving strategies, tips, tricks, and answers to tackle those tricky grade 6 math word problems that have been confusing your students for some time now.

In this page, you will discover why math word problems are important for 6th-graders and simple methods of breaking down complex word problems into manageable steps.

Nevertheless, we will introduce you to Mathskills4kids.com , an outstanding website with thousands of common types of grade 6 math word problems and a step-by-step approach to solving them. Interestingly, we will illustrate how to use diagrams and models to solve math word problems efficiently.

Learn to love Grade 6 Math word problems with these worksheets and answers

Hello and welcome to Grade 6 Math word problems worksheets and answers , where your 6 th Grade students will learn to love and solve math problems and activities at all times.

We understand that word problems can often frustrate students, as they require a solid understanding of mathematical concepts and the ability to interpret and apply them to real-life situations. That's why we have compiled a collection of proven strategies and techniques to empower your students to approach word problems confidently and accurately.

From understanding problem-solving strategies to breaking down complex questions into manageable steps, this guide will equip you with the knowledge and resources to make math word problems a breeze. So, let's dive in and unlock the secrets to conquering grade 6 math word problems together!

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Grade 6 Math Word Problems: Tips, Tricks, and Answers - How do you estimate to solve word problems

Start practice on Sixth Grade here

Why are math word problems important for 6th-graders.

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6 th graders because they help them to:

  • Learn how to use different math concepts and skills in various contexts
  • Develop their logical thinking and reasoning abilities
  • Enhance their communication and literacy skills
  • Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

Strategies for solving Grade 6 math word problems

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

  • Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
  • They should rewrite the problem in their own words or summarize it in a sentence.
  • Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
  • They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
  • Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

Breaking down complex word problems into manageable steps

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

Words like "difference," "subtract," "take away," or "minus" indicate s ubtraction .

Words like "product," "multiply," "times," or "of" indicate multiplication .

Words like "quotient," "divide," "per," or "out of" indicate division .

Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals .

Words like "equal," "same as," or "is" indicate equations .

Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities .

Words like "average," "mean," or "median" indicate statistics .

Words like "area," "perimeter," "volume," or "surface area" indicate geometry , etc.

  • Use parentheses, brackets, or other symbols to group the parts of the problem that belong together . For example, if the problem says:

You can rewrite it as:

  • (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

  • Solve each part of the problem separately and write down the intermediate results . For example, using the previous problem:
  • (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
  • 12 + 8 = 20
  • (total number of apples) / (4 people) = (number of apples per person)

This way, you can keep track of your work and avoid making mistakes.

  • Combine the intermediate results to get the final answer. For example, using the previous problem :

This way, you can answer the question and check your answer.

Common types of grade 6 math word problems

There are many types of word problems that you may encounter in grade 6 math . Some of the most common ones found on Mathskills4kids.com are:

  • Ratio and proportion problems : These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
  • Percent problems : These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
  • Fraction problems : These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
  • Decimal problems : These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
  • Measurement problems : These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
  • Algebra problems : These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

A step-by-step approach to solving different types of word problems

No matter what type of word problem your 6 th graders are faced with, they can use the following steps to solve it:

  • They should read the problem carefully and identify the given information and the question.
  • They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
  • They can now solve the equation or expression and find the variable's value.
  • They can check their answer by plugging it back into the equation or expression to see if it makes sense.
  • They can now write their answer in complete sentences and include the appropriate units.

Using diagrams and models to solve math word problems

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

  • Tape diagrams : These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
  • Number lines : These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
  • Tables : These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
  • Charts : These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
  • Drawings : These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

Providing answers and explanations to sample Mathskills4kids’ Grade 6 math word problems

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com :

Answer : 6 cups of flour

Explanation : This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

Answer : $15

Explanation : This is a percent problem. We can use a formula to find the sale price of the shirt.

Sale price = Original price - Discount

Discount = Percent off x Original price

We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

Discount = 40% x $25

Discount = 0.4 x $25

Discount = $10

Sale price = $25 - $10

Sale price = $15

Tips for improving problem-solving skills in Grade 6 math

Here are some tips that can help students improve their problem-solving skills in grade 6 math :

  • Please encourage them to practice regularly and try different types of word problems.
  • They should review the concepts and skills they have learned and apply them to new situations.
  • They can use different strategies and methods to solve word problems and compare their results.
  • Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
  • They should learn from their mistakes and try to avoid them in the future.

Bonus: additional resources to reinforce Grade 6 math problem skills

If you want to enhance your student's Grade 6 math word problem skills , or if you need some extra help, here are some additional and useful web links that you can check out:

  • Math Playground : This website has a lot of fun and interactive games that let 6 th graders practice different types of math word problems, such as fractions, decimals, ratios, proportions, and more. They can also watch videos explaining how to solve some problems. https://www.mathplayground.com/wordproblems.html .
  • Khan Academy : This website has many videos and exercises covering various topics in Grade 6 math, including word problems. Students can learn at their own pace and track their progress. https://www.khanacademy.org/math/cc-sixth-grade-math .
  • IXL : This website has many practice questions aligned with the Common Core standards for Grade 6 math. Students can choose from different categories of word problems, such as expressions and equations, geometry, statistics, and more. They can also get instant feedback and explanations for their answers. https://www.ixl.com/math/grade-6 .
  • Math Goodies : This website has a lot of worksheets and lessons that teach 6 th graders how to solve different types of word problems, such as percent, ratio, proportion, and more. They can also find tips and tricks for solving word problems faster and easier. https://www.mathgoodies.com/math-mammoth/worksheets/pdf/grade_6_word_problems.pdf .

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Math word problems can be challenging for many 6th-graders, but they are also important for developing their mathematical thinking and reasoning skills.

Using the strategies and steps we discussed in this article, your student's ability to solve different types of word problems in Grade 6 math can be improved.

You can also use the diagrams and models we have shown you to help your students visualize the problem and find the solution. Encourage them to practice as much as possible, and they must not be afraid to ask for help if needed.

You can also use the web links that we have provided to reinforce your student’s learning and have fun with math. We hope this article has helped your 6th-grade students feel more confident and prepared for tackling Grade 6 math word problems.

Happy problem-solving!

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6th Grade Fractions Worksheets, Lessons, and Printables

word problems with fractions 6th grade worksheets

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6th Grade Word Problems With Fractions And Decimal

6th Grade Word Problems With Fractions And Decimal - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Fraction and decimal word problems no problem, 6th grade math work fractions and decimals, Word problem practice workbook, Grade 6 math word problems with percents, One step word problems, Decimals work, Exercise work, Fraction word problems.

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1. Fraction and Decimal Word Problems No Problem!

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Word Problems Involving Fractions Grade 6

Displaying top 8 worksheets found for - Word Problems Involving Fractions Grade 6 .

Some of the worksheets for this concept are Fractions packet, All decimal operations with word problems, Fraction and decimal word problems no problem, Multiplying fractions word problems 1, Adding and subtracting fractions word problems 1, Multiplying decimals word problems, Grade 4 fractions word problems, Fraction word problems grade 5 math.

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1. Fractions Packet

2. all decimal operations with word problems, 3. fraction and decimal word problems no problem, 4. multiplying fractions word problems #1 -, 5. adding and subtracting fractions word problems #1, 6. multiplying decimals word problems -, 7. grade 4 fractions word problems -, 8. fraction word problems grade 5 math -.

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Proportions word problems

Ratios, Proportions and Problem Solving Workbook

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Math worksheets: Proportions word problems

Below are grade 6 math worksheets with proportions word problems.

word problems with fractions 6th grade worksheets

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Word Problems On Fractions Worksheets - 5th Grade Printable

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  • Internet Activities
  • Easel Activity

Description

Word Problems On Fractions are perfect for you if your students have issues with word problems especially fraction in word problems. So if you do not have enough fractions word problems or your students are struggling with them, you have to check this out!

These fractions word problems worksheets allow students to practice 9 different types of questions with 80 unique word problems (Students can use a calculator to solve these word problems.) The concepts are tested in Singapore primary 5 & 6 exams.

This math resource is NO PREP and great for differentiation! They are economical to print as it is black and white-colored, but you can also use them for distance learning with the digital option (TpT Easel).

Do click " View Preview " to have a better idea of the product before buying.

Plus, there are FREE SAMPLES of the worksheets that you can download and use it in the preview!

Math Skills:

  • Remainder Concepts
  • Higher-Order Remainder Concepts
  • Simultaneous Equations
  • Multiplying adding subtracting fractions word problems

Key Features

★ 80 fractions word problems

★ 19 Worksheets

★ 9 Questions Types

★ Include money, mass, and length

★ Include notes and example in Set A

★ Answer Key provided | Handwritten solution provided for reference

★ Differentiated

★ No Prep = Save Time

★ Economical Printing: black and white

★ 2 Versions: Print & Digital (Easel Digital Activity)

★ Singapore Primary 5 & 6 | 5th Grade

Differentiation

  • Set A has 1 example with notes for weaker students or for introducing concepts to Primary 5.
  • Set B has the same questions as Set A without example and notes. Great for Primary 6 or as a review for Primary 5.
  • Set C has different, harder and more variety of questions compared to Set A. Great for Primary 5 or Primary 6.
  • Quiz has 1 similar question from each concept in Set A (exclude Fractions Word Problems question). Use it for review, extra practice or quiz.

Content Page Set A (Pg. 8 – 25)

9 worksheets

1 example, 27 doable questions in total.

Set B (Pg. 27 – 44)

9 worksheets, the same questions as Set A

36 doable questions in total

Set C (Pg. 46 – 63)

9 worksheets, different questions as Set A

Quiz (Pg. 65 – 68)

8 different unguided questions.

Answer Key & Solution (Pg. 69-74)

  • Practice or Drills
  • Math Centers
  • Independent Work
  • Early Finishers
  • Mini-lesson

Printable Worksheets

  • Can be used as task cards or worksheets
  • Include Printing Directions and answers.
  • Great for physical lessons in the classroom.

Easel by TpT Digital Activity

  • Digitalized Worksheets
  • You can use it directly on the TpT platform.
  • Great for online lesson, distance learning or tech station.
  • You can add additional directions if required.
  • You can choose the pages you want to assign to your students or you can assign them all.
  • Assign them to your students all through Google Classroom.

You Might Also Like:

Fractions Word Problems Worksheets

Halloween Fraction Activities

Fraction Paper Craft, Halloween Math Activities

Multiply and Divide Fractions

Quizzes On Fractions

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Solving equations

Here you will learn about solving equations, including linear and quadratic algebraic equations, and how to solve them.

Students will first learn about solving equations in grade 8 as a part of expressions and equations, and again in high school as a part of reasoning with equations and inequalities.

What is solving an equation?

Solving equations is a step-by-step process to find the value of the variable. A variable is the unknown part of an equation, either on the left or right side of the equals sign. Sometimes, you need to solve multi-step equations which contain algebraic expressions.

To do this, you must use the order of operations, which is a systematic approach to equation solving. When you use the order of operations, you first solve any part of an equation located within parentheses. An equation is a mathematical expression that contains an equals sign.

For example,

\begin{aligned}y+6&=11\\\\ 3(x-3)&=12\\\\ \cfrac{2x+2}{4}&=\cfrac{x-3}{3}\\\\ 2x^{2}+3&x-2=0\end{aligned}

There are two sides to an equation, with the left side being equal to the right side. Equations will often involve algebra and contain unknowns, or variables, which you often represent with letters such as x or y.

You can solve simple equations and more complicated equations to work out the value of these unknowns. They could involve fractions, decimals or integers.

What is solving an equation?

Common Core State Standards

How does this relate to 8 th grade and high school math?

  • Grade 8 – Expressions and Equations (8.EE.C.7) Solve linear equations in one variable.
  • High school – Reasoning with Equations and Inequalities (HSA.REI.B.3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

[FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

[FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

Use this quiz to check your grade 6 to 8 students’ understanding of math equations. 10+ questions with answers covering a range of 6th, 7th and 8th grade math equations topics to identify areas of strength and support!

How to solve equations

In order to solve equations, you need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

  • Combine like terms .
  • Simplify the equation by using the opposite operation to both sides.
  • Isolate the variable on one side of the equation.

Solving equations examples

Example 1: solve equations involving like terms.

Solve for x.

Combine like terms.

Combine the q terms on the left side of the equation. To do this, subtract 4q from both sides.

The goal is to simplify the equation by combining like terms. Subtracting 4q from both sides helps achieve this.

After you combine like terms, you are left with q=9-4q.

2 Simplify the equation by using the opposite operation on both sides.

Add 4q to both sides to isolate q to one side of the equation.

The objective is to have all the q terms on one side. Adding 4q to both sides accomplishes this.

After you move the variable to one side of the equation, you are left with 5q=9.

3 Isolate the variable on one side of the equation.

Divide both sides of the equation by 5 to solve for q.

Dividing by 5 allows you to isolate q to one side of the equation in order to find the solution. After dividing both sides of the equation by 5, you are left with q=1 \cfrac{4}{5} \, .

Example 2: solve equations with variables on both sides

Combine the v terms on the same side of the equation. To do this, add 8v to both sides.

7v+8v=8-8v+8v

After combining like terms, you are left with the equation 15v=8.

Simplify the equation by using the opposite operation on both sides and isolate the variable to one side.

Divide both sides of the equation by 15 to solve for v. This step will isolate v to one side of the equation and allow you to solve.

15v \div 15=8 \div 15

The final solution to the equation 7v=8-8v is \cfrac{8}{15} \, .

Example 3: solve equations with the distributive property

Combine like terms by using the distributive property.

The 3 outside the parentheses needs to be multiplied by both terms inside the parentheses. This is called the distributive property.

\begin{aligned}& 3 \times c=3 c \\\\ & 3 \times(-5)=-15 \\\\ &3 c-15-4=2\end{aligned}

Once the 3 is distributed on the left side, rewrite the equation and combine like terms. In this case, the like terms are the constants on the left, –15 and –4. Subtract –4 from –15 to get –19.

Simplify the equation by using the opposite operation on both sides.

The goal is to isolate the variable, c, on one side of the equation. By adding 19 to both sides, you move the constant term to the other side.

\begin{aligned}& 3 c-19+19=2+19 \\\\ & 3 c=21\end{aligned}

Isolate the variable to one side of the equation.

To solve for c, you want to get c by itself.

Dividing both sides by 3 accomplishes this.

On the left side, \cfrac{3c}{3} simplifies to c, and on the right, \cfrac{21}{3} simplifies to 7.

The final solution is c=7.

As an additional step, you can plug 7 back into the original equation to check your work.

Example 4: solve linear equations

Combine like terms by simplifying.

Using steps to solve, you know that the goal is to isolate x to one side of the equation. In order to do this, you must begin by subtracting from both sides of the equation.

\begin{aligned} & 2x+5=15 \\\\ & 2x+5-5=15-5 \\\\ & 2x=10 \end{aligned}

Continue to simplify the equation by using the opposite operation on both sides.

Continuing with steps to solve, you must divide both sides of the equation by 2 to isolate x to one side.

\begin{aligned} & 2x \div 2=10 \div 2 \\\\ & x= 5 \end{aligned}

Isolate the variable to one side of the equation and check your work.

Plugging in 5 for x in the original equation and making sure both sides are equal is an easy way to check your work. If the equation is not equal, you must check your steps.

\begin{aligned}& 2(5)+5=15 \\\\ & 10+5=15 \\\\ & 15=15\end{aligned}

Example 5: solve equations by factoring

Solve the following equation by factoring.

Combine like terms by factoring the equation by grouping.

Multiply the coefficient of the quadratic term by the constant term.

2 x (-20) = -40

Look for two numbers that multiply to give you –40 and add up to the coefficient of 3. In this case, the numbers are 8 and –5 because 8 x -5=–40, and 8+–5=3.

Split the middle term using those two numbers, 8 and –5. Rewrite the middle term using the numbers 8 and –5.

2x^2+8x-5x-20=0

Group the terms in pairs and factor out the common factors.

2x^2+8x-5x-20=2x(x + 4)-5(x+4)=0

Now, you’ve factored the equation and are left with the following simpler equations 2x-5 and x+4.

This step relies on understanding the zero product property, which states that if two numbers multiply to give zero, then at least one of those numbers must equal zero.

Let’s relate this back to the factored equation (2x-5)(x+4)=0

Because of this property, either (2x-5)=0 or (x+4)=0

Isolate the variable for each equation and solve.

When solving these simpler equations, remember that you must apply each step to both sides of the equation to maintain balance.

\begin{aligned}& 2 x-5=0 \\\\ & 2 x-5+5=0+5 \\\\ & 2 x=5 \\\\ & 2 x \div 2=5 \div 2 \\\\ & x=\cfrac{5}{2} \end{aligned}

\begin{aligned}& x+4=0 \\\\ & x+4-4=0-4 \\\\ & x=-4\end{aligned}

The solution to this equation is x=\cfrac{5}{2} and x=-4.

Example 6: solve quadratic equations

Solve the following quadratic equation.

Combine like terms by factoring the quadratic equation when terms are isolated to one side.

To factorize a quadratic expression like this, you need to find two numbers that multiply to give -5 (the constant term) and add to give +2 (the coefficient of the x term).

The two numbers that satisfy this are -1 and +5.

So you can split the middle term 2x into -1x+5x: x^2-1x+5x-5-1x+5x

Now you can take out common factors x(x-1)+5(x-1).

And since you have a common factor of (x-1), you can simplify to (x+5)(x-1).

The numbers -1 and 5 allow you to split the middle term into two terms that give you common factors, allowing you to simplify into the form (x+5)(x-1).

Let’s relate this back to the factored equation (x+5)(x-1)=0.

Because of this property, either (x+5)=0 or (x-1)=0.

Now, you can solve the simple equations resulting from the zero product property.

\begin{aligned}& x+5=0 \\\\ & x+5-5=0-5 \\\\ & x=-5 \\\\\\ & x-1=0 \\\\ & x-1+1=0+1 \\\\ & x=1\end{aligned}

The solutions to this quadratic equation are x=1 and x=-5.

Teaching tips for solving equations

  • Use physical manipulatives like balance scales as a visual aid. Show how you need to keep both sides of the equation balanced, like a scale. Add or subtract the same thing from both sides to keep it balanced when solving. Use this method to practice various types of equations.
  • Emphasize the importance of undoing steps to isolate the variable. If you are solving for x and 3 is added to x, subtracting 3 undoes that step and isolates the variable x.
  • Relate equations to real-world, relevant examples for students. For example, word problems about tickets for sports games, cell phone plans, pizza parties, etc. can make the concepts click better.
  • Allow time for peer teaching and collaborative problem solving. Having students explain concepts to each other, work through examples on whiteboards, etc. reinforces the process and allows peers to ask clarifying questions. This type of scaffolding would be beneficial for all students, especially English-Language Learners. Provide supervision and feedback during the peer interactions.

Easy mistakes to make

  • Forgetting to distribute or combine like terms One common mistake is neglecting to distribute a number across parentheses or combine like terms before isolating the variable. This error can lead to an incorrect simplified form of the equation.
  • Misapplying the distributive property Incorrectly distributing a number across terms inside parentheses can result in errors. Students may forget to multiply each term within the parentheses by the distributing number, leading to an inaccurate equation.
  • Failing to perform the same operation on both sides It’s crucial to perform the same operation on both sides of the equation to maintain balance. Forgetting this can result in an imbalanced equation and incorrect solutions.
  • Making calculation errors Simple arithmetic mistakes, such as addition, subtraction, multiplication, or division errors, can occur during the solution process. Checking calculations is essential to avoid errors that may propagate through the steps.
  • Ignoring fractions or misapplying operations When fractions are involved, students may forget to multiply or divide by the common denominator to eliminate them. Misapplying operations on fractions can lead to incorrect solutions or complications in the final answer.

Related math equations lessons

  • Math equations
  • Rearranging equations
  • How to find the equation of a line
  • Solve equations with fractions
  • Linear equations
  • Writing linear equations
  • Substitution
  • Identity math
  • One step equation

Practice solving equations questions

1. Solve 4x-2=14.

GCSE Quiz False

Add 2 to both sides.

Divide both sides by 4.

2. Solve 3x-8=x+6.

Add 8 to both sides.

Subtract x from both sides.

Divide both sides by 2.

3. Solve 3(x+3)=2(x-2).

Expanding the parentheses.

Subtract 9 from both sides.

Subtract 2x from both sides.

4. Solve \cfrac{2 x+2}{3}=\cfrac{x-3}{2}.

Multiply by 6 (the lowest common denominator) and simplify.

Expand the parentheses.

Subtract 4 from both sides.

Subtract 3x from both sides.

5. Solve \cfrac{3 x^{2}}{2}=24.

Multiply both sides by 2.

Divide both sides by 3.

Square root both sides.

6. Solve by factoring:

Use factoring to find simpler equations.

Set each set of parentheses equal to zero and solve.

x=3 or x=10

Solving equations FAQs

The first step in solving a simple linear equation is to simplify both sides by combining like terms. This involves adding or subtracting terms to isolate the variable on one side of the equation.

Performing the same operation on both sides of the equation maintains the equality. This ensures that any change made to one side is also made to the other, keeping the equation balanced and preserving the solutions.

To handle variables on both sides of the equation, start by combining like terms on each side. Then, move all terms involving the variable to one side by adding or subtracting, and simplify to isolate the variable. Finally, perform any necessary operations to solve for the variable.

To deal with fractions in an equation, aim to eliminate them by multiplying both sides of the equation by the least common denominator. This helps simplify the equation and make it easier to isolate the variable. Afterward, proceed with the regular steps of solving the equation.

The next lessons are

  • Inequalities
  • Types of graph
  • Coordinate plane

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    Hello and welcome to Grade 6 Math word problems worksheets and answers, where your 6 th Grade students will learn to love and solve math problems and activities at all times.

  15. Grade 6 Addition and Subtraction of Fractions Worksheets

    These grade 6 fractions worksheets focus on adding and subtracting fractions and mixed numbers with unlike denominators. All worksheets are pdf files and answer keys follow the questions on a separate page. Sample Grade 6 Fraction Addition Worksheet More fractions worksheets

  16. Grade 6 Fraction Word Problems Worksheets

    Grade 6 Fraction Word Problems - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Fraction word problems, Mathlinks grade 6 student packet 6 fraction addition and, Fun food word problems starring fractions, Math measurement word problems no problem, Cooking with fractions word problems, Word ...

  17. 6th Grade Fractions

    6th Grade FractionsWorksheets, Lessons, and Printables. Number Theory. Divisibility: circle all of the numbers that are divisible by the number. Divisibility: complete the table. Prime or composite. Use the clue to fill in the missing digit. Circle all of the numbers that are multiples of a number.

  18. 6th Grade Word Problems With Fractions And Decimal

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  19. Word Problems Involving Fractions Grade 6

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  20. Grade 6 Math Worksheet: Proportions word problems

    Below are grade 6 math worksheets with proportions word problems. Worksheet #1 Worksheet #2 Worksheet #3 Similar: Proportions word problems - using decimals Ratio word problems What is K5? K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5.

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  22. Solving Equations

    Worksheets; Topic Guides; School and District Leader Guides; ... to check your grade 6 to 8 students' understanding of math equations. 10+ questions with answers covering a range of 6th, 7th and 8th grade math equations topics to identify areas of strength and support! ... For example, word problems about tickets for sports games, cell phone ...

  23. Division Word Problems Grade 6

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