fraction problem solving questions grade 6

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.

6th Grade Fractions Worksheets

6th grade fractions worksheets are used to give students a better idea of the kind of problems that can be framed on the topic. These 6th grade math worksheets consist of questions on applying arithmetic operators to different types of fractions, word problems, converting fractions, and identifying different types of fractions.

Benefits of 6th Grade Math Worksheets Fractions

There are several topics associated with fractions such as ratios and proportions, percentages, etc. If students have clear concept of fractions, they can solve problems based on other topics easily. 6th grade fractions worksheets help kids in achieving their goal of mastering the topic of fractions by providing several practice sums. The answer keys included with the worksheets detail the step-by-step solution to all problems, enabling students to check their answers.

☛ Practice : Grade 6 Interactive Fractions Worksheets

Printable PDFs for Grade 6 Fractions Worksheets

6th Grade fractions math worksheets are free to download, interactive, easy to use, and are available in PDF format.

• Fractions Math Worksheet for Grade 6
• 6th Grade Fraction Math Worksheet
• Fractions Math Worksheet for 6th Grade
• Fractions Worksheet Grade 6

Interactive 6th Grade Fractions Worksheets

• Grade 6 Types of Fractions Worksheet
• Equivalent Fractions Worksheet for Grade 6
• Grade 6 Multiplication of Fractions by Fractions Worksheet
• Multiplication of Fractions by Whole Numbers 6th Grade Worksheet
• A Recap to Fractions Worksheet for Grade 6

Explore more topics at Cuemath's Math Worksheets .

Free Mathematics Tutorials

Solutions to Fractions and Mixed Numbers Questions - Grade 6

Detailed solutions and full explanations to grade 6 fractions and mixed numbers questions are presented.

Detailed Solutions

• 3 1/2 + 5 1/2 = Solution Add whole numbers together and fractions together 3 1/2 + 5 1/2 = (3 + 5) + (1/2 + 1/2) = 8 + 2/2 = 8 + 1 = 9
• 1/2 + 1/14 = Write to the same denominator before you add fractions 1/2 + 1/14 = 7 / 14 + 1 / 14 , common denominator 14 = 8 / 14 , add numerators = 4 / 7 , divide numerator and denominator by 2 to reduce fraction
• 1/3 - 1/12 = Solution Rewrite to the same denominator before you subtract fractions 1 / 3 - 1 / 12 = 4 / 12 - 1 / 12 , common denominator = 3 / 12 , subtract numerator = 1 / 4 , divide numerator and denominator to reduce fraction
• one half is the same as? Solution one half is written as 1 / 2 two quarters is written as 2 / 4 = 1 / 2 , divide numerator and denominator to reduce fraction Hence one half is the same as two quarters.
• 1/2 and 2/4
• 4/3 and 8/6
• 1/5 and 3/15
• 2/3 and 8/9
• 5 2/3 + 5 1/2 = Solution Add whole numbers together and fractions together 5 2/3 + 5 1/2 = (5 + 5) + (2 / 3 + 1 / 2) = 10 + (4 / 6 + 3 / 6) , common denominator for fractions = 10 + 7/6 = 10 + 6/6 + 1/6 , write 7/6 as 6/ + 1/6 = 10 + 1 + 1/6 = 11 1/6 , simplify
• Order from least to greatest: 8/9 , 17/18 , 2/3 , 7/6 . Solution It is easier to campare fractions with the same denominator and so we first write all given fractions to the same denominator 18 8 / 9 = 16 / 18 17 / 18 = 17 / 18 2 / 3 = 12 / 18 7 / 6 = 21 / 18 We now order the fractions from least to greatest 2 / 3 , 8 / 9 , 17 / 18 , 7 / 6
• 5/2 ÷ 2/5 = Solution 5 / 2 ÷ 2 / 5 = 5 / 2 × 5 / 2 = 25 / 4 = 24 / 4 + 1 / 4 = 6 1/4
• 5 ÷ 1/5 = Solution 5 ÷ 1 / 5 = 5 × 5 / 1 = 25
• 2/5 × 7/8 = Solution 2 / 5 × 7 / 8 = (2 × 7) / (5 × 8) = (1 × 7) / (5 × 4) , simplify = 7 / 20
• Write the mixed number 7 7/8 as a fraction. Solution 7 7/8 = 7 × 8 / 8 + 7 / 8 = (7 × 8 + 7) / 8 = 63 / 8
• Write the fraction 31/8 as a mixed number. Solution 31 / 8 = (24 + 7) / 8 = 3 7/8
• 3 × 1/4 = Solution 3 × 1 / 4 = 3 / 1 × 1 / 4 = (3 × 1) / (4 × 1) = 3 / 4
• 3 1/4 ÷ 5 1/3 = Solution Change the mixed numbers 3 1/4 and 5 1/3 to fractions and then divide. 3 1/4 = 13 / 4 5 1/3 = 16 / 3 hence 3 1/4 ÷ 5 1/3 = 13 / 4 ÷ 16 / 3 = 13 / 4 × 3 / 16 = 39 / 64
• 4 2/7 × 5 3/5 = Solution Change the mixed numbers 4 2/7 and 5 3/5 to fractions and then multiply. 4 2/7 = 30 / 7 5 3/5 = 28 / 5 hence 4 2/7 × 5 3/5 = 30 / 7 × 28 / 5 = (30 × 28) / (7 × 5) = 24
• To have F + 2 5/7 = 4 , F must be equal to Solution In order to have F + 2 5/7 = 4, F must be equal to F = 4 - 2 5/7 = 2 - 5/7 = 14 / 7 - 5 / 7 = 9 / 7 = 1 2/7
• Tom runs 3/4 of an hour every Monday, 30 minutes every Tuesday, half an hour every Wednesday, 1 1/4 hours every Thursday and 2/3 of an hour on Friday. How many hours does Tom run from Monday to Friday? Solution Find the time in minutes for each day. Monday: 3 / 4 of an hour = (3 / 4) × 60 = 180 / 4 = 45 minutes Tuesday: 30 minutes Wednesday: half an hour = (1 / 2) × 60 = 30 minutes Thursday: 1 1/4 hours = 1 hour + (1 / 4) of an hour = 60 + 60 / 4 = 75 minutes Friday: 2 / 3 of an hour = (2 / 3) × 60 = 40 minutes Add the times for all 5 days. 45 + 30 + 30 + 75 + 40 = 220 minutes = (180 + 40) minutes = 3 hours and 40 minutes
• Order from least to greatest: 5 3/4 , 3 4/5 , 3 1/5 , 4 5/6 . Solution The mixed number with the smallest whole number is the smallest. Hence 3 1/5 is the smallest and 3 4/5 is the second smallest. The next largest is 4 5/6 and the largest is 5 3/4. Hence the order from least to greatest is given by 3 1/5 , 3 4/5 , 4 5/6 , 5 3/4
• Order from least to greatest: 7 2/3 , 7 3/5 , 7 3/4 , 7 6/11 . Solution The given mixed numbers all have the same whole number and the fractional parts are not easy to compare either. The best way to compare these mixed numbers is to compare their fractional parts and to compare their fractional parts we need to write them to the lowest common denominator 660. 2 / 3 = 440 / 660 3 / 5 = 369 / 660 3 / 4 = 495 / 660 6 / 11 = 360 / 660 It is easier to compare fractions with common denominator. Hence the order from least to greatest of the given mixed numbers is 7 6/11 , 7 3/5 , 7 2/3 , 7 3/4
• What fraction of 1 hour is 50 minutes? Solution A fraction is a part of a whole. 50 minutes = (50 / 60) × 60 = 50 / 60 of one hour = 5 / 6 of one hour. Hence 50 minutes is 5 / 6 of an hour.
• 1/3 is 1/8 of what number? Solution Let the number be n. Rewrite the given question in mathematical terms 1 / 3 = 1 / 8 of n 1 / 3 = (1 / 8) × n 1 / 3 = n / 8 The above may be written with fractions having common denominator. (1 × 8) / (3 × 8) = (n × 3) / (8 × 3) 8 / 24 = 3 n / 24 The above fractions have common denominator and they are equal if the numerators are equal. Hence 8 = 3 (8 / 3) = 3 n , hence n = 8 / 3

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Fractions Problems

Sixth grade fractions problems.

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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

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

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

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

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

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

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.

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» Ratio Word Problems

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Grade 6 Fraction Word Problems

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 problem practice workbook, Fraction word problems grade 5 math, Word grade 6 word problems.

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• 6th Grade Math
• Solving word problems

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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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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• RD Sharma Solutions
• Chapter 6 Fractions

RD Sharma Solutions for Class 6 Maths Chapter 6: Fractions

For the students of Class 6, RD Sharma Solutions are valuable resources for the exam. While solving the RD Sharma textbook, students can make use of the PDF as reference material to get their doubts cleared immediately. The expert faculty creates answers with pictorial representation in order to make the concepts easier for students.

Subject experts prepare accurate solutions based on the exam pattern followed by the current CBSE board. The students can use the solutions PDF to solve exercise-wise problems and analyse areas of improvement. RD Sharma Solutions for Class 6   Maths Chapter 6 Fractions are provided here.

• RD Sharma Solutions Class 6 Maths Chapter 1 Knowing Our Numbers
• RD Sharma Solutions Class 6 Maths Chapter 2 Playing with Numbers
• RD Sharma Solutions Class 6 Maths Chapter 3 Whole Numbers
• RD Sharma Solutions Class 6 Maths Chapter 4 Operations on Whole Numbers
• RD Sharma Solutions Class 6 Maths Chapter 5 Negative Numbers and Integers
• RD Sharma Solutions Class 6 Maths Chapter 6 Fractions
• RD Sharma Solutions Class 6 Maths Chapter 7 Decimals
• RD Sharma Solutions Class 6 Maths Chapter 8 Introduction to Algebra
• RD Sharma Solutions Class 6 Maths Chapter 9 Ratio, Proportion and Unitary Method
• RD Sharma Solutions Class 6 Maths Chapter 10 Basic Geometrical Concepts
• RD Sharma Solutions Class 6 Maths Chapter 11 Angles
• RD Sharma Solutions Class 6 Maths Chapter 12 Triangles
• RD Sharma Solutions Class 6 Maths Chapter 13 Quadrilaterals
• RD Sharma Solutions Class 6 Maths Chapter 14 Circles
• RD Sharma Solutions Class 6 Maths Chapter 15 Pair of Lines and Transversal
• RD Sharma Solutions Class 6 Maths Chapter 16 Understanding Three-Dimensional Shapes
• RD Sharma Solutions Class 6 Maths Chapter 17 Symmetry
• RD Sharma Solutions Class 6 Maths Chapter 18 Basic Geometrical Tools
• RD Sharma Solutions Class 6 Maths Chapter 19 Geometrical Constructions
• RD Sharma Solutions Class 6 Maths Chapter 20 Mensuration
• RD Sharma Solutions Class 6 Maths Chapter 21 Data Handling – I (Presentation of Data)
• RD Sharma Solutions Class 6 Maths Chapter 22 Data Handling – II (Pictographs)
• RD Sharma Solutions Class 6 Maths Chapter 23 Data Handling – III (Bar Graphs)
• Exercise 6.1 Chapter 6 Fractions
• Exercise 6.2 Chapter 6 Fractions
• Exercise 6.3 Chapter 6 Fractions
• Exercise 6.4 Chapter 6 Fractions
• Exercise 6.5 Chapter 6 Fractions
• Exercise 6.6 Chapter 6 Fractions
• Exercise 6.7 Chapter 6 Fractions
• Exercise 6.8 Chapter 6 Fractions
• Exercise 6.9 Chapter 6 Fractions
• Objective Type Questions Chapter 6 Fractions

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Access answers to Maths RD Sharma Solutions for Class 6 Chapter 6 Fractions

Exercise 6.1 page: 6.4.

1. Write the fraction representing the shaded portion:

We know that

Fraction of the shaded portion = Number of shaded parts/ Total number of parts

(i) From the figure we know that

Total number of parts = 3

Number of parts which are shaded = 2

Fraction of the shaded portion = 2/3

(ii) From the figure we know that

Total number of parts = 15

Number of parts which are shaded = 11

Fraction of the shaded portion = 11/15

(iii) From the figure we know that

Total number of parts = 9

Number of parts which are shaded = 8

Fraction of the shaded portion = 8/9

(iv) From the figure we know that

Total number of parts = 7

Number of parts which are shaded = 3

Fraction of the shaded portion = 3/7

(v) From the figure we know that

Number of parts which are shaded = 4

Fraction of the shaded portion = 4/9

(vi) From the figure we know that

Total number of parts = 4

Fraction of the shaded portion = 2/4 = 1/2

(vii) From the figure we know that

Total number of parts = 2

Number of parts which are shaded = 1

Fraction of the shaded portion = 1/2

(viii) From the figure we know that

Total number of parts = 5

Fraction of the shaded portion = 1/5

(ix) From the figure we know that

Fraction of the shaded portion = 1/4

2. Write the fraction representing the shaded parts:

Fraction of the shaded portion = 3/9 = 1/3

Total number of parts = 8

Fraction of the shaded portion = 4/8 = 1/2

Total number of parts = 12

Fraction of the shaded portion = 3/12 = 1/4

Total number of parts = 10

Number of parts which are shaded = 5

Fraction of the shaded portion = 5/10 = 1/2

3. Write the fraction representing the shaded portion:

Fraction of the shaded portion = 4/8

4. Colour the part according to the fraction given:

5. What fraction of an hour is 20 minutes?

Minutes in an hour = 60

So 20 minutes of an hour = 20/ 60 = 1/3

Therefore, 1/3 of an hour is 20 minutes.

6. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

We know that natural numbers from 2 to 12 are

2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12

The prime numbers from 2 to 12 are

2, 3, 5, 7 and 11

So 5 numbers are prime among the 11 numbers

Therefore, 5/11 of them are prime numbers.

7. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

We know that the natural numbers from 102 to 113 are

102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 and 113

The prime numbers from 102 to 113 are

103, 107, 109 and 113

So 4 numbers are prime among the 12 numbers

We get the fraction of prime numbers = 4/ 12 = 1/3

Therefore, 1/3 fraction of them are prime numbers.

8. Mukesh has a box of 24 pencils. He gives half of them to Sunita. How many does Sunita get? How many does Mukesh still have?

Number of pencils Mukesh has = 24

He gives half of them to Sunita = 24/ 2 = 12

So the number of pencils Mukesh still has = 24 – 12 = 12

Therefore, Mukesh gives 12 pencils to Sunita and still has 12 pencils.

9. Kavita has 44 cassettes. She gives ¾ of them to Sonia. How many does Sonia get? How many does Kavita keep?

Number of cassettes Kavita has = 44

She gives ¾ of them to Sonia = ¾ (44) = 33

So the number of cassettes Kavita keeps = 44 – 33 = 11

Therefore, Kavita gives 33 cassettes to Sonia and still keeps 11 cassettes.

10. Shikhas has three frocks that she wears when playing. The material is good, but the colours are faded. Her mother buys some blue dye and uses it on two of the frocks. What fraction of all of the Shikha play frocks did her mother dye?

Number of frocks = 3

Number of frocks Shikha’s mother dyed = 2

So the fraction of dyed frocks = 2/3

Hence, Shikha’s mother dyed 2/3 fraction of all of Shika’s play frocks.

Exercise 6.2 page: 6.7

1. Represent 2/5 on a number line.

The fraction 2/5 is represented on a number line as given below:

2. Represent 0/10, 1/10, 5/10 and 10/10 on a number line.

The fraction 0/10, 1/10, 5/10 and 10/10 are represented on a number line as given below:

3. Represent 2/7, 5/7 and 6/7 on a number line.

The fraction 2/7, 5/7 and 6/7 are represented on a number line as given below:

4. How many fractions lie between 0 and 1.

Infinite number of fractions lie between 0 and 1

This can be done by taking numerator less than denominator in a fraction.

5. Represent 0/8 and 8/8 on a number line.

The fraction 0/8 and 8/8 are represented on a number line as given below:

Exercise 6.3 page: 6.8

1. Write each of the following divisions as fractions:

(i) 6 ÷ 3

(ii) 25 ÷ 5

(iii) 125 ÷ 50

(iv) 55 ÷ 11

(i) The division 6 ÷ 3 can be written as 6/3.

(ii) The division 25 ÷ 5 can be written as 25/5.

(iii) The division 125 ÷ 50 can be written as 125/50.

(iv) The division 55 ÷ 11 can be written as 55/11.

2. Write each of the following fractions as divisions:

(iii) 90/63

(i) The fraction 9/7 can be written as 9 ÷ 7.

(ii) The fraction 3/11 can be written as 3 ÷ 11.

(iii) The fraction 90/63 can be written as 90 ÷ 63.

(iv) The fraction 1/5 can be written as 1 ÷ 5.

Exercise 6.4 page: 6.11

1. Convert each of the following into a mixed fraction:

(ii) 226/15

(iii) 145/9

(i) 28/9 can be written as a mixed fraction as 3 1/9.

(ii) 226/15 can be written as a mixed fraction as 15 1/15.

(iii) 145/9 can be written as a mixed fraction as 16 1/9.

(iv) 128/5 can be written as a mixed fraction as 25 3/5.

2. Convert each of the following into an improper fraction:

(i) 7 ¼

(iii) 5 3/10

(iv) 12 7/15

(i) 7 ¼ can be written as an improper fraction as 29/4.

(ii) 8 5/7 can be written as an improper fraction as 61/7.

(iii) 5 3/10 can be written as an improper fraction as 53/10.

(iv) 12 7/15 can be written as an improper fraction as 187/15.

Exercise 6.5 page: 6.15

1. Write the fractions and check whether they are equivalent or not:

(i) We know that

Fraction = ½

Fraction = 2/4 = 1/2

Fraction = 3/6 = ½

Fraction = 4/8 = ½

Hence, they are equivalent.

(ii) We know that

Fraction = 5/15 = 1/3

Fraction = 3/9 = 1/3

Fraction = 2/6 = 1/3

Fraction = 1/3

2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II.

3. Replace ☐ in each of the following by the correct number:

(i) 2/7 = 6/ ☐

(ii) 5/8 = 10/☐

(iii) 4/5 = ☐/20

(iv) 45/60 = 15/ ☐

(v) 18/24 = ☐/4

(i) 2/7 = 6/21

(ii) 5/8 = 10/16

(iii) 4/5 = 16/20

(iv) 45/60 = 15/20

(v) 18/24 =3/4

4. Find the equivalent fraction of 3/5, having:

(i) numerator 9

(ii) denominator 30

(iii) numerator 21

(iv) denominator 40

(i) The given fraction = 3/5

By considering numerator = 9

We know that 3 × 3 = 9

Multiply the numerator and denominator of the fraction by 3

3/5 × 3/3 = 9/15

(ii) The given fraction = 3/5

By considering denominator = 30

We know that 5 × 6 = 30

Multiply the numerator and denominator of the fraction by 6

3/5 × 6/6 = 18/30

(iii) The given fraction = 3/5

By considering numerator = 21

We know that 3 × 7 = 21

Multiply the numerator and denominator of the fraction by 7

3/5 × 7/7 = 21/35

(iv) The given fraction = 3/5

By considering denominator = 40

We know that 5 × 8 = 40

Multiply the numerator and denominator of the fraction by 8

3/5 × 8/8 = 24/40

5. Find the fraction equivalent to 45/60, having:

(i) numerator 15

(ii) denominator 4

(iii) denominator 240

(iv) numerator 135

(i) The given fraction = 45/60

By considering numerator = 15

We know that 45 ÷ 3 = 15

Dividing the numerator and denominator of the fraction by 3

45/60 ÷ 3/3 = 15/20

(ii) The given fraction = 45/60

By considering denominator = 4

We know that 60 ÷ 15 = 4

Dividing the numerator and denominator of the fraction by 15

45/60 ÷ 15/15 = 3/4

(iii) The given fraction = 45/60

By considering denominator = 240

We know that 60 × 4 = 240

Multiply the numerator and denominator of the fraction by 4

45/60 × 4/4 = 180/240

(iv) The given fraction = 45/60

By considering numerator = 135

We know that 45 × 3 = 135

45/60 × 3/3 = 135/180

6. Find the fraction equivalent of 35/42, having:

(ii) denominator 18

(iii) denominator 30

(iv) numerator 30

The given fraction = 35/42

In order to reduce the fraction, divide the numerator and denominator by the HCF of 35 and 42

35/42 ÷ 7/7 = 5/6

(i) So the fraction = 5/6

We know that 5 × 3 = 15

5/6 × 3/3 = 15/18

(ii) So the fraction = 5/6

By considering denominator = 18

We know that 6 × 3 = 18

(iii) So the fraction = 5/6

We know that 6 × 5 = 30

Multiply the numerator and denominator of the fraction by 5

5/6 × 5/5 = 25/30

(iv) So the fraction = 5/6

By considering numerator = 30

5/6 × 6/6 = 30/36

7. Check whether the given fractions are equivalent:

(i) 5/9, 30/54

(ii) 2/7, 16/42

(iii) 7/13, 5/11

(iv) 4/11, 32/88

(v) 3/10, 12/50

(vi) 9/27, 25/75

5/9 × 6/6 = 30/54

Therefore, 5/9 is equivalent to 30/54.

2/7 × 8/8 = 16/56

Therefore, 2/7 is not equivalent to 16/42.

(iii) We know that

7/13 × 5/5 = 35/65

The same way

5/11 × 7/7 = 35/77

Therefore, 7/13 is not equivalent to 5/11.

(iv) We know that

4/11 × 8/8 = 32/88

Therefore, 4/11 is equivalent to 32/88.

(v) We know that

3/10 × 4/4 = 12/40

Therefore, 3/10 is not equivalent to 12/50.

(vi) We know that

9/27 = 1/3 and 25/75 = 1/3

Therefore, 9/27 is equivalent to 25/75.

8. Match the equivalent fractions and write another 2 for each:

(i) 250/400 (a) 2/3

(ii) 180/200 (b) 2/5

(iii) 660/990 (c) ½

(iv) 180/360 (d) 5/8

(v) 220/550 (e) 9/10

(i) 250/400

By dividing numerator and denominator by HCF of 250 and 400

= (250/50)/ (400/ 50) = 5/8

So the match is (d)

(ii) 180/200

By dividing numerator and denominator by HCF of 180 and 200

= (180/20)/ (200/20) = 9/10

So the match is (e)

(iii) 660/990

By dividing numerator and denominator by HCF of 660 and 990

= (660/90)/ (990/90) = 2/3

So the match is (a)

(iv) 180/360

By dividing numerator and denominator by HCF of 180 and 360

= (180/180)/ (360/180) = ½

So the match is (c)

(v) 220/550

By dividing numerator and denominator by HCF of 220 and 550

= (220/11)/ (550/11) = 2/5

So the match is (b)

9. Write some equivalent fractions which contain all digits from 1 to 9 once only.

The equivalent fractions which contain all digits from 1 to 9 once only are

2/6 = 3/9 = 58/174, 2/4 = 3/6 = 79/158

10. Ravish had 20 pencils, Shikha had 50 pencils and Priya had 80 pencils. After 4 months, Ravish used up 10 pencils, Shikha used up 25 pencils and Priya used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of their pencils?

Number of pencils Ravish had = 20

Number of pencils Ravish used = 10

By dividing the numerator and denominator by HCF of 10 and 20

We get the fraction of pencils used = (10 ÷ 10)/ (20 ÷ 10) = 1/2

Number of pencils Shikha had = 50

Number of pencils used by Shikha = 25

By dividing the numerator and denominator by HCF of 25 and 50

We get the fraction of pencils used = (25 ÷ 25)/ (50 ÷ 25) = 1/2

Number of pencils Priya had = 80

Number of pencils used by Priya = 40

By dividing the numerator and denominator by HCF of 40 and 80

We get the fraction of pencils used = (40 ÷ 40)/ (80 ÷ 40) = 1/2

Yes, each has used up an equal fraction of their pencils.

Exercise 6.6 PAGE: 6.19

Reduce each of the following fractions to its lowest term (simplest form):

1. (i) 40/75

(iii) 12/52

Factors of 40 are

1, 2, 4, 5, 8, 10, 20 and 40

Factors of 75 are

1, 3, 5, 15 and 75

So the common factors are 1 and 5

We get HCF = 5

By dividing numerator and denominator by 5

40/75 ÷ 5/5 = 8/15

Hence, the simplest form of 40/75 is 8/15.

Factors of 42 are

1, 2, 3, 6, 7, 14, 21 and 42

Factors of 28 are

1, 2, 4, 7, 14 and 28

So the common factors are 1, 2 and 14

We get HCF = 14

By dividing numerator and denominator by 14

42/28 ÷ 14/14 = 3/2

Hence, the simplest form of 42/28 is 3/2.

Factors of 12 are

1, 2, 3, 4, 6 and 12

Factors of 52 are

1, 2, 4, 13, 26 and 52

So the common factors are 1, 2 and 4

We get HCF = 4

By dividing numerator and denominator by 4

12/52 ÷ 4/4 = 3/13

Hence, the simplest form of 12/52 is 3/13.

Factors of 72 are

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

So the common factors are 1, 2, 4 and 8

We get HCF = 8

By dividing numerator and denominator by 8

40/72 ÷ 8/8 = 5/9

Hence, the simplest form of 40/72 is 5/9.

Factors of 80 are

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

Factors of 24 are

1, 2, 3, 4, 6, 8, 12 and 24

80/24 ÷ 8/8 = 10/3

Hence, the simplest form of 80/24 is 10/3.

Factors of 84 are

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84

Factors of 56 are

1, 2, 4, 7, 8, 14, 28 and 56

So the common factors are 1, 2, 4, 7, 14 and 28

We get HCF = 28

By dividing numerator and denominator by 28

84/56 ÷ 28/28 = 3/2

Hence, the simplest form of 84/56 is 3/2.

2. Simplify each of the following to its lowest term:

(iii) 84/98

(vi) 162/108

1, 3, 5, 15, 25 and 75

1, 2, 4, 5, 8, 10, 12, 16, 20, 40 and 80

75/80 ÷ 5/5 = 15/16

Hence, the simplest form of 75/80 is 15/16.

Factors of 76 are

1, 2, 4, 19, 38 and 76

52/76 ÷ 4/4 = 13/19

Hence, the simplest form of 52/76 is 13/19.

Factors of 98 are

1, 2, 7, 14, 49 and 98

So the common factors are 1, 2, 7 and 14

84/98 ÷ 14/14 = 6/7

Hence, the simplest form of 84/98 is 6/7.

Factors of 68 are

1, 2, 4, 17, 34 and 68

Factors of 17 are

So the common factors are 1 and 17

We get HCF = 17

By dividing numerator and denominator by 17

68/17 ÷ 17/17 = 4/1

Hence, the simplest form of 68/17 is 4/1.

Factors of 150 are

1, 2, 3, 5, 6, 10, 15, 25, 50 and 150

Factors of 50 are

1, 2, 5, 10, 25 and 50

So the common factors are 1, 2, 5, 10, 25 and 50

We get HCF = 50

By dividing numerator and denominator by 50

150/50 ÷ 50/50 = 3/1

Hence, the simplest form of 150/50 is 3/1.

Factors of 162 are

1, 2, 3, 6, 9, 18, 27, 54, 81 and 162

Factors of 108 are

1, 2, 3, 4, 6, 9, 12, 18, 27 and 54

So the common factors are 1, 2, 3, 6, 9, 18, 27 and 54

We get HCF = 54

By dividing numerator and denominator by 54

162/108 ÷ 54/54 = 3/2

Hence, the simplest form of 162/108 is 3/2.

Exercise 6.7 page: 6.24

1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions:

2. Mark 2/6, 4/6, 8/6 and 6/6 on the number line and put appropriate signs between fractions given below:

(i) 5/6 …….. 2/6

(ii) 3/6 ……. 0/6

(iii) 1/6 …… 6/6

(iv) 8/6 …… 5/6

5/6 > 2/6 as 5 > 2 and the denominator is same.

3/6 > 0/6 as 3 > 0 and the denominator is same.

1/6 < 6/6 as 6 > 1 and the denominator is same.

8/6 > 5/6 as 8 > 5 and the denominator is same.

3. Compare the following fractions and put an appropriate sign:

(i) 3/6 …… 5/6

(ii) 4/5 …… 0/5

(iii) 3/20 …… 4/20

(iv) 1/7 ……. 1/4

3/6 < 5/6 as 3 < 5 and the denominator is same.

4/5 > 0/5 as 4 > 0 and the denominator is same.

3/20 < 4/20 as 3 < 4 and the denominator is same.

1/7 < 1/4 as 7 > 4 and the fraction having smaller denominator is larger.

4. Compare the following fractions using the symbol > or <:

(i) 6/7 and 6/11

(ii) 3/7 and 5/7

(iii) 2/3 and 8/12

(iv) 1/5 and 4/15

(v) 8/3 and 8/13

(vi) 4/9 and 15/8

6/7 > 6/11 as the fraction having smaller denominator is larger.

3/7 < 5/7 as 3 < 5 and the denominator is same.

8/12 = (2 × 2 × 2)/ (2 × 2 × 3) = 2/3

Hence, 2/3 = 8/12

1/5 = (1/ 5) × (3/3) = 3/15 which is lesser than 4/15

Hence, 1/5 < 4/15

8/3 > 8/13 as the fraction having smaller value of denominator is larger.

4/9 = (4/9) × (8/8) = 32/72

15/8 = (15/8) × (9/9) = 135/72

So we get 32/72 < 135/72

Hence, 4/9 < 15/8.

5. The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form:

(iv) 16/100

(vii) 12/60

(viii) 16/96

We know that HCF of 2 and 12 = 2

By dividing numerator and denominator by HCF of 2 and 12

2/12 ÷ 2/2 = 1/6

We know that HCF of 3 and 15 = 3

By dividing numerator and denominator by HCF of 3 and 15

3/15 ÷ 3/3 = 1/5

We know that HCF of 8 and 50 = 2

By dividing numerator and denominator by HCF of 8 and 50

8/50 ÷ 2/2 = 4/25

We know that HCF of 16 and 100 = 4

By dividing numerator and denominator by HCF of 16 and 100

16/100 ÷ 4/4 = 4/25

We know that HCF of 10 and 60 = 10

By dividing numerator and denominator by HCF of 10 and 60

10/60 ÷ 10/10 = 1/6

We know that HCF of 15 and 75 = 15

By dividing numerator and denominator by HCF of 15 and 75

15/75 ÷ 15/15 = 1/5

We know that HCF of 2 and 12 = 12

12/60 ÷ 12/12 = 1/5

We know that HCF of 16 and 96 = 16

By dividing numerator and denominator by HCF of 16 and 96

16/96 ÷ 16/16 = 1/6

We know that HCF of 12 and 75 = 3

By dividing numerator and denominator by HCF of 12 and 75

12/75 ÷ 3/3 = 4/25

We know that HCF of 12 and 72 = 12

By dividing numerator and denominator by HCF of 12 and 72

12/72 ÷ 12/12 = 1/6

We know that HCF of 3 and 18 = 3

By dividing numerator and denominator by HCF of 3 and 18

3/18 ÷ 3/3 = 1/6

We know that HCF of 4 and 25 = 1

By dividing numerator and denominator by HCF of 4 and 25

4/25 ÷ 1/1 = 4/25

Three groups of equal fractions: 2/12, 10/60, 16/96, 12/72, 3/18, 3/15, 15/75, 12/60, 8/50, 16/100, 12/75, 4/25

6. Isha read 25 pages of a book containing 100 pages. Nagma read ½ of the same book. Who read less?

No. of pages in the book = 100

Fraction of book Isha read = (25/100) ÷ (25/25) = 1/4 by dividing both numerator and denominator by HCF of 25 and 100

So the fraction of book Nagma read = 1/2

By comparing 1/4 and 1/2 we get the LCM of 4 and 2 = 4

Now convert the fraction into equivalent fraction having denominator as 4

1/4 × 1/1 and 1/2 × 2/2

1/4 < ½

Hence, Isha read less.

7. Arrange the following fractions in the ascending order:

(i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9

(ii) 7/8, 7/25, 7/11, 7/18, 7/10

(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41

(iv) 3/5, 1/5, 4/5, 2/5

(v) 2/5, 3/4, 1/2, 3/5

(vi) 3/8, 3/12. 3/6, 3/4

(vii) 4/6, 3/8, 6/12, 5/16

(i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9 can be written in ascending order as

1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9

(ii) 7/8, 7/25, 7/11, 7/18, 7/10 can be written in ascending order as

7/25, 7/18, 7/11, 7/10, 7/8

(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41 can be written in ascending order as

37/1000, 37/100, 37/85, 37/50, 37/47, 37/41

(iv) 3/5, 1/5, 4/5, 2/5 can be written in ascending order as

1/5, 2/5, 3/5, 4/5

(v) 2/5, 3/4, 1/2, 3/5 can be written in ascending order as

2/5, 1/2, 3/5, 3/4

(vi) 3/8, 3/12, 3/6, 3/4 can be written in ascending order as

3/12, 3/8, 3/6, 3/4

(vii) 4/6, 3/8, 6/12, 5/16 can be written in ascending order as

5/16, 3/8, 6/12, 4/6

8. Arrange in descending order in each of the following using the symbol >:

(i) 8/17, 8/9, 8/5, 8/13

(ii) 5/9, 3/12, 1/3, 4/15

(iii) 2/7, 11/35, 9/14, 13/28

(i) 8/17, 8/9, 8/5, 8/13 can be written in the descending order as

8/5 > 8/9 > 8/13 > 8/17

(ii) 5/9, 3/12, 1/3, 4/15 can be written in the descending order as

5/9 > 1/3 > 4/15> 3/12

(iii) 2/7, 11/35, 9/14, 13/28 can be written in the descending order as

9/14 > 13/28 > 11/35 > 2/7

9. Find answers to the following. Write and indicate how you solved them.

(i) Is 5/9 equal to 4/5?

(ii) Is 9/16 equal to 5/9?

(iii) Is 4/5 equal to 16/20?

(iv) Is 1/15 equal to 4/30?

(i) No. We know that 5 × 5 ≠ 9 × 4

(ii) No. We know that 9 × 9 ≠ 16 × 5

(iii) Yes. We know that 4 × 20 = 16 × 5

(iv) No. We know that 1 × 30 ≠ 15 × 4

Exercise 6.8 PAGE: 6.29

1. Write these fractions appropriately as additions or subtractions:

(i) It can be written as

1/5 + 2/5 = 3/5

(ii) It can be written as

3/6 + 2/6 = 5/6

(i) 5/12 + 1/12

(ii) 3/15 + 7/15

(iii) 3/22 + 7/22

(iv) 1/4 + 0/4

(v) 4/13 + 2/13 + 1/13

(vi) 0/15 + 2/15 + 1/15

(vii) 7/31 – 4/31 + 9/31

(viii) 3 2/7 + 1/7 – 2 3/7

(ix) 2 1/3 – 1 2/3 + 4 1/3

(x) 1 – 2/3 + 7/3

(xi) 16/7 – 5/7 + 9/7

It can be written as

5/ 12 + 1/12 = (5 + 1)/ 12

On further calculation

5/ 12 + 1/12 = 6/12 = 1/2

3/15 + 7/15 = (3 + 7)/ 15

3/15 + 7/15 = 10/15 = 2/3

3/22 + 7/22 = (3 + 7)/ 22

3/22 + 7/22 = 10/22 = 5/11

1/4 + 0/4 = (1 + 0)/4

1/4 + 0/4 = ¼

4/13 + 2/13 + 1/13 = (4 + 2 + 1)/ 13

4/13 + 2/13 + 1/13 = 7/13

0/15 + 2/15 + 1/15 = (0 + 2 + 1)/ 15

0/15 + 2/15 + 1/15 = 3/15 = 1/5

7/31 – 4/31 + 9/31 = (7 – 4 + 9)/ 31

7/31 – 4/31 + 9/31 = 12/31

3 2/7 + 1/7 – 2 3/7 = (23 + 1 – 17)/ 7

3 2/7 + 1/7 – 2 3/7 = 7/7 = 1

2 1/3 – 1 2/3 + 4 1/3 = (7 – 5 + 13)/ 3

2 1/3 – 1 2/3 + 4 1/3 = 15/3 = 5

1 – 2/3 + 7/3 = (3 – 2 + 7)/3

1 – 2/3 + 7/3 = 8/3

16/7 – 5/7 + 9/7 = (16 – 5 + 9)/ 7

16/7 – 5/7 + 9/7 = 20/7

3. Shikha painted 1/5 of the wall space in her room. Her brother Ravish helped and painted 3/5 of the wall space. How much did they paint together? How much the room is left unpainted?

Fraction of wall space painted by Shikha = 1/5

Fraction of wall space painted by Ravish = 3/5

So the wall space painted by both = 1/5 + 3/5

We get the unpainted space = (5 – 4)/ 5 = 1/5

Therefore, Shikha and Ravish painted 4/5 of the wall space together and the room space left unpainted is 1/5.

4. Ramesh bought 2 ½ kg sugar whereas Rohit bought 3 ½ kg of sugar. Find the total amount of sugar bought by both of them.

Sugar bought by Ramesh = 2 ½ kg

Sugar bought by Ramesh = ((2 × 2) + 1)/ 2 = 5/2 kg

Sugar bought by Rohit = 3 ½ kg

Sugar bought by Rohit = ((2 × 3) + 1)/ 2 = 7/2 kg

So the total sugar bought by both of them = Sugar bought by Ramesh + Sugar bought by Rohit

By substituting the values

Total sugar bought by both of them = 5/2 + 7/2 = 12/2 = 6kg

Therefore, the total amount of sugar bought by both of them is 6kg.

5. The teacher taught 3/5 of the book, Vivek revised 1/5 more on his own. How much does he still have to revise?

Fraction of book teacher taught = 3/5

Fraction of book Vivek revised = 1/5

So the fraction of book Vivek still have to revise = 3/5 – 1/5

= (3 – 1)/ 5

Hence, Vivek still have to revise 2/5 of the book.

6. Amit was given 5/7 of a bucket of oranges. What fraction of oranges was left in the basket?

Fraction of oranges Amit has = 5/7

So the fraction of oranges left in the basket = 1 – 5/7

= (7 – 5)/ 7

Hence, the fraction of oranges left in the basket is 2/7.

7. Fill in the missing fractions:

(i) 7/10 – ☐ = 3/10

(ii) ☐ – 3/21 = 5/21

(iii) ☐ – 3/6 = 3/6

(iv) ☐ – 5/27 = 12/27

7/10 – 3/10 = ☐

(7 – 3)/ 10 = 2/5

☐ = 5/21 + 3/21

(5 + 3)/ 21 = 8/21

☐ = 3/6 + 3/6

(3 + 3)/ 6 = 6/6 = 1

☐ = 12/27 + 5/27

(12 + 5)/ 27 = 17/27

Exercise 6.9 page: 6.35

(i) 3/4 and 5/6

(ii) 7/10 and 2/15

(iii) 8/13 and 2/3

(iv) 4/5 and 7/15

We know that the LCM of 4 and 6 is 12

In order to convert fraction into equivalent fraction having 12 as denominator

= [(3 × 3)/ (4 × 3)] + [(5 × 2)/ (6 × 2)]

= 9/12 + 10/ 12

= (9 + 10)/ 12 = 19/12

7/10 + 2/15

We know that the LCM of 10 and 15 is 30

In order to convert fraction into equivalent fraction having 30 as denominator

= [(7 × 3)/ (10 × 3)] + [(2 × 2)/ (15 × 2)]

= 21/30 + 4/ 30

= (21 + 4)/ 30 = 25/30 = 5/6

We know that the LCM of 13 and 3 is 39

In order to convert fraction into equivalent fraction having 39 as denominator

= [(8 × 3)/ (13 × 3)] + [(2 × 13)/ (3 × 13)]

= 24/39 + 26/39

= (24 + 26)/ 39 = 50/39

We know that the LCM of 5 and 15 is 1

In order to convert fraction into equivalent fraction having 15 as denominator

= [(4 × 3)/ (5 × 3)] + [(7 × 1)/ (15 × 1)]

= 12/15 + 7/ 15

= (12 + 7)/ 15 = 19/15

2. Subtract:

(i) 2/7 from 19/21

(ii) 21/25 from 18/20

(iii) 7/16 from 2

(iv) 4/15 from 2 1/5

19/21 – 2/7

We know that LCM of 21 and 7 is 21

In order to convert fraction into equivalent fraction having 21 as denominator

= [(19 × 1)/ (21 × 1)] – [(2 × 3)/ (7 × 3)]

= 19/21 – 6/21

= (19 – 6)/21 = 13/21

18/20 – 21/25

We know that LCM of 20 and 25 is 100

In order to convert fraction into equivalent fraction having 100 as denominator

= [(18 × 5)/ (20 × 5)] – [(21 × 4)/ (25 × 4)]

= 90/100 – 84/100

= (90 – 84)/100 = 6/100 = 3/50

2/1 – 7/16

We know that LCM of 1 and 16 is 16

In order to convert fraction into equivalent fraction having 16 as denominator

= [(16 × 2)/ (16 × 1)] – [(7 × 1)/ (16 × 1)]

= 32/16 – 7/16

= (32 – 7)/16 = 25/16

11/5 – 4/15

We know that LCM of 5 and 15 is 15

= [(11 × 3)/ (5 × 3)] – [(4 × 1)/ (15 × 1)]

= 33/15 – 4/15

= (33 – 4)/15 = 29/15

3. Find the difference of:

(i) 13/24 and 7/16

(ii) 5/18 and 4/15

(iii) 1/12 and 3/4

(iv) 2/3 and 6/7

13/24 – 7/16

We know that LCM of 24 and 16 is 48

In order to convert fraction into equivalent fraction having 48 as denominator

= [(13 × 2)/ (24 × 2)] – [(7 × 3)/ (16 × 3)]

= 26/48 – 21/48

= (26 – 21)/48 = 5/48

5/18 – 4/15

We know that LCM of 18 and 15 is 90

In order to convert fraction into equivalent fraction having 90 as denominator

= [(5 × 5)/ (18 × 5)] – [(4 × 6)/ (15 × 6)]

= 25/90 – 24/90

= (25 – 24)/90 = 1/90

3/4 – 1/12

We know that LCM of 4 and 12 is 12

= [(3 × 3)/ (4 × 3)] – [(1 × 1)/ (12 × 1)]

= 9/12 – 1/12

= (9 – 1)/12 = 8/12 = 2/3

6/7 – 2/3

We know that LCM of 7 and 3 is 21

= [(6 × 3)/ (7 × 3)] – [(2 × 7)/ (3 × 7)]

= 18/21 – 14/21

= (18 – 14)/21 = 4/21

4. Subtract as indicated:

(i) 8/3 – 5/9

(ii) 4 2/5 – 2 1/5

(iii) 5 6/7 – 2 2/3

(iv) 4 3/4 – 2 1/6

8/3 – 5/9

We know that LCM of 3 and 9 is 9

In order to convert fraction into equivalent fraction having 9 as denominator

= [(8 × 3)/ (3 × 3)] – [(5 × 1)/ (9 × 1)]

= 24/9 – 5/9

= (24 – 5)/9 = 19/9

22/5 – 11/5

= (22 – 11)/5 = 11/5

41/7 – 8/3

= [(41 × 3)/ (7 × 3)] – [(8 × 7)/ (3 × 7)]

= 123/21 – 56/21

= (123 – 56)/21 = 67/21

19/4 – 13/6

We know that LCM of 4 and 6 is 12

= [(19 × 3)/ (4 × 3)] – [(13 × 2)/ (6 × 2)]

= 57/12 – 26/12

= (57 – 26)/12 = 31/12

5. Simplify:

(i) 2/3 + 3/4 + 1/2

(ii) 5/8 + 2/5 + 3/4

(iii) 3/10 + 7/15 + 3/5

(iv) 3/4 + 7/16 + 5/8

(v) 4 2/3 + 3 1/4 + 7 1/2

(vi) 7 1/3 + 3 2/3 + 5 1/6

(vii) 7 + 7/4 + 5 1/6

(viii) 5/6 + 3 + 3/4

(ix) 7/18 + 5/6 + 1 1/12

We know that the LCM of 3, 4 and 2 is 12

= [(2 × 4)/ (3 × 4)] + [(3 × 3)/ (4 × 3)] + [(1 × 6)/ (2 × 6)]

= 8/12+ 9/12 + 6/12

= (8 + 9 + 6)/ 12 = 23/12

We know that the LCM of 8, 5 and 4 is 40

In order to convert fraction into equivalent fraction having 40 as denominator

= [(5 × 5)/ (8 × 5)] + [(2 × 8)/ (5 × 8)] + [(3 × 10)/ (4 × 10)]

= 25/40 + 16/40 + 30/40

= (25 + 16 + 30)/ 40 = 71/40

We know that the LCM of 10, 15 and 5 is 30

= [(3 × 3)/ (10 × 3)] + [(7 × 2)/ (15 × 2)] + [(3 × 6)/ (5 × 6)]

= 9/30+ 14/30 + 18/30

= (9 + 14 + 18)/ 30 = 41/30

We know that the LCM of 4, 16 and 8 is 16

= [(3 × 4)/ (4 × 4)] + [(7 × 1)/ (16 × 1)] + [(5 × 2)/ (8 × 2)]

= 12/16 + 7/16 + 10/16

= (12 + 7 + 10)/ 16 = 29/16

14/3 + 13/4 + 15/2

= [(14 × 4)/ (3 × 4)] + [(13 × 3)/ (4 × 3)] + [(15 × 6)/ (2 × 6)]

= 56/12 + 39/12 + 90/12

= (56 + 39 + 90)/ 12 = 185/12

22/3 + 11/3 + 31/6

We know that the LCM of 3, 3 and 6 is 6

In order to convert fraction into equivalent fraction having 6 as denominator

= [(22 × 2)/ (3 × 2)] + [(11 × 2)/ (3 × 2)] + [(31 × 1)/ (6 × 1)]

= 44/6 + 22/6 + 31/6

= (44 + 22 + 31)/ 6 = 97/6

7/1 + 7/4 + 31/6

We know that the LCM of 1, 4 and 6 is 12

= [(7 × 12)/ (1 × 12)] + [(7 × 3)/ (4 × 3)] + [(31 × 2)/ (6 × 2)]

= 84/12 + 21/12 + 62/12

= (84 + 21 + 62)/12 = 167/12

We know that the LCM of 6, 1 and 4 is 12

= [(5 × 2)/ (6 × 2)] + [(3 × 12)/ (1 × 12)] + [(3 × 3)/ (4 × 3)]

= 10/12 + 36/12 + 9/12

= (10 + 36 + 9)/ 12 = 55/12

7/18 + 5/6 + 13/12

We know that the LCM of 18, 6 and 12 is 36

= [(7 × 2)/ (18 × 2)] + [(5 × 6)/ (6 × 6)] + [(13 × 3)/ (12 × 3)]

= 14/36 + 30/36 + 39/36

= (14 + 30 + 39)/36 = 83/36

6. Replace ☐ by the correct number:

(i) ☐ – 5/8 = 1/4

(ii) ☐ – 1/5 = 1/2

(iii) 1/2 – ☐ = 1/6

☐ = 1/4 + 5/8

☐ = [(1 × 2)/ (4 × 2)] + [(5 × 1)/ (8 × 1)]

☐ = 2/8 + 5/8

By addition

☐= (2 + 5)/ 8 = 7/8

☐ = 1/2 + 1/5

☐ = [(1 × 5)/ (2 × 5)] + [(1 × 2)/ (5 × 2)]

☐ = 5/10 + 2/10

☐ = (2 + 5)/ 10 = 7/10

☐ = 1/2 – 1/6

☐ = [(1 × 3)/ (2 × 3)] – [(1 × 1)/ (6 × 1)]

☐ = 3/6 – 1/6

☐ = (3 – 1)/ 6 = 2/6 = 1/3

7. Savita bought 2/5 m of ribbon and Kavita 3/4 m of the ribbon. What was the total length of the ribbon they bought?

Length of ribbon Savita bought = 2/5 m

Length of ribbon Kavita bought = 3/4 m

So the total length of ribbon they bought = 2/5 + 3/4

We know that the LCM of 5 and 4 is 20

= [(2 × 4)/ (5 × 4)] + [(3 × 5)/ (4 × 5)]

= 8/20 + 15/20

= (8 + 15)/20 = 23/20 m

Hence, the total length of the ribbon they bought is 23/20 m.

8. Ravish takes 2 1/5 minutes to walk across the school ground. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?

Time taken by Ravish to walk across the school ground = 2 1/5 minutes = 11/5 minutes

Time taken by Rahul to walk across the school ground = 7/4 minutes

By comparing 11/5 and 7/4 minutes

We know that LCM of 4 and 5 is 20

In order to convert fraction into equivalent fraction having 20 as denominator

So we get 44/20 > 35/20

So Rahul takes less time

44/20 – 35/20 = (44 – 35)/20 = 9/20 minutes

Hence, Rahul takes less time by 9/20 minutes.

9. A piece of a wire 7/8 metres long broke into two pieces. One piece was ¼ meter long. How long is the other piece?

It is given that

Length of wire = 7/8 m

Length of first piece = 1/4 m

Consider x m as the length of second piece

Length of wire = Length of first piece + Length of second piece

7/8 = 1/4 + x

x = 7/8 – 1/4

We know that the LCM of 8 and 4 is 8

x = [(7 × 1)/ (8 × 1)] – [(1 × 2)/ (4 × 2)]

x = 7/8 – 2/8

By subtraction

x = (7 – 2)/ 8 = 5/8 m

Hence, the length of second piece of wire is 5/8 m.

10. Shikha and Priya have bookshelves of the same size Shikha’s shelf is 5/6 full of book and Priya’s shelf is 2/5 full. Whose bookshelf is more full? By what fraction?

Fraction of Shikha’s shelf filled with books = 5/6

Fraction of Priya’s shelf filled with books = 2/5

We know that LCM of 5 and 6 is 30

= [(5 × 5)/ (6 × 5)], [(2 × 6)/ (5 × 6)]

So we get 25/30 > 12/30

So Shikha’s shelf is more full.

25/30 – 12/30 = (25 – 12)/ 30 = 13/30

Hence, Shikha’s bookshelf is more full by 13/30.

11. Ravish’s house is 9/10 km from his school. He walked some distance and then took a bus for 1/2km upto the school. How far did he walk?

Distance of Ravish’s house from his school = 9/10 km

Distance covered by bus = 1/2 km

Distance between house and school = Distance covered by walking + Distance covered by bus

Distance covered by walking = Distance between house and school – Distance covered by bus

Substituting values

Distance covered by walking = 9/10 – 1/2

We know that LCM of 10 and 2 is 10

In order to convert fraction into equivalent fraction having 10 as denominator

Distance covered by walking = [(9 × 1)/ (10 × 1)] – [(1 × 5)/ (2 × 5)]

Distance covered by walking = 9/10 – 5/10

Distance covered by walking = (9 – 5)/ 10 = 4/10 = 2/5 km

Hence, the distance covered by Ravish by walking is 2/5km.

Objective Type Questions page: 6.36

Mark the correct alternative in each of the following:

1. Which of the following is a proper fraction? (a) 4/3 (b) 3/4 (c) 13/4 (d) 21/5

The option (b) is correct answer.

We know that in a proper fraction, the numerator is less than the denominator.

2. Which of the following is an improper fraction? (a) 1/2 (b) 3/7 (c) 7/3 (d) 3/15

The option (c) is correct answer.

We know that in an improper fraction, the numerator is more than the denominator.

3. Which of the following is a fraction equivalent of 2/3? (a) 4/5 (b) 8/6 (c) 10/25 (d) 10/15

The option (d) is correct answer.

By cross multiplication

10 × 3 = 2 × 15

4. A fraction equivalent to 3/5is (a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these

We know that by dividing the numerator and denominator by 2, we obtain 3/5.

5. If 5/12 is equivalent of x/3, then x = (a) 5/4 (b) 4/5 (c) 5/3 (d) 3/5

The option (a) is correct answer.

Consider 5/12 = x/3

5 × 3 = 12 × x

x = (5 × 3)/12 = (5 × 3)/ (4 × 3) = 5/4

6. Which of the following are like fractions? (a) 3/5, 3/7, 3/11, 3/16 (b) 5/11, 7/11, 15/11, 2/11 (c) 2/3, 3/4,4/5, 6/7 (d) None of these

We know that like fractions are the fractions with the same denominator.

7. If 11/4 = 77/x, then x = (a) 28 (b) 77/28 (c) 44 (d) 308

11/4 = 77/x

11 × x = 77 × 4

x = (77 × 4)/ 11 = (7 × 11 × 4)/ 11

Dividing both the numerator & denominator by 11, we obtain 28.

8. 1/ (2 1/3) +1/ (1 3/4) is equal to (a) 7/14 (b) 12/49 (c) 4 1/12 (d) None of these

9. If 1/3 + 1/2 + 1/x = 4, then x = ? (a) 5/18 (b) 6/19 (c) 18/5 (d) 24/11

1/3 + ½ + 1/x = 4

1/x = 4 – 1/3 – 1/2

By taking LCM of 3 and 2 as 6

1/x = 24/6 – 2/6 – 3/6

1/x = (24 – 2 – 3)/ 6 = 19/6

Hence, x = 6/19

10. If 1/2 + 1/x = 2, then x = (a) 2/5 (b) 5/2 (c) 3/2 (d) 2/3

½ + 1/x = 2

1/x = 2 – 1/2

By taking LCM as 2 we get

1/x = 4/2 – 1/2 = (4 – 1)/2 = 3/2

Hence, x = 2/3

11. Which of the following fractions is the smallest? 1/2,3/7,3/5,4/9 (a) 4/9 (b) 3/5 (c) 3/7 (d) 1/2

We know that the LCM of numerator is 12

By converting each fraction to an equivalent fraction having 12 as numerator

1/2 = 1/2 × 12/12 = 12/24

3/7 = 3/7 × 4/4 = 12/28

3/5 = 3/5 × 4/4 = 12/20

4/9 = 4/9 × 3/3 = 12/27

We know that if the numerator is same the fraction having larger denominator is the smallest.

Hence, 3/7 is the smallest fraction.

12. Which of the following fractions is the greatest of all?

7/8, 6/7, 4/5, 5/6 (a) 6/7 (b) 4/5 (c) 5/6 (d) 7/8

We know that the LCM of 8, 7, 6 and 5 is 840

By converting each fraction to an equivalent fraction having 840 as denominator

7/8 = 7/8 × 105/105 = 735/840

6/7 = 6/7 × 120/120 = 720/840

4/5 = 4/5 × 168/168 = 672/840

5/6 = 5/6 × 140/140 = 700/840

We know that if the denominator is same the fraction having larger numerator is the greatest.

Hence, 7/8 is the greatest fraction.

13. What is the value of a+b/ a−b, If a/b=4? (a) 3/5 (b) 5/3 (c) 4/5 (d) 5/4

It is given that a/b = 4

We can write it as a = 4b

By substituting the value of a in a+b/a-b

a+b/a-b = 4b+b/4b-b = 5b/3b

Dividing numerator and denominator by b, the value is 5/3.

14. If a/b = 4/3, then the value of 6a+4b/ 6a-5b is (a) −1 (b) 3 (c) 4 (d) 5

It is given that a/b = 4/3

We can write it as a = 4b/3

By substituting the value of a in 6a+4b/6a-5b

15. If 1/5 – 1/6 = 4/x, then x = (a) −120 (b) −100 (c) 100 (d) 120

1/5 – 1/6 = 4/x

LCM of 5 and 6 is 30

4/x = 6/30 – 5/30

x = 4 (30) = 120

16. The fraction to be added to 6 7/15 to get 8 1/5 is equal to (a) 11/15 (b) 1 1/15 (c) 44/3 (d) 3/44

17. If 45/60 is equivalent to 3/x, then x = (a) 5 (b) 4 (c) 6 (d) 20

45/60 = 3/x

45 × x = 3 × 60

x = (3 × 60)/45 = 180/45

Dividing the fraction by HCF

(180 ÷ 45)/(45÷45) = 4

18. A fraction equivalent to 45/105 is (a) 6/14 (b) 4/7 (c) 5/7 (d) 7/5

The given fraction is 45/105

By dividing the numerator and denominator with the HCF

(45 ÷ 15)/(105÷15) = 3/7

3/7 = 3/7 × 2/2 = 6/14

19. 5/8 + 3/4 – 7/12 is equal to (a) 15/24 (b) 17/24 (c) 19/24 (d) 21/24

The given fraction is

5/8 + 3/4 – 7/12

We know that the LCM is 24

= (5 × 3)/ (8 × 3) + (3 × 6)/ (4 × 6) – (7 × 2)/ (12 × 2)

= 15/24 + 18/24 – 14/24

20. The correct fraction in the box □ is □ – 5/8=1/4 (a) 6/8 (b) 7/8 (c) 1/2 (d) None of these

The given equation is

□ – 5/8 = 1/4

□ = 1/4 + 5/8

We know that the LCM is 8

□ = 2/8 + 5/8 = 7/8

Chapter 6 Fractions has 9 exercises, which explain the methods used in solving problems, along with diagrammatic representation. Chapter 6 of RD Sharma Solutions contains some of the basic concepts, like

• Representation of fractions on the number line
• Fraction as division
• Types of fractions
• Equivalent fractions
• Fractions in the lowest terms
• Like and Unlike Fractions
• Comparing and ordering of fractions
• Addition and Subtraction of like fractions
• Addition and subtraction of unlike fractions

Chapter Brief of RD Sharma Solutions for Class 6 Maths Chapter 6 – Fractions

Concepts explained in Class 6 are important, as they are continued in higher classes as well. This chapter contains methods for solving types of fractions using operations. The solutions are prepared by subject-matter experts in order to improve conceptual knowledge and logical thinking abilities among students.

Some of the applications of fractions in our daily life are ingredients used for cooking and their proportion, the portion of painted wall and the amount of sugar in the vessel, etc. The PDF can be downloaded to get further information regarding the concepts explained in this chapter.

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