## Grade 7 Maths Problems With Answers

Grade 7 math word problems with answers are presented. Some of these problems are challenging and need more time to solve. The Solutions and explanatiosn are included.

- In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
- In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
- If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?
- The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
- A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
- A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
- Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
- Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
- 15 cm is the height of water in a cylindrical container of radius r. What is the height of this quantity of water if it is poured into a cylindrical container of radius 2r?
- John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
- How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
- The rectangular playground in Tim's school is three times as long as it is wide. The area of the playground is 75 square meters. What is the primeter of the playground?
- John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
- N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? A) 1 1/2 B) 1 1/3 C) 5/3 D) 3/2
- In 2008, the world population is about 6,760,000,000. Write the 2008 world population in scientific notation.
- Calculate the circumference of a circular field whose radius is 5 centimeters.

## Answers to the Above Problems

- 6 balls are blue
- 10 students are 10 years old
- x = 5/6 meter
- 20,000 square meters
- 368 square units
- 1250 meters per minute
- 78.74 inches
- 40 square meters
- 10? centimeters

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## Fraction Worksheets

Conversion :: Addition :: Subtraction :: Multiplication :: Division

## Conversions

Fractions - addition, fractions - subtraction, fractions - multiplication, fractions - division.

## Free Printable Fraction Word Problems Worksheets for 7th Year

Math Fraction Word Problems: Discover a collection of free printable worksheets tailored for Year 7 students, designed to help them master fractions through engaging word problems. Empower your teaching with Quizizz!

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## Explore printable Fraction Word Problems worksheets for 7th Year

Fraction Word Problems worksheets for Year 7 are an essential resource for teachers looking to challenge their students with real-life math scenarios. These worksheets provide a variety of math word problems that require students to apply their knowledge of fractions, decimals, and percentages to solve practical problems. By incorporating these worksheets into their lesson plans, teachers can help students develop critical thinking and problem-solving skills, while also reinforcing their understanding of key math concepts. With a wide range of topics and difficulty levels, these Year 7 math worksheets offer a comprehensive and engaging way for students to practice and improve their skills in solving fraction word problems.

In addition to Fraction Word Problems worksheets for Year 7, teachers can also utilize Quizizz as a supplementary tool to enhance their students' learning experience. Quizizz offers a vast library of interactive quizzes and games that cover a wide range of subjects, including Math Word Problems. Teachers can easily create custom quizzes tailored to their lesson plans, or choose from the extensive collection of pre-made quizzes available on the platform. By incorporating Quizizz into their teaching strategies, educators can provide a fun and interactive way for students to review and reinforce their understanding of math concepts, while also tracking their progress and identifying areas that may require additional support. With Quizizz, teachers have access to a wealth of resources that can help them create engaging and effective learning experiences for their Year 7 students.

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## Year 7 - Fractions

Subject: Mathematics

Age range: 11-14

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22 February 2018

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## Fraction Word Problems (Difficult)

Here are some examples of more difficult fraction word problems. We will illustrate how block models (tape diagrams) can be used to help you to visualize the fraction word problems in terms of the information given and the data that needs to be found.

Related Pages Fraction Word Problems Singapore Math Lessons Fraction Problems Using Algebra Algebra Word Problems

Block modeling (also known as tape diagrams or bar models) are widely used in Singapore Math and the Common Core to help students visualize and understand math word problems.

Example: 2/9 of the people on a restaurant are adults. If there are 95 more children than adults, how many children are there in the restaurant?

Solution: Draw a diagram with 9 equal parts: 2 parts to represent the adults and 7 parts to represent the children.

5 units = 95 1 unit = 95 ÷ 5 = 19 7 units = 7 × 19 = 133

Answer: There are 133 children in the restaurant.

Example: Gary and Henry brought an equal amount of money for shopping. Gary spent $95 and Henry spent $350. After that Henry had 4/7 of what Gary had left. How much money did Gary have left after shopping?

350 – 95 = 255 3 units = 255 1 unit = 255 ÷ 3 = 85 7 units = 85 × 7 = 595

Answer: Gary has $595 after shopping.

Example: 1/9 of the shirts sold at Peter’s shop are striped. 5/8 of the remainder are printed. The rest of the shirts are plain colored shirts. If Peter’s shop has 81 plain colored shirts, how many more printed shirts than plain colored shirts does the shop have?

Solution: Draw a diagram with 9 parts. One part represents striped shirts. Out of the remaining 8 parts: 5 parts represent the printed shirts and 3 parts represent plain colored shirts.

3 units = 81 1 unit = 81 ÷ 3 = 27 Printed shirts have 2 parts more than plain shirts. 2 units = 27 × 2 = 54

Answer: Peter’s shop has 54 more printed colored shirts than plain shirts.

Solve a problem involving fractions of fractions and fractions of remaining parts

Example: 1/4 of my trail mix recipe is raisins and the rest is nuts. 3/5 of the nuts are peanuts and the rest are almonds. What fraction of my trail mix is almonds?

How to solve fraction word problem that involves addition, subtraction and multiplication using a tape diagram or block model

Example: Jenny’s mom says she has an hour before it’s bedtime. Jenny spends 3/5 of the hour texting a friend and 3/8 of the remaining time brushing her teeth and putting on her pajamas. She spends the rest of the time reading her book. How long did Jenny read?

How to solve a four step fraction word problem using tape diagrams?

Example: In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second graders. If there are 96 students in the auditorium, how many second graders are there?

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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

- 1st Grade Fraction Worksheets
- Fraction Worksheets for Grade 2
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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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## Unit 2: Rates and percentages

About this unit, rate problems with fractions.

- Fractions, decimals, & percentages FAQ (Opens a modal)
- Rates with fractions (Opens a modal)
- Rates with fractions Get 3 of 4 questions to level up!

## Converting fractions to decimals

- Rewriting decimals as fractions: 2.75 (Opens a modal)
- Worked example: Converting a fraction (7/8) to a decimal (Opens a modal)
- Fraction to decimal: 11/25 (Opens a modal)
- Fraction to decimal with rounding (Opens a modal)
- Comparing rational numbers (Opens a modal)
- Rewriting decimals as fractions challenge Get 5 of 7 questions to level up!
- Converting fractions to decimals Get 3 of 4 questions to level up!
- Order rational numbers Get 3 of 4 questions to level up!

## Percent word problems

- Solving percent problems (Opens a modal)
- Percent word problem: magic club (Opens a modal)
- Percent word problems: tax and discount (Opens a modal)
- Percent word problem: guavas (Opens a modal)
- Multi-step ratio and percent problems (Opens a modal)
- Equivalent expressions with percent problems Get 3 of 4 questions to level up!
- Percent problems Get 3 of 4 questions to level up!
- Tax and tip word problems Get 3 of 4 questions to level up!
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Home / United States / Math Classes / 5th Grade Math / Problem Solving using Fractions

## Problem Solving using Fractions

Fractions are numbers that exist between whole numbers. We get fractions when we divide whole numbers into equal parts. Here we will learn to solve some real-life problems using fractions. ...Read More Read Less

## Table of Contents

## What are Fractions?

Types of fractions.

- Fractions with like and unlike denominators
- Operations on fractions
- Fractions can be multiplied by using
- Let’s take a look at a few examples

## Solved Examples

- Frequently Asked Questions

Equal parts of a whole or a collection of things are represented by fractions . In other words a fraction is a part or a portion of the whole. When we divide something into equal pieces, each part becomes a fraction of the whole.

For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction \(\frac{1}{2}\) .

Similarly, if it is divided into 4 equal parts, then each part is one fourth of the whole, that can be represented by the fraction \(\frac{1}{4}\) .

Proper fractions

A fraction in which the numerator is less than the denominator value is called a proper fraction.

For example , \(\frac{3}{4}\) , \(\frac{5}{7}\) , \(\frac{3}{8}\) are proper fractions.

Improper fractions

A fraction with the numerator higher than or equal to the denominator is called an improper fraction .

Eg \(\frac{9}{4}\) , \(\frac{8}{8}\) , \(\frac{9}{4}\) are examples of improper fractions.

Mixed fractions

A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction.

We express improper fractions as mixed numbers.

For example , 5\(\frac{1}{3}\) , 1\(\frac{4}{9}\) , 13\(\frac{7}{8}\) are mixed fractions.

Unit fraction

A unit fraction is a fraction with a numerator equal to one. If a whole or a collection is divided into equal parts, then exactly 1 part of the total parts represents a unit fraction .

## Fractions with Like and Unlike Denominators

Like fractions are those in which two or more fractions have the same denominator, whereas unlike fractions are those in which the denominators of two or more fractions are different.

For example,

\(\frac{1}{4}\) and \(\frac{3}{4}\) are like fractions as they both have the same denominator, that is, 4.

\(\frac{1}{3}\) and \(\frac{1}{4}\) are unlike fractions as they both have a different denominator.

## Operations on Fractions

We can perform addition, subtraction, multiplication and division operations on fractions.

Fractions with unlike denominators can be added or subtracted using equivalent fractions. Equivalent fractions can be obtained by finding a common denominator. And a common denominator is obtained either by determining a common multiple of the denominators or by calculating the product of the denominators.

There is another method to add or subtract mixed numbers, that is, solve the fractional and whole number parts separately, and then, find their sum to get the final answer.

## Fractions can be Multiplied by Using:

Division operations on fractions can be performed using a tape diagram and area model. Also, when a fraction is divided by another fraction then we can solve it by multiplying the dividend with the reciprocal of the divisor.

## Let’s Take a Look at a Few Examples

Addition and subtraction using common denominator

( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )

We apply the method of equivalent fractions. For this we need a common denominator, or a common multiple of the two denominators 6 and 5, that is, 30.

\(\frac{1}{6} ~+ ~\frac{2}{5}\)

= \(\frac{5~+~12}{30}\)

= \(\frac{17}{30}\)

( \(\frac{5}{2}~-~\frac{1}{6}\) )

= \(\frac{12~-~5}{30}\)

= \(\frac{7}{30}\)

Examples of Multiplication and Division

Multiplication:

(\(\frac{1}{6}~\times~\frac{2}{5}\))

= (\(\frac{1~\times~2}{6~\times~5}\)) [Multiplying numerator of fractions and multiplying denominator of fractions]

= \(\frac{2}{30}\)

(\(\frac{2}{5}~÷~\frac{1}{6}\))

= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\)) [Multiplying dividend with the reciprocal of divisor]

= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))

= \(\frac{12}{5}\)

Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)

Let’s add \(\frac{7}{8}\) and \(\frac{2}{3}\) using equivalent fractions. For this we need to find a common denominator or a common multiple of the two denominators 8 and 3, which is, 24.

\(\frac{7}{8}\) + \(\frac{2}{3}\)

= \(\frac{21~+~16}{24}\)

= \(\frac{37}{24}\)

Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)

Solution:

Let’s subtract \(\frac{12}{17}\) from \(\frac{11}{13}\) using equivalent fractions. For this we need a common denominator or a common multiple of the two denominators 13 and 17, that is, 221.

\(\frac{11}{13}\) – \(\frac{12}{17}\)

= \(\frac{187~-~156}{221}\)

= \(\frac{31}{221}\)

Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)

Multiply the numerators and multiply the denominators of the 2 fractions.

\(\frac{15}{13}~\times~\frac{18}{17}\)

= \(\frac{15~~\times~18}{13~~\times~~17}\)

= \(\frac{270}{221}\)

Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)

Divide by multiplying the dividend with the reciprocal of the divisor.

\(\frac{25}{33}~\div~\frac{41}{45}\)

= \(\frac{25}{33}~\times~\frac{41}{45}\) [Multiply with reciprocal of the divisor \(\frac{41}{45}\) , that is, \(\frac{45}{41}\) ]

= \(\frac{25~\times~45}{33~\times~41}\)

= \(\frac{1125}{1353}\)

Example 5:

Sam was left with \(\frac{7}{8}\) slices of chocolate cake and \(\frac{3}{7}\) slices of vanilla cake after he shared the rest with his friends. Find out the total number of slices of cake he had with him. Sam shared \(\frac{10}{11}\) slices from the total number he had with his parents. What is the number of slices he has remaining?

To find the total number of slices of cake he had after sharing we need to add the slices of each cake he had,

= \(\frac{7}{8}\) + \(\frac{3}{7}\)

= \(\frac{49~+~24}{56}\)

= \(\frac{73}{56}\)

To find out the remaining number of slices Sam has \(\frac{10}{11}\) slices need to be deducted from the total number,

= \(\frac{73}{56}~-~\frac{10}{11}\)

= \(\frac{803~-~560}{616}\)

= \(\frac{243}{616}\)

Hence, after sharing the cake with his friends, Sam has \(\frac{73}{56}\) slices of cake, and after sharing with his parents he had \(\frac{243}{616}\) slices of cake left with him.

Example 6: Tiffany squeezed oranges to make orange juice for her juice stand. She was able to get 25 ml from one orange. How many oranges does she need to squeeze to fill a jar of \(\frac{15}{8}\) liters? Each cup that she sells carries 200 ml and she sells each cup for 64 cents. How much money does she make at her juice stand?

First \(\frac{15}{8}\) l needs to be converted to milliliters.

\(\frac{15}{8}\)l into milliliters = \(\frac{15}{8}\) x 1000 = 1875 ml

To find the number of oranges, divide the total required quantity by the quantity of juice that one orange can give.

The number of oranges required for 1875 m l of juice = \(\frac{1875}{25}\) ml = 75 oranges

To find the number of cups she sells, the total quantity of juice is to be divided by the quantity of juice that 1 cup has

= \(\frac{1875}{200}~=~9\frac{3}{8}\) cups

We know that, the number of cups cannot be a fraction, it has to be a whole number. Also each cup must have 200ml. Hence with the quantity of juice she has she can sell 9 cups, \(\frac{3}{8}\) th of a cup cannot be sold alone.

Money made on selling 9 cups = 9 x 64 = 576 cents

Hence she makes 576 cents from her juice stand.

## What is a mixed fraction?

A mixed fraction is a number that has a whole number and a fractional part. It is used to represent values between whole numbers.

## How will you add fractions with unlike denominators?

When adding fractions with unlike denominators, take the common multiple of the denominators of both the fractions and then convert them into equivalent fractions.

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## Year 7 Problem Solving

Year 7 Problem Solving - Displaying top 8 worksheets found for this concept.

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Do you feel a little rusty when it comes to Year 7 fractions? In this article, we will show you how to solve a variety of questions dealing with fractions, give you worked examples and provide some checkpoint questions at the end!

Grade 7 Maths Problems With Answers with answers are presented. Some of these problems are challenging and need more time to solve. The Solutions and explanatiosn are included. Problems In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?

Next: Fractions - Finding Original Practice Questions GCSE Revision Cards. 5-a-day Workbooks

Worksheet Example Fractions (Same Denominator) 1 5 + 2 5 Unit Fractions 1 3 + 1 9 Easy Proper Fractions 3 8 + 2 7 Harder Proper Fractions 7 12 + 15 25 Easy Mixed Fractions 1 2 3 + 2 1 4 Harder Mixed Fractions 1 7 9 + 3 5 11 Easy Improper Fractions 5 9 + 7 4 Harder Improper Fractions 33 15 + 43 11 top> Fractions - Subtraction

Fraction Word Problems worksheets for Year 7 are an essential resource for teachers looking to challenge their students with real-life math scenarios. These worksheets provide a variety of math word problems that require students to apply their knowledge of fractions, decimals, and percentages to solve practical problems.

File previews. pptx, 1.24 MB. (a) Be able to simplify, add, subtract, multiply and divide fractions, including mixtures of improper fractions, integers and mixed numbers. (b) Deal with fractions nested within fractions. (c) Solve problems involving successive fractions of a remaining amount. (d) Solve problems involving finding the original ...

Solution: Answer: The Cocozzelli family took one-half more days to drive home. Example 7: A warehouse has 12 and nine-tenths meters of tape in one area of the building, and eight and three-fifths meters of tape in another part. How much tape does the warehouse have in all?

Class 7 (Foundation) 11 units · 59 skills. Unit 1 Knowing our numbers. Unit 2 Whole numbers. Unit 3 Playing with numbers. Unit 4 Integers. Unit 5 Fractions. Unit 6 Decimals. Unit 7 Ratio and proportion.

Welcome to IXL's year 7 maths page. Practise maths online with unlimited questions in more than 200 year 7 maths skills. ... Add, subtract, multiply and divide fractions and mixed numbers: word problems 25. Evaluate numerical expressions involving fractions I. Rational numbers. 1. ... Use Venn diagrams to solve problems 5. Find the number of ...

Fun maths practice! Improve your skills with free problems in 'Multiply fractions: word problems' and thousands of other practice lessons.

Resources for Fraction Problems Questions 10 With Worked Solution Click Here Video Tutorials 4 Click Here Create account Access content straight away with a two week free trial I am.. Please enter your details First Name. Curriculum-based maths in NSW. Year 7 Maths.

Solution: Draw a diagram with 9 equal parts: 2 parts to represent the adults and 7 parts to represent the children. 5 units = 95. 1 unit = 95 ÷ 5 = 19. 7 units = 7 × 19 = 133. Answer: There are 133 children in the restaurant. Example: Gary and Henry brought an equal amount of money for shopping. Gary spent $95 and Henry spent $350.

Fractions problem solving. In this lesson, we will be learning how to solve fraction problems relating to shape, including calculating the perimeter and finding missing lengths. This quiz includes images that don't have any alt text - please contact your teacher who should be able to help you with an audio description.

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.

(15 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. (15 Worksheets) Related Worksheets » Decimal Word Problems » Ratio Word Problems

Answer: Word problems with fractions: involving a fraction and a whole number Finally, we are going to look at an example of a word problem with a fraction and a whole number. Now we will have to convert all the information into a fraction with the same denominator (as we did in the example above) in order to calculate

Welcome to IXL's year 7 maths page. Practise maths online with unlimited questions in more than 200 year 7 maths skills. ... Add, subtract, multiply or divide two fractions: word problems 12. Evaluate numerical expressions involving fractions 13. Add, subtract, multiply or divide two integers ... Solve word problems by finding two-variable ...

Learn Fractions, decimals, & percentages FAQ Rates with fractions Practice Up next for you: Rates with fractions Get 3 of 4 questions to level up! Start Not started Converting fractions to decimals Learn Rewriting decimals as fractions: 2.75 Worked example: Converting a fraction (7/8) to a decimal

Malta Ages 7-11 Maths Fractions, Decimals, Percentages and Proportions Fractions Solving Problems Catch-Up Resources Maths DfE Ready-to-Progress Criteria Year 5 5F-1 Find Non-Unit Fractions of Quantities

Operations on Fractions Rational Numbers Understanding Rational Numbers Equivalent Rational Numbers Comparison of Rational Numbers Representation of Rational Numbers on the Real Line Addition and Subtraction of Rational Numbers Multiplication and Division of Rational Numbers Rational Numbers Lying Between Two Rational Numbers

When we divide something into equal pieces, each part becomes a fraction of the whole. For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction \ (\frac {1} {2}\). Similarly, if it is divided into 4 equal parts, then each part is one ...

Year 7. Top Mathematicians. Number Properties. 7.1 / ... Divide Fractions Up to 1/5, 1/7, 1/9 7.41 / Divide Fractions and Mixed Numbers ... Teachers go over rules, tips, and multiple problems helping students to be able to solve the problems themselves. Students learn about ratios, mixed properties, statistics and other seventh grade skills. ...

Year 7 Problem Solving. Year 7 Problem Solving - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Year 7, Handouts emotional regulation social skills problem solving, Word problem practice workbook, Problem solving booklet, Work decision making problem solving, Year 2 use arrays reasoning and ...