problem solving with fractions and percentages

Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:

Here, have a play with it yourself:

Example Values

Here is a table of commonly used values shown in Percent, Decimal and Fraction form:

Conversions!

From percent to decimal.

To convert from percent to decimal divide by 100 and remove the % sign.

An easy way to divide by 100 is to move the decimal point 2 places to the left :

Don't forget to remove the % sign!

From Decimal to Percent

To convert from decimal to percent multiply by 100%

An easy way to multiply by 100 is to move the decimal point 2 places to the right :

 Don't forget to add the % sign!

From Fraction to Decimal

To convert a fraction to a decimal divide the top number by the bottom number:

Example: Convert 2 5 to a decimal

Divide 2 by 5: 2 ÷ 5 = 0.4

Answer: 2 5 = 0.4

From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

Example: To convert 0.75 to a fraction

From fraction to percentage.

To convert a fraction to a percentage divide the top number by the bottom number, then multiply the result by 100%

Example: Convert 3 8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375

Then multiply by 100%: 0.375 × 100% = 37.5%

Answer: 3 8 = 37.5%

From Percentage to Fraction

To convert a percentage to a fraction , first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

5.2.1: Solving Percent Problems

• Last updated
• Save as PDF
• Page ID 62169

• The NROC Project

Learning Objectives

• Identify the amount, the base, and the percent in a percent problem.
• Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100, so they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

• The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.
• The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.
• The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price.

You will return to this problem a bit later. The following examples show how to identify the three parts: the percent, the base, and the amount.

Identify the percent, amount, and base in this problem.

30 is 20% of what number?

Percent: The percent is the number with the % symbol: 20%.

Base : The base is the whole amount, which in this case is unknown.

Amount: The amount based on the percent is 30.

Percent=20%

Base=unknown

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Identify the percent, base, and amount in this problem:

What percent of 30 is 3?

The percent is unknown, because the problem states " What percent?" The base is the whole in the situation, so the base is 30. The amount is the portion of the whole, which is 3 in this case.

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

\[\ \text { Percent } {\color{red}\cdot}\text { Base }{\color{blue}=}\text { Amount } \nonumber \]

In the examples below, the unknown is represented by the letter \(\ n\). The unknown can be represented by any letter or a box \(\ \square\) or even a question mark.

Write an equation that represents the following problem.

\(\ 20 \% \cdot n=30\)

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as \(\ 20 \% \cdot n=30\), you can divide 30 by 20% to find the unknown: \(\ n=30 \div 20 \%\).

You can solve this by writing the percent as a decimal or fraction and then dividing.

\(\ n=30 \div 20 \%=30 \div 0.20=150\)

What percent of 72 is 9?

\(\ 12.5 \% \text { of } 72 \text { is } 9\).

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

\(\ 10 \% \text { of } 72=0.1 \cdot 72=7.2\)

\(\ 20 \% \text { of } 72=0.2 \cdot 72=14.4\)

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

What is 110% of 24?

\(\ 26.4 \text { is } 110 \% \text { of } 24\).

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

18 is what percent of 48?

• \(\ 0.375 \%\)
• \(\ 8.64 \%\)
• \(\ 37.5 \%\)
• \(\ 864 \%\)

Incorrect. You may have calculated properly, but you forgot to move the decimal point when you rewrote your answer as a percent. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Incorrect. You may have used \(\ 18\) or \(\ 48\) as the percent, rather than the amount or base. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Correct. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives \(\ 37.5 \%\).

Incorrect. You probably used 18 or 48 as the percent, rather than the amount or base, and also forgot to rewrite the percent as a decimal before multiplying. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Using Proportions to Solve Percent Problems

Percent problems can also be solved by writing a proportion. A proportion is an equation that sets two ratios or fractions equal to each other. With percent problems, one of the ratios is the percent, written as \(\ \frac{n}{100}\). The other ratio is the amount to the base.

\(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\)

Write a proportion to find the answer to the following question.

30 is 20% of 150.

18 is 125% of what number?

• \(\ 0.144\)
• \(\ 694 \frac{4}{9}\) (or about \(\ 694.4\))

Incorrect. You probably didn’t write a proportion and just divided 18 by 125. Or, you incorrectly set up one fraction as \(\ \frac{18}{125}\) and set this equal to the base, \(\ n\). The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Correct. The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably put the amount (18) over 100 in the proportion, rather than the percent (125). Perhaps you thought 18 was the percent and 125 was the base. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably confused the amount (18) with the percent (125) when you set up the proportion. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price .

The coupon will take $33 off the original price.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

\(\ \begin{array}{l} 10 \% \text { of } 220=0.1 \cdot 220=22 \\ 20 \% \text { of } 220=0.2 \cdot 220=44 \end{array}\)

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Evelyn bought some books at the local bookstore. Her total bill was $31.50, which included 5% tax. How much did the books cost before tax?

The books cost $30 before tax.

Susana worked 20 hours at her job last week. This week, she worked 35 hours. In terms of a percent, how much more did she work this week than last week?

Since 35 is 175% of 20, Susana worked 75% more this week than she did last week. (You can think of this as, “Susana worked 100% of the hours she worked last week, as well as 75% more.”)

Percent problems have three parts: the percent, the base (or whole), and the amount. Any of those parts may be the unknown value to be found. To solve percent problems, you can use the equation, \(\ \text { Percent } \cdot \text { Base }=\text { Amount }\), and solve for the unknown numbers. Or, you can set up the proportion, \(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\), where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

Fractions, Decimals and Percentages

Fractions, Decimals And Percentages

Here we will learn about fractions, decimals and percentages , including what they are, how to calculate with them and to solve problems involving them.

There are also fractions, decimals and percentages worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are fractions, decimals and percentages?

Fractions, decimals and percentages are different ways of representing a proportion of the same amount.

There is equivalence between fractions, decimals and percentages.

E.g. \frac{43}{100}=0.43=43\%

What are fractions?

Fractions are a way of writing equal parts of one whole.

They have a numerator (top number) and a denominator (bottom number).  The denominator shows how many equal parts the whole has been divided into.  The numerator shows how many of the equal parts we have.

E.g. This shape has 9 equal parts and 4 of them are shaded. This represents four ninths: \frac{4}{9}

What are decimals?

Decimals are a way of writing numbers that are not whole.

Decimal numbers can be recognised as they have a decimal point. A decimal place is a position after the decimal point.

E.g. 0.37 has two decimal places.

There is a 3 in the tenths place and 7 in the hundredths place.

E.g. This shows the fraction \frac{7}{10}

\frac{7}{10} can also be written as 0.7

What are percentages?

Percentages are numbers which are expressed as parts of 100 .

Percent means “number of parts per hundred” and the symbol we use for this is the percent sign (%).

There are 100 equal parts and 43 of them are shaded.

How to use fractions, decimals and percentages

There are various ways of using fractions, decimals and percentages.

For examples, practice questions and worksheets on each one follow the links to the step by step guides below:

Percentages

Comparing fractions, decimals and percentages.

In order to compare fractions, decimals and percentages you need to be able to convert between them, including:

• Converting fractions to decimals 
• Converting decimals to fractions
• Converting fractions to percentages
• Converting percentages to fractions
• Converting decimals to percentages
• Converting percentages to decimals
• Converting recurring decimals to fractions

Step-by-step guide: Converting fractions, decimals and percentages

Fractions, decimals and percentages worksheet

Get your free fractions, decimals and percentages worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Fractions, decimals and percentages examples

1. adding fractions.

To add fractions they need to have a common denominator .

• Step-by-step guide: Adding fractions

2. Subtracting fractions

To subtract fractions they need to have a common denominator .

• Step-by-step guide: Subtracting fractions

3. Multiplying fractions

To multiply fractions we need to multiply the numerators together and multiply the denominators together.

• Step-by-step guide: Multiplying fractions

4. Dividing fractions

To divide fractions we need to find the reciprocal of (flip) the second fraction , change the divide sign to a multiply and then multiply the fractions together.

• Step-by-step guide: Dividing fractions

5. Equivalent fractions

Equivalent fractions are fractions that have the same value . 

• Step-by-step guide: Equivalent fractions

6. Improper fractions and mixed numbers

An improper fraction is a fraction where the numerator (top number) is larger than the denominator (bottom number).

A mixed number has a whole number part and a fractional part .

We can convert between improper fractions and mixed numbers:

• Step-by-step guide: Improper fractions and mixed numbers

7. Ordering fractions

To order fractions they need to have a common denominator .

Write these fractions in order of size from smallest to largest:

• Step-by-step guide: Ordering fractions

8. Fractions of an amount

We can calculate a fraction of a given amount.

Calculate \frac{3}{4} of 28 :

• Step-by-step guide: Fractions amounts

1. Adding decimals

We can add decimals together:

Use the column method.

• Step-by-step guide: Adding decimals

2. Subtracting decimals

We can subtract decimals from each other:

• Step-by-step guide: Subtracting decimals

3. Multiplying decimals

We can multiply decimals:

2.3 \times 1.7 becomes 23 \times 17

391 becomes 3.91

• Step-by-step guide: Multiplying decimals

4. Dividing decimals

We can divide decimals by using equivalent fractions to ensure that the divisor (the denominator) is an integer:

• Step-by-step guide: Dividing decimals

1. Percentage of an amount

We can find a percentage of an amount by breaking the percentage down:

E.g. Find 35\% of 400

• Step-by-step guide: Percentage of an amount

2. Percentage multipliers

We can use percentage multipliers to find a percentage of an amount or to increase/decrease by a percentage:

E.g. Find 27\% of 320

The multiplier for 27\% is 0.27

• Step-by-step guide: Percentage multipliers

3. Percentage increase

We can increase a value by a percentage:

E.g. Increase 40 by 12\%

Either find 12\% of 40 and add it on to 40 , or use a multiplier.

• Step-by-step guide: Percentage increase

4. Percentage decrease

We can decrease a value by a percentage:

E.g. Decrease 90 by 23\% .

Either find 23\% of 90 and subtract it from 90 , or use a multiplier.

• Step-by-step guide: Percentage decrease

5. Percentage change

We can calculate the percentage change between two values:

E.g. Calculate the percentage change from 200 to 240 .

Therefore the percentage change is 20\% .

• Step-by-step guide: Percentage change

6. Reverse percentages

We can use reverse percentages to calculate the original number:

E.g. 80\% of a number is 240 . What was the original number?

• Step-by-step guide: Reverse percentages

1. Fractions to decimals

Converting fractions to decimals:

Write \frac{5}{8} as a decimal.

Divide the numerator by the decimal by using a written method or a calculator.

• Step-by-step guide: Fractions to decimals

2. Decimals to fractions

Converting decimals to fractions:

Write 0.34 as a fraction.

Then cancel so that the fraction is in its simplest form.

• Step-by-step guide: Decimals to fractions

3. Fractions to percentages

Converting fractions to percentages:

Write \frac{7}{8} as a percentage.

• Step-by-step guide: Fractions to percentages

4. Percentages to fractions

Converting percentages to fractions:

Write 56\% as a fraction.

• Step-by-step guide: Percentages to fractions

5. Decimal to percentage

Converting decimals to percentages:

Write 0.63 as a percentage.

• Step-by-step guide: Decimal to percentage

6. Percentage to decimal

Converting percentages to decimals:

Write 32\% as a decimal.

• Step-by-step guide: Percentage to decimal

7. Recurring decimals to fractions

Converting recurring decimals to fractions:

• Step-by-step guide: Recurring decimals to fractions

Common misconceptions

• Common denominators

To be able to add, subtract or compare fractions they must have a common denominator. To do this you need to find a common multiple for the denominators. The lowest common denominator is the easiest to use.

• Fractions in their simplest form

Often fraction questions ask for the answer to be in its simplest form. This means you need to consider the numerator (the top number) and the denominator (the bottom number) and cancel by looking for common factors.

• Percentages can be greater than 100

Percentages can be more than 100 . This can happen for a percentage increase and for calculating percentage change.

• The equivalence of one-third

Take care with one-third and its decimal and percentage equivalence.

Practice fractions, decimals and percentage questions

1.  Calculate:

2. Convert the following mixed number to an improper fraction:

3. Calculate:

4. Calculate:

5.  Increase 45 by 12\%

6. 65\% of a number is 520 . What is the original number?

Fractions, decimals and percentages GCSE questions

1.  (a) Write \frac{3}{4} as a decimal

(b) Write 0.7 as a fraction

(c) Write 0.6 as a percentage

(a) \frac{3}{4}=0.75

(b) 0.7=\frac{7}{10}

(c) 0.6=\frac{6}{10}=\frac{60}{100}=60\%

2. Gordon buys a car.

The cost of the car is £13 600 plus VAT at 20\%

Gordon pays a deposit of £4000

He pays the rest in 10 equal payments.

Work out the amount of each of the 10 payments.

(for finding 20\% of the price)

(for finding 120\% of the price)

(for finding calculating the remainder to be paid)

3. Prove algebraically that the recurring decimal 0.4\dot{3}\dot{2} has the value of \frac{214}{495}

(for the correct recurring decimal)

(for the second recurring decimal and the subtraction)

(for the correct fraction)

Learning checklist

You have now learned how to:

• Order decimals and fractions
• Understand and use place value for decimals
• Use the 4 operations, including formal written methods, applied to decimals, proper and improper fractions, and mixed numbers
• Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100\%
• Convert fractions, decimals and percentages

The next lessons are

• Compound interest
• Simple interest and compound interest

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

Privacy Overview

Calcworkshop

How to Solve Percent Problems? 13 Amazing Examples!

// Last Updated: January 20, 2020 - Watch Video //

Ratios and proportions help us in solving problems with percents .

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Because a percent is the ratio (fraction) of one number to another.

In other words, its a number divided by 100.

What is most important to note is that our overall goal is to translate each problem into an algebraic expression by looking for keywords such as “of” and “is,” and then solve for the unknown variable.

First, we will look at how a percent is created by understanding it is simply a proportion:

Percents as a Proportion

And we will quickly see that most problems will follow a very simple Percents Formula, as Khan Academy so accurately states.

Together will look at how to change percents to fractions, percents to decimals, and decimals to percents for various problems.

Additionally, we will look at real-world examples, such as finding the percent of commission, the price of an item with a percent discount, change in population, as well as mixture problems.

Solving Percents (How-To) – Video

Get access to all the courses and over 450 HD videos with your subscription

Monthly and Yearly Plans Available

Get My Subscription Now

Still wondering if CalcWorkshop is right for you? Take a Tour and find out how a membership can take the struggle out of learning math.

Or search by topic

Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

Published 2013 Revised 2019

Exploring Fractions

• The first group  gives you some starting points to explore with your class, which are applicable to a wide range of ages.  The tasks in this first group will build on children's current understanding of fractions and will help them get to grips with the concept of the part-whole relationship. 
• The second group of tasks  focuses on the progression of ideas associated with fractions, through a problem-solving lens.  So, the tasks in this second group are curriculum-linked but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills.   

• are applicable to a range of ages;
• provide contexts in which to explore the part-whole relationship in depth;
• offer opportunities to develop conceptual understanding through talk.

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. 

Check out our other courses

Grades 1 - 12

Level 1 - 10

PROBLEM SOLVING WITH FRACTIONS DECIMALS AND PERCENTAGES WORKSHEET

Problems with fractions.

(1)  A fruit merchant bought mangoes in bulk. He sold 5/8  of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy? 

(2)  A family requires 2 1/2 liters of milk per day. How much milk would family require in a month of 31 days?  

(3)  A ream of paper weighs 12 1/2 kg.  What is the weight per quire ?

(4)   It was Richard's birthday. He distributed 6 kg of candies to his friends. If he had given 1/8  kg of candies to each friend, how many friends were there ?

(5)  Rachel bought a pizza and ate 2/5 of it. If he had given 2/3 of the remaining to his friend, what fraction of the original pizza will be remaining now ?

Answer Key :

(1)  960 mangoes

(2)   77 1/2 liter

(3)  5/8 kg

(4)   48 friends

(5)  1/5

Fraction Word Problems Mixed Operations

(1)  Linda walked 2 1/3 miles on the first day and 3 2/5   miles on the next day. How many miles did she walk in all ?                Solution

(2)   David ate 2 1/7 pizzas and he gave 1 3/14    pizzas to his mother. How many pizzas did David have initially ?

(3)   Mr. A has 3 2/3 acres of land. He gave 1 1/4 acres of land to his friend. How many acres of land does Mr. A have now ?          Solution

(4)   Lily added 3 1/3 cups of walnuts to a batch of trail mix. Later she added 1 1/3 cups of almonds. How many cups of nuts did Lily put in the trail mix in all? 

(5)   In the first hockey games of the year, Rodayo played 1 1/2 periods and 1 3/4 periods. How many periods in all did he play ?         Solution

(6)   A bag can hold 1 1/2 pounds of flour. If Mimi has 7 1/2 pounds of flour, then how many bags of flour can Mimi make ?        Solution

(7)   Jack and John went fishing Jack caught 3 3/4 kg of fish and while John  caught 2 1/5 kg of fish. What is the total weight of the fish they caught?

(8)   Amy has 3 1/2 bottles in her refrigerator. She used 3/5 bottle in the morning 1 1/4 bottle in the afternoon. How many bottles of milk does Amy have left over ?  

(9)   A tank has 82 3/4 liters of water. 24 4/5 liters of water were used and the tank was filled with another 18 3/4 liters. What is the final volume of the water in the tank ?

(10)   A trader prepared 21 1/2 liters of lemonade. At the end of the day he had 2 5/8 liters left over. How many liters of lemonade was sold by the Trader? 

Answer key :

Problems on Decimals

(1)  A chemist mixed 6.35 grams of one compound with 2.45 grams of another compound. How many grams were there in the mixture.      Solution

(2)   If the cost of a pen is $10.50, a book is $25.75 and a bag is $45.50, the  find the total cost of 2 books, 3 pens and 1 bag.         Solution

(3)    John wants to buy a bicycle that cost $ 450.75. He has saved $ 125.35. How much more money must John save in order to have enough money to buy the bicycle ?

(4)   Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?

(5)   The inner radius of a pipe is 12.625 mm and the outer radius is 18.025 mm. Find the thickness of the pipe.          Solution

(6)   A copy of English book weighs 0.45 kg. What is the weight of 20 copies ?          Solution

(7)   Find the weight of 25.5 meters of copper wire in kilograms, if one meter weighs 10 grams.          Solution

(8)   Robert paid $140 for 2.8 kg of cooking oil. How much did 1 kg of the cooking oil cost ?         Solution

(9)   If $20.70 is earned in 6 hours, how much money will be earned in 5 hours ?            Solution

(10)   A pipe is 76.8 meters long. What will the greatest number of pieces of pipe each 8 meters long that can be cut from this pipe ?          Solution

Answers Key :

Problems on Percentage

(1)  In a particular store the number of TV's sold the week of Black Friday was 685. The number of TVs sold the following week was 500. TV sales the week following Black Friday were what percent less than TV sales the week of Black Friday ?

(A)  17%   (B)  27%   (C)  37%   (D)  47%

(2)  In March, a city zoo attracted 32000 visitors to its polar bear exhibit. In April, the number of visitors to the exhibit increased by 15%. How many visitors did the zoo attract to its polar bear exhibit in April ?

(A)  32150   (B)  32480   (C)  35200  (D)  36800

(3)  A charity organization collected 2140 donations last month. With the help of 50 additional volunteers, the organization collected 2690 donations this month. To the nearest tenth of a percent, what was the percent increase in the number of donations the charity organization collected ?

(A) 20.4%   (B)  20.7%    (C)  25.4%   (D)  25.7%

(4)  The discount price of a book is 20% less than the retail price. James manages to purchase the book at 30% off the discount price at the special book sale. What percent of the retail price did James pay ?

(A)  42%   (B)  48%    (C)  50%   (D)  56%

(5)  Each day, Robert eats 40% of the pistachios left in his jar at the time. At the end of the second day, 27 pistachios remain. How many pistachios were in the jar at the start of the first day ?

(A)  75   (B)  80   (C)  85  (D)  95

(6) Joanne bought a doll at a 10 percent discount off the original price of $105.82. However, she had to pay a sales tax of x% on the discounted price. If the total amount she paid for the doll was $100, what is the value of x ?

(A)  2   (B)  3   (C)  4  (D)  5

(7)  In 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B. If 70 houses were built in Town A during 2010, how many were built in Town B ?

(A)  56   (B)  50    (C)  48   (D)  20

(8)  Over two week span, John ate 20 pounds of chicken wings and 15 pounds of hot dogs. Kyle ate 20 percent more chicken wings and 40 percent more hot dogs. Considering only chicken wings and hot dogs, Kyle ate approximately x percent more food, by weight, than John, what is x (rounded to the nearest percent) ?

(A)  25   (B)  27    (C)  29   (D)  30

(9) Due to deforestation, researchers, expect the deer population to decline by 6 percent every year. If the current deer population is 12000, what is the approximate expected population size in 10 years from now ?

(A)  25000   (B)  48000    (C)  56000   (D)  30000

(10)  In 2000 the price of a house was $72600. By 2010 the price of the house has increased to 125598.

(A)  70%    (B)  62%    (C)  73%    (D)  90%

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

• Sat Math Practice
• SAT Math Worksheets
• PEMDAS Rule
• BODMAS rule
• GEMDAS Order of Operations
• Math Calculators
• Transformations of Functions
• Order of rotational symmetry
• Lines of symmetry
• Compound Angles
• Quantitative Aptitude Tricks
• Trigonometric ratio table
• Word Problems
• Times Table Shortcuts
• 10th CBSE solution
• PSAT Math Preparation
• Privacy Policy
• Laws of Exponents

Recent Articles

First Fundamental Theorem of Calculus - Part 1

Apr 17, 24 11:27 PM

Polar Form of a Complex Number

Apr 16, 24 09:28 AM

Conjugate of a Complex Number

Apr 15, 24 11:17 PM

Fraction of Amounts Practice Questions

Click here for questions, click here for answers.

GCSE Revision Cards

5-a-day Workbooks

Primary Study Cards

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Course: 7th grade   >   Unit 2

• Solving percent problems
• Equivalent expressions with percent problems
• Percent word problem: magic club

Percent problems

• Percent word problems: tax and discount
• Tax and tip word problems
• Percent word problem: guavas
• Discount, markup, and commission word problems
• Multi-step ratio and percent problems
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

• International
• Schools directory
• Resources Jobs Schools directory News Search

Mixed Worded Fractions Decimals Percentages Questions (Exam Style)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

20 December 2017

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

exactly what I was looking for thank you!

Empty reply does not make any sense for the end user

ColinDeanoDean

Looks good, with a good mix. Thanks.

julianamich7

Please could you provide the answers<br /> <br /> Thank you

ozzyshortstop34

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: