how to solve word problems using percentage

Percentages in Word Problems

Hi, and welcome to this video lesson on percentages in word problems.

I know word problems are most people’s worst nightmare, but never fear, we’re going to learn how to turn a big, scary, word percentage problem into a 3-step breeze!

Okay, let’s look at our problem:

The bill for dinner is $62.00. The diners decide to leave their server a 20% tip. Determine the total cost of dining at the restaurant, including tip.

Okay, so what is our goal? We always want to understand the goal in a word problem. Our goal here is: “Determine the total cost of dining at the restaurant, including tip.” That means finding the cost of the meal and finding the cost of the tip so we can add them together. We already know the bill for dinner, so we’re halfway home. Let’s solve the rest of this problem in three easy steps.

STEP 1: Change the percentage to a decimal. Remove the % sign from the 20% and drop a period in front of the 20 so we have .20. We are allowed to do this because when we are finding percents, we are really multiplying a decimal number against another number. This is because 20 percent of a number can be written as a ratio of a part per hundred: \(20\% = \frac{20}{100}=.20\)

STEP 2: Multiply the bill by 0.20 to find the amount of the tip: \($62.00(0.20)=$12.40\)

STEP 3: Add the tip and bill to find the total. The total cost of dining will be the sum of the bill for dinner and the tip: \($62.00+$12.40=$74.40\)

The total cost is $74.40.

I hope that helps. Thanks for watching this video lesson, and, until next time, happy studying.

Practice Questions

  Lauren went to her favorite taco truck for lunch. Her bill was $24.80, and she wants to leave a 20% tip. Help Lauren determine what her tip should be.

The correct answer is Tip $4.96. In order to calculate Lauren’s tip, we need to determine what 20% of $24.80 is. Let’s convert 20% to a decimal, which would be 0.20. Now we can simply multiply \($24.80×0.20\) in order to determine the tip. \($24.80×0.20=$4.96\)

  Michael wants to mow lawns in order to make some extra money this summer, but he needs to find a lawn mower to use. Michael’s brother tells him that he will loan Michael his lawn mower if he gives him 4% of the money he makes on each lawn. If Michael agrees, and he earns 40 dollars on his first lawn mowed, how much money does he own his brother?

The correct answer is $1.60. In order to calculate 4% of 40, we need to convert 4% to a decimal. 4% is 0.04 as a decimal. Now we can multiply 0.04 and $40 in order to determine what Michael owes his brother. \(0.04×$40=1.6=$1.60\)

  In a study of 250 high school students, 90% of students have taken the driver’s education course. How many students have not taken the course?

15 students

20 students

25 students

30 students

The correct answer is 25 students. 90% of the students have taken the driver’s education course, and there are 250 students total. Let’s start by determining how many students have taken the course. To do this we can multiply \(0.9×250\) which equals 225. This means that 225 students have taken the course. If 225 students have taken the course, and there are 250 students total, we can find the difference between 225 and 250 in order to determine how many students have not taken the course. \(250-225=25\) students have not taken the course.

  Julian scored 90% on his math test. The test had 60 questions. How many questions did he answer correctly?

The correct answer is 54. If Julian answered 90% of the questions correctly, and there were 60 questions total, we can calculate 90% of 60 in order to determine how many questions he answered correctly. Let’s convert 90% to a decimal (0.9), and then multiply this by 60. \(0.9×60=54\) questions answered correctly

  A video game costs $45 before tax. If the sales tax is 5%, what will the total cost of the game be including tax?

The correct answer is $47.25. Let’s first calculate the tax. If the game costs $45 and the tax is 5%, we can multiply \(45×0.05\) in order to determine the tax. \(45×0.05 = 2.25\), which means there will be a $2.25 tax on the purchase. Now let’s add this tax to the price of the game in order to calculate the total cost of the game plus the tax. \($45+$2.25=$47.25\)

by Mometrix Test Preparation | This Page Last Updated: August 2, 2023

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Tricks to Solving Percentage Word Problems

How to Convert Percent to Decimal

Word problems test both your math skills and your reading comprehension skills. In order to answer them correctly, you'll need to examine the questions carefully. Always make sure you know what is being asked, what operations are necessary and what units, if any, you need to include in your answer.

Eliminate Extraneous Data

Sometimes, word problems include extraneous data that is not necessary to solve the problem. For example:

Kim won 80 percent of her games in June and 90 percent of her games in July. If she won 4 games in June and played 10 games in July, how many games did Kim win in July?

The simplest way to eliminate extraneous data is to identify the question; in this case, "How many games did Kim win in July?" In the example above, any information that doesn't deal with the month of July is unnecessary to answer the question. You are left with 90 percent of 10 games, allowing you to do a simple calculation:

0.9*10=9 games

Calculate Additional Data

Read the question portion twice to make sure you know what data you need to answer the question:

On a test with 80 questions, Abel got 4 answers wrong. What percentage of questions did he get right?

The word problem only gives you two numbers, so it would be easy to assume that the questions involves those two numbers. However, in this case, the question requires that you calculate another answer first: the number of questions Abel got right. You'll need to subtract 4 from 80, then calculate the percentage of the difference:

80-4=78, and 78/80*100=97.5 percent

Rephrase Difficult Problems

Remember that you can often rearrange problems to make them simpler. This is especially useful if you don't have a calculator available:

Gina needs to score at least 92 percent on her final exam to get an A for the semester. If there are 200 questions on the exam, how many questions does Gina need to get right in order to earn an A?

The standard approach would be to multiply 200 by 0.92: 200*.92=184. While this is a simple process, you can make the process even simpler. Instead of finding 92 percent of 200, find 200 percent of 92 by doubling it:

This method is particularly useful when you are dealing with numbers with known ratios. If, for example, the word problem asked you to find 77 percent of 50, you could simply find 50 percent of 77:

50*.77=38.5, or 77/2=38.5

Account for Units

Convert your answers into appropriate units:

Cassie works from 7 a.m. to 4 p.m. each weekday. If Cassie worked 82 percent of her shift on Wednesday and worked 100 percent of her other shifts, what percent of the week did she miss? How much time did she work in total?

First, calculate how many hours Cassie works per day, taking noon into account, then per week:

4+(12-7)=9 9*5=45

Next, calculate 82 percent of 9 hours:

0.82*9=7.38

Subtract the product from 9 for the total hours missed:

9-7.38=1.62

Calculate what percentage of the week she missed:

1.62/45*100=3.6 percent

The second question asks for an amount of time, which means you'll need to convert the decimal into time increments. Add the product to the other four work days:

7.38+(9*4)=43.38

Convert the decimal into minutes:

0.38*60=22.8

Convert the remaining decimal into seconds:

So Cassie missed 3.6 percent of her week, and worked 43 hours, 22 minutes and 48 seconds total.

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• Central New Mexico Communicty College: Percent Word Problems
• Basic Mathematics: Percentage Word Problems

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Basic "Percent of" Word Problems

Basic Set-Up Markup / Markdown Increase / Decrease

When you learned how to translate simple English statements into mathematical expressions, you learned that "of" can indicate "times". This frequently comes up when using percentages.

Suppose you need to find 16% of 1400 . You would first convert the percentage " 16% " to its decimal form; namely, the number " 0.16 ".

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Percent Word Problems

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Why does the percentage have to be converted to decimal form?

When you are doing actual math, you need to use actual numbers. Percents, being the values with a "percent" sign tacked on, are not technically numbers. This is similar to your grade-point average ( gpa ), versus your grades. You can get an A in a class, but the letter "A" is not a numerical grade which can be averaged. Instead, you convert the "A" to the equivalent "4.0", and use this numerical value for finding your gpa .

When you're doing computations with percentages, remember always to convert the percent expressions to their equivalent decimal forms.

Once you've done this conversion of the percentage to decimal form, you note that "sixteen percent OF fourteen hundred" is telling you to multiply the 0.16 and the 1400 . The numerical result you get is (0.16)(1400) = 224 . This value tells you that 224 is sixteen percent of 1400 .

How do you turn "percent of" word problems into equations to solve?

Percentage problems usually work off of some version of the sentence "(this) is (some percentage) of (that)", which translates to "(this) = (some decimal) × (that)". You will be given two of the values — or at least enough information that you can figure out what two of the values must be — and then you'll need to pick a variable for the value you don't have, write an equation, and solve the equation for that variable.

What is an example of solving a "percent of" word problem?

• What percent of 20 is 30 ?

We have the original number 20 and the comparative number 30 . The unknown in this problem is the rate or percentage. Since the statement is "(thirty) is (some percentage) of (twenty)", then the variable stands for the percentage, and the equation is:

30 = ( x )(20)

30 ÷ 20 = x = 1.5

Since x stands for a percentage, I need to remember to convert this decimal back into a percentage:

Thirty is 150% of 20 .

What is the difference between "percent" and "percentage"?

"Percent" means "out of a hundred", its expression contains a specific number, and the "percent" sign can be used interchangeably with the word (such as " 24% " and "twenty-four percent"); "percentage" is used in less specific ways, to refer to some amount of some total (such as "a large percentage of the population"). ( Source )

In real life, though, including in math classes, we tend to be fairly sloppy in using these terms. So there's probably no need for you to worry overmuch about this technicallity.

• What is 35% of 80 ?

Here we have the rate (35%) and the original number (80) ; the unknown is the comparative number which constitutes 35% of 80 . Since the exercise statement is "(some number) is (thirty-five percent) of (eighty)", then the variable stands for a number and the equation is:

x = (0.35)(80)

Twenty-eight is 35% of 80 .

• 45% of what is 9 ?

Here we have the rate (45%) and the comparative number (9) ; the unknown is the original number that 9 is 45% of. The statement is "(nine) is (forty-five percent) of (some number)", so the variable stands for a number, and the equation is:

9 = (0.45)( x )

9 ÷ 0.45 = x = 20

Nine is 45% of 20 .

The format displayed above, "(this number) is (some percent) of (that number)", always holds true for percents. In any given problem, you plug your known values into this equation, and then you solve for whatever is left.

• Suppose you bought something that was priced at $6.95 , and the total bill was $7.61 . What is the sales tax rate in this city? (Round answer to one decimal place.)

The sales tax is a certain percentage of the price, so I first have to figure what the actual numerical amount of the tax was. The tax was:

7.61 – 6.95 = 0.66

Then (the sales tax) is (some percentage) of (the price), or, in mathematical terms:

0.66 = ( x )(6.95)

Solving for x , I get:

0.66 ÷ 6.95 = x      = 0.094964028... = 9.4964028...%

The sales tax rate is 9.5% .

In the above example, I first had to figure out what the actual tax was, before I could then find the answer to the exercise. Many percentage problems are really "two-part-ers" like this: they involve some kind of increase or decrease relative to some original value.

Note : Always figure the percentage of change of increase or decrease relative to the original value.

• Suppose a certain item used to sell for seventy-five cents a pound, you see that it's been marked up to eighty-one cents a pound. What is the percent increase?

First, I have to find the absolute (that is, the actual numerical value of the) increase:

81 – 75 = 6

The price has gone up six cents. Now I can find the percentage increase over the original price.

Note this language, "increase/decrease over the original", and use it to your advantage: it will remind you to put the increase or decrease over the original value, and then divide.

This percentage increase is the relative change:

6 / 75 = 0.08

...or an 8% increase in price per pound.

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Percentage Word Problems 5th Grade

Welcome to our Percentage Word Problems. In this area, we have a selection of percentage problem worksheets for 5th grade designed to help children learn to solve a range of percentage problems.

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Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

• 50% = 0.5 = ½
• 25% = 0.25 = ¼
• 75% = 0.75 = ¾
• 10% = 0.1 = 1 ⁄ 10
• 1% = 0.01 = 1 ⁄ 100

Percentage Word Problems

How to work out percentages of a number.

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

• Percentage Of Calculator

This is the calculator to use if you want to find a percentage of a number.

Simple choose your number and the percentage and the calculator will do the rest.

Here you will find a selection of worksheets on percentages designed to help your child practise how to apply their knowledge to solve a range of percentage problems..

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

• spot the percentage problems where the aim is to use the given facts to find the missing percentage;
• solving percentage of number problems, where the aim is to work out the percentage of a number.

Each of the sheets on this page has also been split into 3 different worksheets:

• Sheet A which is set at an easier level;
• Sheet B which is set at a medium level;
• Sheet C which is set at a more advanced level for high attainers.

Spot the Percentages Problems

• Spot the Percentage 1A
• PDF version
• Spot the Percentage 1B
• Spot the Percentage 1C
• Spot the Percentage 2A
• Spot the Percentage 2B
• Spot the Percentage 2C

Percentage of Number Word Problems

• Percentage of Number Problems 1A
• Percentage of Number Problems 1B
• Percentage of Number Problems 1C
• Percentage of Number Problems 2A
• Percentage of Number Problems 2B
• Percentage of Number Problems 2C
• Percentage of Number Problems 3A
• Percentage of Number Problems 3B
• Percentage of Number Problems 3C

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

6th Grade Percentage Word Problems

The sheets in this area are at a harder level than those on this page.

The problems involve finding the percentage of numbers and amounts, as well as finding the amounts when the percentage is given.

• 6th Grade Percent Word Problems
• Percentage Increase and Decrease Worksheets

We have created a range of worksheets based around percentage increases and decreases.

Our worksheets include:

• finding percentage change between two numbers;
• finding a given percentage increase from an amount;
• finding a given percentage decrease from an amount.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

• Money Percentage Worksheets

Percentage of Number Worksheets

If you would like some practice finding the percentage of a range of numbers, then try our Percentage Worksheets page.

You will find a range of worksheets starting with finding simple percentages such as 1%, 10% and 50% to finding much trickier ones.

• Percentage of Numbers Worksheets

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

• Converting Fractions to Percentages

• Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

• Online Percentage Practice
• Ratio Part to Part Worksheets

These sheets are a great way to introduce ratio of one object to another using visual aids.

The sheets in this section are at a more basic level than those on this page.

How to Print or Save these sheets

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

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How to Solve Word Problems Involving the Percentage of a Number?

In this complete step-by-step guide, you will learn how to solve different types of word problems involving the Percentage of a Number.

Percentages are a common concept in mathematics, and they often appear in word problems. Solving word problems involving percentages can be challenging, but it’s a valuable skill to have.

A step-by-step guide to word problems involving the percentage of a number

Since percentages have no dimensions, it is known as dimensionless numbers. The percentage problems may have \(3\) quantities: the percent, the base, and the amount. The percent comes with the percent symbol \((\%)\) or the word “percent.” The base is the total amount. The amount is part of the whole.

Here is a step-by-step guide on how to solve word problems involving percentages:

• Read the problem carefully and identify the information given. This may include the percentage, the whole, and the part. Make sure you understand what is being asked in the problem.
• Identify the keywords or phrases that indicate a percentage is involved. Words such as “percent,” “percentage,” “out of \(100\),” or “per \(100\)” are clues that a percentage is involved.
• Write an equation to represent the information given in the problem.
• Use math operations to solve for the unknown value.
• Check your answer by plugging it back into the original equation and seeing if it is true.

Word Problems Involving the Percentage of a Number – Example 1

The cinema has \(230\) seats. \(161\) seats were sold for the animated movie. What percent of seats are sold?

Solution : 161 is a part of the number \(230\). Let \(x\) represent the percent to find a percent of \(161\) out of \(230\). Write a proportion for \(x\) and solve. \(\frac{161}{230}=\frac{x}{100}→161×100=230x→16100=230x→16100÷230=x→70=x\)

Word Problems Involving the Percentage of a Number– Example 2

There are \(30\) students in a class and 6 of them are girls. What percent are girls? Solution : \(6\) is a part of the number \(30\). Let \(x\) represent the percent to find a percent of \(6\) out of \(30\). Write a proportion for \(x\) and solve. \(\frac{6}{30}=\frac{x}{100}→6×100=30x→600=30x→600÷30=x→20=x\)

by: Effortless Math Team about 10 months ago (category: Articles )

Effortless Math Team

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Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

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Percent Word Problems

In these lessons we look at some examples of percent word problems. The videos will illustrate how to use the block diagrams (Singapore Math) method to solve word problems.

Related Pages More Math Word Problems Algebra Word Problems More Singapore Math Word Problems

How to solve percent problems with bar models? Examples:

• Marilyn saves 30% of the money she earns each month. She earns $1350 each month. How much does she save?
• At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?
• Bill bought cards to celebrate Pi day. He sent 60% of his cards to his friends. He sent 42 cards to his friends. How many cards did he buy altogether?
• Bruce cooked 80% of the pancakes at the pancake breakfast last weekend. They made 1120 pancakes. How many pancakes did Bruce cook?

Sales Tax and Discount An example of finding total price with sales tax and an example of finding cost after discount.

• Alejandro bought a TV for $900 and paid a sales tax of 8%. How much did he pay for the TV?
• Alice saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?

Percent Word Problems Example: There are 600 children on a field. 30% of them were boys. After 5 teams of boys join the children on the field, the percentage of children who were boys increased to 40%. How many boys were there in the 5 teams altogether?

Problem Solving - Choosing a strategy to solve percent word problems An explanation of how to solve multi-step percentage problems using bar models or choosing an operation. Example: The $59.99 dress is on sale for 15% off. How much is the price of the dress?

How to solve percent problems using a tape diagram or bar diagram? Example: An investor offers $200,000 for a 20% stake in a new company. What amount does the investor believe the toatl value of the business is worth at this time? How to use a tape diagram or bar diagram to find the answer?

• First draw a bar that represents the company’s whole value.
• Divide into 5 equal parts because 100%/20% = 5.
• Label one side with the percentages.
• Label the other side $200,000 across from 20% because that was given.
• Finish labeling the money side.
• Find solution.

Solve Percent Problems Using a Tape Diagram (Bar Diagram) Example: a) If $300 is increased by 25% what is the new amount? b) What is 19% of 120? c) Joe went to an athletic store to purchase new running shoes. To his surprise, the store was having a 20% off athletic shoes sale. He purchased a new pair of shoes that were regularly priced $60. How much did Joe pay for his shoes?

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25 Percentage Word Problems For Year 5 To Year 8 With Tips On Supporting Pupils’ Progress

Emma johnson.

Percentage word problems and the concept of calculating percentages first appears in Upper Key Stage 2. As pupils progress through school from KS2 to KS3, the skills they need to solve percentage word problems develop.

It is important to expose students to percentage word problems alongside any fluency work on percentages, to help them understand how percentages are used in real-life. To help you with this, we have put together a collection of 25 percentage word problems which can be used by pupils from Year 5 to Year 8. Don’t miss our downloadable word problems worksheet to develop these skills further!

How pupils develop the necessary skills to solve percentage word problems

Percentage word problems in the national curriculum, why are word problems important for children’s understanding of percentage , how to teach solving percentage word problems in ks2 and early ks3, percentage word problems for year 5, percentage word problems for year 6, percentage word problems for key stage 3, more word problems resources, percentage word problems faqs, all kinds of word problems four operations.

Download this free, printable pack of word problems covering all four operations; a great way to build students' problem solving skills.

Initially, pupils are introduced to the per cent symbol (%) in Year 5. At this stage they are expected to understand that percent relates to ‘number of parts per hundred’ and should be able to solve problems requiring knowing percentage and decimal form equivalents of simple fractions.

As pupils progress into Year 6, they should be able to recall and use equivalences between simple fractions, mixed numbers, decimals and percentages. They also need to be able to solve word problems involving percentages of amounts and percentage increase and decrease.

Moving into Key Stage 3, pupils continue to build on the percentage work from primary, to solve percent problems, interpreting percentages and percentage change; expressing one quantity as a percentage of another; comparing two quantities using percentages and working with percentages greater than 100%.

Concrete resources (such as percentages cubes) and visual images (such as bar models) are important during the early stages of learning and understanding percentages. Word problems for year 3 and word problems for year 4 will often include visual aids. Upper Key Stage 2 teachers and pupils often have the mistaken belief that concrete resources are only for children who are struggling; however, with a new topic, such as percentages, it is important all children are initially introduced to the topic through the use of visual and concrete aids.

Children are first introduced to percentage problems in Year 5. The National Curriculum expectations for percentages are that children will be able to:

Percentage in Year 5

• Recognise the percent symbol (5)  and understand that per cent relates to ‘number of parts per hundred’.
• Write percentages as a fraction with a denominator 100, and in its decimal form.
• Solve problems which require knowing percentage and decimal equivalents of \frac{1}{2},\frac{1}{4},\frac{1}{5},\frac{2}{5},\frac{4}{5} , and fractions with a denominator of a multiple of 10 or 25.

Percentage in Year 6

• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
• Solve problems involving the calculation of percentages (for example, measures and such as 15% of 360) and use percentages for comparison.

Percentage in Key Stage 3

• Define percentage as ‘number of parts per hundred’
• Interpret percentages and percentage changes as a fraction or a decimal. Interpret these multiplicatively.
• Express one quantity as a percentage of another.
• Compare two quantities using percentages.
• Work with percentages greater than 100%.
• Interpret fractions and percentages as operators.

Percentage word problems will often include other skills, such as fraction word problems , multiplication word problems , addition word problems , subtraction word problems and division word problems .

Percentage word problems help children to develop their understanding of percentages and the different ways percentages are used in everyday life. Taken out of context, percentages can be quite an abstract concept, which some children can find quite difficult to understand. 

Real-life problems involving percentages enable students to see how they will make use of this key skill outside the classroom.

As with all word problems, students need to learn the skills required to solve percentage word problems. It’s important that children make sure they have read the questions carefully and thought about exactly what is being asked and whether they have fully understood this. They then need to identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which they can use to help them. Even pupils in Key Stage 3 can benefit from drawing a quick picture, to understand what a word problem is asking.

Third Space Learning’s online, one-to-one tutoring programmes work to build students’ maths fluency and reasoning skills. Personalised to the needs of each individual student, our programmes fill gaps and build students’ confidence in maths.

Percent word problem example :

A box of cupcakes sold by a bakery cost £3.40.

Due to the increased costs involved with running a bakery, the owner has decided to increase the price of everything sold by 20%.

How much will a box of cupcakes cost once the price has been increased?

How to solve step-by-step:

What do you already know?

–        We know that the original price of a box of cupcakes is £3.40.

–        If the price of the box is being increased by 20%, we need to work out how much 20% of £3.40 is.

–        To do this, we need to work out how much 10% of £3.40 is. We therefore need to divide £3.40 by 10 = £0.34

–        To calculate what 20% is, we need to multiply the £0.34 by 2 = £0.68

–        Finally, we need to add the 20% (£0.68) onto the original price.

–        £3.40 + £0.68 = £4.08

How can this be represented pictorially?

• We can draw a bar model to represent what 10% of £3.40 equals.
• Once we know what 10% of £3.40 is (34p), we can double it to calculate 20% of £3.40 (68p).
• We can then add this on to the original price of £3.40.
• £3.40 + 68p = £4.08.

To solve word problems for year 5 , children need to be able to convert fractions to percentages and calculate fractions of an amount.

Gemma saves \frac{1}{2} of her pocket money every week.

She receives £5 per week and is saving to buy a game costing £25.

• What percentage does she save each week?
• How long will it take her to save for the game?
• She saves 50% of her pocket money each week

Gemma saves £2.50 per week.

£2.50 x 10 = £25

Sam gives \frac{4}{10} of his sweets to Ahmed.

What percentage of the sweets does he keep for himself?

Answer : 60%

  \frac{4}{10} =  \frac{40}{100} = 40%

100 – 40 = 60%

A school football team has 11 players and 5 substitutes.

  \frac{3}{4} of the players are boys, the rest are girls.

What percentage are girls?

Answer: 25%

\frac{3}{4} of 16 are boys

  \frac{1}{4} are girls

  \frac{1}{4} = 25%

Children in Year 5 voted on their favourite food.

35% of children voted for pizza.

60 children took part in the survey.

How many voted for pizza?

Answer : 21 children 

10% of 60: 60 ÷ 10 = 6

5% of 60: Half of 10% (6) = 3

30%: 6 x 3 = 18

35% = 18 + 3 = 21

Ben was given a maths worksheet to complete for his homework.

He got  \frac{6}{10} of the maths problems correct

If there were 20 questions on the paper:

• How many questions did he get right?
• What percentage did he score?

  \frac{1}{10} of 20  = 2

  \frac{6}{10} of 20  = 12

• 60% correct

  \frac{12}{20} =  \frac{60}{100} .

An ice cream seller has been researching the most popular ice creams.

He knows the percentage of each flavour of ice cream sold, but wants to work out how many of each flavour were sold.

80 ice creams were sold in total.

40% vanilla

25% strawberry

20% cookie dough

15% mint choc chip

How many of each ice cream flavour were sold?

20 strawberry

16 cookie dough

12 mint choc chip

10% of 80 = 8 ice creams

5% of 80 = 4 ice creams

Vanilla: 4 x 8 = 32

Strawberry: 2 x 8 = 16. 16 + 4 = 20

Cookie dough: 2 x 8 = 16

Mint choc chip: 8 + 4 = 12

Pupils in Year 5 held a vote on where to go for their next school trip.

The vote was between the zoo and the aquarium.

90 children voted. 

40% voted for the zoo

How many pupils voted for the aquarium?

Answer : 54 children

60% voted for the aquarium

10% of 90 = 9 children

60% = 6 x 9 = 54 children

The price of burgers being sold by a burger van have increased by 25%

If the original price was £2 per burger. How much are the burgers now?

Answer : £2.50

25% of £2 = £2 ÷ 4 = 50p

£2 + 50p = £2.50

Word problems for year 6 involve solving problems involving equivalence between fractions, decimals and percentages; calculation of percentages and using percentages for comparison. Year 6 students will also tackle multi-step problems .

A rugby game lasts for 80 minutes.

A player is on the pitch for 85% of the game.

How long is he on the pitch for?

Answer : 68 minutes

10% of 80  = 8 minutes

5%  = Half of 8 minutes = 4 minutes

80% = 8 x 8 = 64 minutes

64 + 4 = 68 minutes

There are 480 pupils in a primary school.

15% in foundation

25% in Key Stage 1

How many pupils are in Key Stage 2?

Answer : 288 pupils

In foundation there are 15% + 25% (40% of the pupils)

Therefore, 60% of pupils are in KS2

10% of 480 = 48 pupils

60% = 6 x 48 = 288 pupils

A pizza restaurant decided to add a 15% increase to the cost of all their pizzas.

The cost of a meat feast pizza before the increase was £12.60

What is the new price of the pizza?

Answer : £14.49

10% of £12.60 = £1.26

5% = Half of £1.26 = £0.63

15% = £1.26 + £0.63 = £1.89

New price: £12.60 + £1.89 = £14.49

Oliver was shopping for a new pair of jeans.

The jeans were 15% off  in the sale, but the new sale price sticker had fallen off.

The original price of the jeans was £35.

How much did they cost in the sale?

Answer : £29.75

10% of £35 = £3.50

5% = Half of £3.50 = £1.75

35% = £3.50 + £1.75 = £5.25

New price: £35 – £5.25 = £29.75

200g of sugar is needed for a chocolate brownies recipe.

A 1kg bag of sugar is used.

25% of the remaining sugar is used to bake a cake too.

How much sugar was used to bake the cake?

Answer : 200g sugar

 200g sugar used for brownies, therefore 1000g – 200g = 800g remaining

25% of 800g = 800 ÷ 4 = 200g

Mr Jones bought a second hand car for £12,400

A year later, it had decreased in value by 15%

What was the value of the car after a year?

Answer : £10,540

10% of 12,400 = £1,240

5%  = half of £1240 = £620

15% = 1240 + 620 = £1,860

Value after a year = 12,400 – 1860 = £10,540

The number of visitors to a theme park in 2021 was 286,000.

The following year, there was a 24 percent increase in visitors.

How many visited the theme park in 2022?

Answer : 354,640 visitors

10% of 286,000 = 28,600

20% = 2 x 28,600 = 57,200

1% of 286,000 = 2,860

4% = 4 x 2860 = 11,440

24% = 57,200 + 11,440 = 68.640

Total number of visitors: 286,000 + 68,640 = 354,640

A library has 16,200 books

55% are fiction and 45% are non-fiction

968 non-fiction books are taken out in one week.

How many non-fiction books are left in the library, from the books which were there at the start of the week? 

Answer : 6,322 non-fiction books

10% of 16,200 = 1,620

40% = 1,620 x 4 = 6,480 books

5% = half of 1,620 = 810

45% = 6,480 + 810 = 7,290

7,290 – 968 = 6,322

In Key Stage 3, the work pupils carry out on percentages, builds upon the percentage skills developed in primary. Students need to be able to solve percent word problems involving interpreting percentages and percentage change as a fraction or decimal; expressing one quantity as a percentage of another; comparing two quantities using percentages; working with percentages greater than 100% and interpreting fractions and percentages as operators.

Jasmine wins £600

She gives 30% to her sister and 20% to her friend.

She keeps the rest.

How much does each person have?

Sister: £180

Friend: £120

Jasmine: £300

She gives 30% to her sister.

10% of £600 = £60

30% = 3 x 60 = £180

She gives 20% to her friend.

20% = 2 x 60 = £120

She must keep 50% for herself, if she has given 30% and 40% away.

50% of 600 =  \frac{1}{2} of 600 = £300

A car is reduced in the sale by 15%

If the original price was £18,500, what is the price of the car now?

Answer: £16,225

10% of 18500 = 1,850

5% = half of 1,850 = £925

15% = 1,850 + 925 = £2,275

New price: 18,500 – 2,275 = £16,225

Sales tax in Florida is 6%

Maisie has bought a pair of jeans, 3 T shirts and a jacket, which came to $150

How much will she have to pay, once she has added on the sales tax?

Answer: $159

1% of 150 = 1.5

6% = 6 x 1.5 = $9

150 + 9 = $159

A packet of biscuits is 300g

As a special offer, the biscuits currently have an extra 15% free.

How many grams of biscuit do you get with the special offer?

Answer : 345g

10% of 300 = 30g

5% = half of 30 = 15g

15% = 30 + 15 = 45g

New weight: 300 + 45 = 345g

Jason is travelling to Birmingham from Manchester.

His average speed is 62 miles per hour

On the return journey, the traffic on the M6 is terrible and his average speed it reduced by 35%

What is his average speed on the return journey?

Answer : 40.3mph

10% of 62 = 6.2mph

30% = 6.2 x 3 = 18.6mph

5% = half of 6.2 = 3.1mph

35% = 18.6 + 3.1 = 21.7mph

62 – 21.7 = 40.3 mph

Mr Andrews bought a car in January 2021 for £15000.

By January 2022 his car had depreciated in value by 20%.

By January 2023, his car had depreciated in value by another 30%.

What was the value of his car in January 2023?

Answer : £8400

January 2022

20% of £15000 = £3000, so the value of the car is £12000.

January 2023

30% of £12000 = £3600, so the value of the car is £8400.

Alternative method – using decimal multiplier

20% decrease means 80% of January 2021 value – decimal multiplier of 0.8

30% decrease means 70% of January 2022 value – decimal multiplier of 0.7

15000 x 0.8 x 0.7 = £8400.

In her half term test, Jasmine did a French test and scored 15 out of 30.

In her next half term test, Jasmine scored 21 out of 30 in her French test.

By what percentage did Jasmine improve?

Answer : 40% improvement

Percentage change

= 21 – 15/15  x 100

= 6/15  x 100 = 40% improvement.

In 2021, a company made a profit of $600000.

In 2022, the same company made a profit of $1350000.

By what percentage had their profit increased?

Answer : 125% improvement

= 1350000 – 600000/600000 x 100

= 750000/600000 x 100 = 125% improvement.

In 2022, Thomas earned £1800 a month for his job.

As part of his annual review in February 2023, he is going to ask for a pay rise of 3.5%.

If the pay rise is agreed, what will Thomas’ annual salary be?

Answer: £22356

3.5% of £1800 = £63

So new monthly salary would be £1863

£1863 x 12 = £22356.

Alternative method 1

£1800 x 12 = £21600

3.5% of £21600 = £756

£21600 + £756 = £22356.

Looking for more word problems practice questions? Take a look at our collection of addition and subtraction word problems , time word problems , money word problems and ratio word problems . Teaching percentages to KS3 or KS4? Check out our percentage worksheets here.

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

There are different types of percentage problems. If you want to find the percentage of an amount, it can be calculated by writing the percentage as a decimal or a fraction and then multiplying it by the amount.

Pupils in Year 5 held a vote on where to go for their next school trip. The vote was between the zoo and the aquarium. 90 children voted.  40% voted for the zoo How many pupils voted for the aquarium?

1. Calculating a discount when shopping 2. Understanding bank interest rates 3. Understanding your grades in school

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• Physics Mechanics
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• Finance Simple Interest Compound Interest Present Value Future Value
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• Conversions Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time
• Pre Algebra
• One-Step Addition
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• Solve by Factoring
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• Age Problems
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• Dice Problems
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• Pre Calculus
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Most Used Actions

Number line.

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{Bob's\:age\:is\:twice\:that\:of\:Barry's.\:Five\:years\:ago,\:Bob\:was\:three\:times\:older\:than\:Barry.\:Find\:the\:age\:of\:both.}
• \mathrm{Two\:men\:who\:are\:traveling\:in\:opposite\:directions\:at\:the\:rate\:of\:18\:and\:22\:mph\:respectively\:started\:at\:the\:same\:time\:at\:the\:same\:place.\:In\:how\:many\:hours\:will\:they\:be\:250\:apart?}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

word-problems-calculator

• High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,... Read More