Percent word problems

Every percent word problem uses a part, a whole and a percent. Find which one is missing, draw a bar, then calculate.

Three numbers in every problem

Read the story and look for three things: the whole (the total, often after “of”), the part (a piece of it) and the percent. Two are given, and the question asks for the third.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

40%100%2460percentamount
24 of 60 children walk: the shaded part is 40% of the bar.
percentamount0%030%9100%30
If 9 children are 30% of a class, the class has 30 children.
Week 1: 20 cmWeek 4: 25 cm
A plant grows 5 cm from 20 cm: a 25% increase.

Four steps for any word problem

  1. Read the story twice. What is the question really asking?
  2. Label the part, the whole and the percent. Mark the missing one with a question mark.
  3. Draw a bar or a double number line.
  4. Calculate, then check the answer makes sense in the story.

Draw a bar model

A bar model shows the whole as a long bar, marked 0% to 100%. Shade the part. The picture makes it clear what is known and what is missing.

For example, “24 of the 60 children walk to school. What percent walk?” Draw a bar for 60 children and shade 24. 24 ÷ 60 = 0.4, so 40% walk.

Check an answer

Choose the question type, type the two numbers you know, and see each step.

Change stories

Some problems describe a change: a price goes up, a score improves, a plant grows. Find the change, then divide by the starting amount.

For example, a plant grows from 20 cm to 25 cm. The change is 5 cm, and 5 ÷ 20 = 25%. See percent change for more.

Money stories: discounts, tax and tips

Shopping problems often have two steps. First find the percent of the price, then add or subtract it. For example, a $50 game is 20% off: $10 off, so it costs $40.

Look for the small words: “off” means subtract, “tax” and “tip” mean add. The lessons on discounts, sales tax and tips go further.

Check that the answer makes sense

A quick estimate catches most mistakes. If 30% of the class is 9 children, the class must be bigger than 9. An answer of 2.7 cannot be right.

Also check the units. A percent question should end in %, a money question in dollars, and a count of people in whole numbers.

Quiz: percent word problems

Read each story and type the answer.

Where this fits: percentages step by step

  1. What is a percent
  2. Percent to fraction
  3. Fraction to percent
  4. Percent to decimal
  5. Decimal to percent
  6. Comparing fractions, decimals and percents
  7. Benchmark percents
  8. Percent mental math
  9. Over 100% and under 1%
  10. Percent of a number
  11. Finding the percent
  12. Finding the whole
  13. Percent change
  14. Percent increase and decrease
  15. Discounts and sale price
  16. Sales tax
  17. Tips
  18. Simple interest
  19. Markup, commission and percent error
  20. Percent word problems (this page)

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “There are 30 children, and 20% have a dog. What is the whole?” (30.)
  2. “What is the percent?” (20%.)
  3. “What is missing?” (The part.)
  4. “So how many have a dog?” (6.)
  5. “Does 6 make sense? Is it less than 30?” (Yes.)

More worked examples

Example 1: the part

A class of 25 has 40% girls. 0.4 × 25 = 10 girls.

Example 2: the percent

Ali scored 18 out of 24. 18 ÷ 24 = 0.75 = 75%.

Example 3: the whole

12 apples are 20% of a box. 10% is 6, so the box has 60.

Example 4: a change

A $40 price rises to $46. Change $6. 6 ÷ 40 = 15%.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 20% of 40 students wear glasses. How many?
  2. 15 out of 20 is what percent?
  3. 6 is 25% of what?
  4. A $30 shirt is 10% off. Price?
  5. $50 with 8% tax
  6. A score goes from 40 to 50. Percent increase?
  7. A tank holds 80 L and is 35% full. How much water?
  8. 9 of 36 marbles are red. Percent red?
  9. In a group, 45 people are 90%. Whole group?
  10. Stretch: a price drops from $80 to $68. Percent decrease?
Show the answers
  1. 8
  2. 75%
  3. 24
  4. $27
  5. $54
  6. 25%
  7. 28 L
  8. 25%
  9. 50
  10. 15%

Common mistakes

Mixing up the part and the wholeDivides 60 by 24.Fix: divide the part by the whole: 24 ÷ 60.
Answering the wrong questionGives the discount, not the price.Fix: re-read the question before writing the answer.
Skipping the checkWrites 2.7 children.Fix: people must be whole numbers; check the calculation.

How to teach it at home

Story swap

Make up percent stories about your family and swap them.

Sports stats

Turn match stats into percents: 7 goals from 10 shots.

Survey

Ask friends a question and work out the percent who said yes.

By grade

More for each grade: Grade 6 math and the CBSE class 6 maths guide; Grade 7 math and the CBSE class 7 maths guide.

Worksheets and practice

Percent word problems worksheet, page 1

Percent word problems worksheet: printable PDF with an answer key. · Make a fresh test

Percent practice · percent calculator · fraction, decimal and percent converter · percentage quiz · percent levels · percent games · percentages for kids

Last reviewed

Questions parents ask

How do you solve percent word problems?

Find the part, the whole and the percent, decide which is missing, draw a bar, then multiply or divide.

How do you know which number is the whole?

The whole is the total amount, often the number after the word “of”.

When do you multiply and when do you divide?

Multiply to find the part. Divide to find the percent (part ÷ whole) or the whole (part ÷ percent).

What are two-step percent problems?

Problems like discounts and tax, where you find a percent and then add or subtract it.

What grade learns percent word problems?

Grades 6 and 7, under Common Core 6.RP.A.3c and 7.RP.A.3.