How to find the whole from a percent

When you know a part and its percent, work back to 100%. If 15 is 30%, then 5 is 10%, and the whole is 50.

The idea: work back to 100%

Most percent questions give the whole and ask for a part. This one is the other way round. You know a part, and you know what percent it is. The job is to find the whole, which is always 100%.

For example, “15 is 30% of what number?” Here 15 is the part and 30% is its percent. The answer is the whole: the number that 15 is 30% of.

A good first step is to ask “is the whole bigger or smaller than the part?” Since 30% is less than 100%, the whole must be bigger than 15. That check catches most mistakes.

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.

A double number line: 30% matches 15, so 10% matches 5 and 100% matches 50.

The bar model: the shaded 30% is 15, so the whole bar is 50.

25% is a quarter: four lots of 8 make the whole, 32.

Method 1: find 1%, then 100%

Divide the part by the percent to find 1%. 15 ÷ 30 = 0.5, so 1% is 0.5.
Multiply by 100 to find 100%. 0.5 × 100 = 50.
Check: 30% of 50 is 15. Correct.

This method always works, even with awkward percents like 37%. It is the method behind the formula whole = part ÷ percent × 100.

Method 2: find a friendly percent first

When the percent is a multiple of 10 or 25, a friendlier step is quicker. If 30% is 15, then 10% is a third of that: 5. Ten lots of 10% make 100%, so the whole is 50.

For example, 8 is 25% of what? 25% is a quarter, so four quarters make the whole: 8 × 4 = 32. Children who know the benchmark percents can do many of these in their head.

Find the whole

Type the part and its percent. The calculator shows each step, so you can check your own work.

Method 3: write an equation

Older children can write the question as an equation. “15 is 30% of what?” becomes 15 = 0.3 × w. Divide both sides by 0.3: w = 15 ÷ 0.3 = 50.

This is the method grade 7 uses for harder problems, such as finding an original price after a discount. The percent of a number page shows the same equation the other way round.

Which kind of percent question is it?

There are three kinds of percent question, and they use the same three numbers: the part, the whole and the percent. The question tells you which one is missing.

“What is 30% of 50?” The part is missing. See percent of a number.
“15 is what percent of 50?” The percent is missing. See finding the percent.
“15 is 30% of what?” The whole is missing. That is this page.

The words “of what” or “of what number” are the clue that the whole is missing.

Finding the whole in real life

This skill answers everyday questions. A child saved $12, which is 40% of the price of a game. What does the game cost? 10% is $3, so 100% is $30.

It also works backwards from sales. A jacket costs $60 after 25% off, so $60 is 75% of the original price. 25% is $20, so the original price was $80.

Quiz: find the whole

Find the whole from a part and its percent. Type the number only.

Where this fits: percentages step by step

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.

“I spent 6 dollars, and that was 20% of my money. How much did I have?”
“What is 10% then?” (3 dollars.)
“How many tens make 100%?” (10.) “So 10 × 3 is …” (30 dollars.)
“Check: is 20% of 30 equal to 6?” (Yes.)
“Is the whole bigger or smaller than the part?” (Bigger.)

More worked examples

Example 1: a friendly percent

12 is 50% of what? 50% is half, so the whole is double: 24.

Example 2: using 10%

18 is 60% of what? 10% is 18 ÷ 6 = 3, so 100% is 30.

Example 3: using 1%

21 is 35% of what? 1% is 21 ÷ 35 = 0.6, so 100% is 60.

Example 4: a price

$9 is 15% of a bill. 5% is $3, so 100% is $60.

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.

10 is 50% of what?
6 is 25% of what?
4 is 10% of what?
9 is 30% of what?
14 is 20% of what?
12 is 75% of what?
3 is 1% of what?
45 is 90% of what?
$8 is 40% of a price. What is the price?
Stretch: 18 is 120% of what?

Show the answers

Common mistakes

Finding the percent of the partWorks out 30% of 15 = 4.5.Fix: the part is 30% of the answer, so the answer must be bigger than 15.

Multiplying by the percentWrites 15 × 30 = 450.Fix: divide by the percent to find 1%, then multiply by 100.

Forgetting the last stepStops at 1% or 10%.Fix: always go all the way to 100%.

How to teach it at home

Pocket money puzzles

“I spent $4. That was 20% of my money. How much did I have?”

Battery maths

“The battery is 50% and has 3 hours left. How long when full?”

Reverse sales

Look at sale prices and work out the original price together.

By grade

Grade 6 (6.RP.A.3c): find the whole, given a part and the percent.
Grade 7 (7.RP.A.3): multi-step problems, like original prices before a discount.
In India, this comes in class 7 and class 8 maths.
Next: percent change.

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