HSPT: Percents: find the whole from a part
Learn to find a whole amount when you know a part of it and what percent that part is.
If you know a part and its percent, how do you find the whole amount?
Short answer
Divide the part by the percent written as a decimal or fraction. Then check by taking that percent of your answer.
Know first: Percents as decimals and fractions, Dividing by a decimal
Step 1 of 5
The part is known, the whole is missing
Most percent questions give you a whole and ask for a part: What is 30% of 60? A reverse-percent question flips that. It gives you the part and the percent, and asks for the whole: 18 is 30% of what number?
Write it as an equation: part = percent × whole. To find the whole, divide the part by the percent written as a decimal or fraction.
| Percent | Fraction | To get the whole from the part |
|---|---|---|
| 25% | 1/4 | Multiply by 4 |
| 40% | 2/5 | Divide by 2, then multiply by 5 |
| 60% | 3/5 | Divide by 3, then multiply by 5 |
| 75% | 3/4 | Divide by 3, then multiply by 4 |
Divide by the top of the fraction to find one share, then multiply by the bottom to get the whole.
Step 2 of 5
Divide the part by the percent
Worked example: Finding the whole team
18 players are 30% of a team. How many players are on the whole team?
- A60
- B5.4
- C54
- D48
- 1
Set up
30% of the team is 18, so 0.3 × team = 18.
- 2
Divide
team = 18 ÷ 0.3 = 180 ÷ 3 = 60.
- 3
Check
30% of 60 is 18. And 60 is bigger than 18, as it should be.
- 4
See why the other choices are there
5.4 finds 30% of 18, which runs the percent forward. 54 multiplies 18 by 3. 48 adds 30 to 18.
Answer
60 players
Find the wrong step
A student solves: 27 is 75% of what number?
- 1
Writes 75% as the fraction 3/4.
- 2
Finds 3/4 of 27 and gets 20.25.
What went wrong
That takes 75% of the part. The question says 27 is the part, so the whole has to be bigger than 27.
- 3
Answers 20.25.
The fix
27 is 3 shares of 4, so one share is 27 ÷ 3 = 9 and the whole is 9 × 4 = 36. Check: 3/4 of 36 is 27.
Step 3 of 5
Recover the whole, then check
Check yourself · Question 1
12 is 25% of what number?
Answer: B
25% is 1/4, so 12 is one quarter of the whole. The whole is 12 × 4 = 48. Check: 25% of 48 is 12.
Trap answer: 3
Taking the percent of the part
- Why it looks right
- Finding a percent of a number is the move you practice most, so it happens on autopilot.
- Why it's wrong
- The question already tells you 12 is the part. The whole must be larger than 12, and 3 is smaller.
- The right answer
- 48, because 25% of 48 is 12.
Check yourself · Question 2
45 students are 60% of a grade. How many students are in the whole grade?
Answer: C
60% is 3/5. So 45 is 3 shares of 5: one share is 45 ÷ 3 = 15, and the whole is 15 × 5 = 75. Check: 60% of 75 is 45.
Common mistake
"I find the percent of the number I was given."
- Why it's tempting
- Most percent questions ask for a percent of a number, so the same move feels right here.
- Do this instead
- Ask which number is the part and which is the whole. If the part is given, divide by the percent, then check that the whole is bigger.
Step 4 of 5
What to remember
Remember
- When the part and the percent are given, the whole is part ÷ percent.
- Friendly percents work as fractions: divide by the top, multiply by the bottom.
- Check by taking the percent of your answer; you should get the part back.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
In the practice question, which number was the part, and how did you check your whole?