Reverse percentage problems · grades 6–7
Finding the Whole from a Percent Worksheet Generator
Practice working backward from a known part and percent to the original whole. Problems are generated from an exact whole first, so students are not forced into accidental rounding.
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Finding the Whole Practice
Finding the whole · Multiples of 5% · Seed 261301
306 is 45% of ____
95 is 50% of ____
33 is 5% of ____
238 is 35% of ____
442 is 85% of ____
448 is 70% of ____
99 is 20% of ____
460 is 80% of ____
247 is 50% of ____
516 is 75% of ____
32 is 5% of ____
261 is 45% of ____
44 is 80% of ____
133 is 70% of ____
72 is 75% of ____
22 is 55% of ____
231 is 55% of ____
117 is 45% of ____
Finding the whole when you know a percent
When a number is a percent of an unknown whole, divide the known part by the percent written as a decimal. You can also write a proportion, part over whole equals percent over 100, and solve for the whole. Estimate first: if the part is 30% of the whole, the whole must be greater than the part.
Worked examples
- 24 is 30% of what number? 24 ÷ 0.30 = 80.
- 25% of a number is 20. Since 25% is one fourth, the whole is four groups of 20, which is 80. Dividing gives the same result: 20 ÷ 0.25 = 80.
- With a proportion: 15 is 60% of w, so 15/w = 60/100. Then w = 15 × 100 ÷ 60 = 25.
Common slips
- Multiplying instead of dividing. 24 × 0.30 = 7.2 finds 30% of 24, not the whole.
- Using 3 instead of 0.30 for 30%.
- Skipping the estimate, so an answer smaller than the part goes unnoticed.
How to use this worksheet
Have students estimate the whole before calculating and compare the estimate with the answer key. A result that is smaller than the part is a signal to recheck the setup.
Common Core connection
- 6.RP.A.3.c · Find a percent of a quantity and solve problems involving the whole or percent.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Ask students to estimate the whole before calculating. If 25% is 20, the whole must be larger than 20 and should be near four groups of 20.
Keep the rate set narrow when the learning goal is reverse reasoning rather than percent-fact recall.
Once the structure is stable, mix this skill with finding-the-percent problems so students must decide which quantity is missing.
Show both setups for '24 is 30% of what number?': 24 divided by 0.30 equals 80, and the proportion 24 over w equals 30 over 100 gives w equals 2400 divided by 30, which is 80.
If a student multiplies (24 times 0.30 equals 7.2), point out that the whole must be larger than the part whenever the percent is below 100%.
More percentage practice
Switch the missing quantity
Frequently asked questions
Why are the missing-whole answers clean?
The generator chooses the whole first, calculates an exact part, and then hides the whole.
Which standard does this practice?
CCSS 6.RP.A.3c and 7.RP.A.3: given a part and a percent, find the whole, including as a multistep percent problem.
Why is the answer usually bigger than the number in the question?
Because that number is only a percent of the whole. For any rate under 100%, the whole is always larger than the given part.
Can I use benchmark percentages only?
Yes. Benchmark mode focuses on 10%, 20%, 25%, 50%, and 75%.
Does custom mode support 1% to 200%?
Yes. Custom mode uses whole-number percentages within that range.
Can the answer key be removed for student copies?
Yes. Turn off Include answer key before downloading the PDF.