Finding a whole from a percentage
Work backwards from a known part and distinguish a count from a percentage.
Before you begin
- Percentages as proportions
- Division with decimals
Scale the known percentage to one hundred
If 30% of a collection contains 18 items, 18 is a part rather than the whole. One route is to divide by 30 to find one percent, then multiply by 100. Another is to solve 0.30 × whole = 18. Both routes reverse the original percentage calculation. Multiplying 18 by 0.30 would find a smaller part of the known part.
Find an unknown percentage
When both part and whole are known, divide the part by the whole and multiply by 100. The order matters because the whole is the reference amount. Use the result to check an inverse-percentage answer: the part divided by your proposed whole should give the stated percentage. In collection problems, also check that the whole is a sensible integer count.
Worked example
27 students represent 45% of a club. How many students are in the club?
Show the worked solution
- Let the whole club be n students. Then 0.45n = 27.
- Divide: n = 27 ÷ 0.45 = 60.
- Check: 45% of 60 is 27, and the whole exceeds the part.
60 students.
Try it yourself
12 of 48 seedlings flower. What percentage flower?
Common mistakes
- Recovering the whole requires division by the proportion.
- Do not confuse the amount already present with the amount still needed.
What can you explain now?
A tank contains 18 L when it is 30% full. Find its capacity and the amount needed to fill it.
Compare with the explanation
Capacity 60 L; another 42 L needed.
18 ÷ 0.30 = 60. Subtract the current 18 L from the 60 L capacity to get 42 L.
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Common Core mathematics standards ↗