Find the whole given a part and its percent.
Free, timed SHSAT practice sets on finding the whole— every question includes a full worked explanation, and there's no account required.
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Here you know the part and its percent, and you need the whole. Since part = percent × whole, divide the part by the percent (as a decimal):
\(\text{whole} = \text{part} \div \text{percent}\)
Example: 84 students are 35% of a school. The whole school is \(84 \div 0.35 = 240\) students.
Another way: find 1% first, then multiply by 100. If 35% is 84, then 1% is \(84 \div 35 = 2.4\), and 100% is 240.
Traps:
Check your answer: \(0.35 \times 240 = 84\).
If 64% of the whole is $256.00, the whole is \(256 \div (64/100) = 256 \times 100 \div 64 = 400\). Check: 64% of $400.00 is $256.00. (Dividing by 36% instead of 64% (\(256 \times 100 \div 36\)) gives about $711.11. Adding 64% of 256 to 256 (\(256 \times 1.64\)) gives $419.84. Taking 64% of 256 instead of dividing (\(256 \times 64/100\)) gives $163.84.) The full goal is $400.00.
If 12% of the whole is 75, the whole is \(75 \div (12/100) = 75 \times 100 \div 12 = 625\). Check: 12% of 625 is 75. (Adding 12% of 75 to 75 (\(75 \times 1.12\)) gives 84. Finding the whole and then subtracting the part (\(625 - 75\)) gives 550. Adding the missing 88% as 88 players (\(75 + 88\)) gives 163.) There are 625 players in all.
If 85% of the whole is 306, the whole is \(306 \div (85/100) = 306 \times 100 \div 85 = 360\). Check: 85% of 360 is 306. (Dividing by 15% instead of 85% (\(306 \times 100 \div 15\)) gives 2040. Finding the whole and then subtracting the part (\(360 - 306\)) gives 54. Adding the missing 15% as 15 volunteers (\(306 + 15\)) gives 321.) There are 360 volunteers in all.