Read a Percent as Parts per Hundred
Find the part of a batch represented by a percent.
Supplied materials
- Paper or a note app.
- Fictional batch: 40 cups in total, of which 25% are blue paint. Work only with the supplied numbers.
Learn the idea
Percent means per hundred. Twenty-five percent names 25/100 of the total, which is equivalent to 1/4. The total batch, not the other ingredient alone, is the whole used to calculate the percent.
Multiply the total by the percent fraction to find the blue amount. The remaining amount is the total minus blue. These two amounts should add back to the whole; a part cannot exceed this whole when the percent is between zero and one hundred.
- Write 25% = 25/100 = 1/4.
- Find one quarter of 40 cups by dividing 40 by 4.
- Find the nonblue remainder and check both amounts sum to 40.
See the method in action
25% of 40 is (25/100) × 40 = 10 cups blue. The remaining 40 − 10 = 30 cups are nonblue, and 10 + 30 = 40.
Check your reasoning
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See the answer and explanation
12 cups
40% = 40/100 = 2/5. Two fifths of 30 is 30 ÷ 5 × 2 = 12 cups blue. The other 18 cups complete the 30-cup total.
Take it further
Keep the 30-cup total but change blue to 20%. Then 20/100 × 30 = 6 cups blue, half the blue amount at 40%. The remainder becomes 24 cups.
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