Find 35% of 80 mentally
- 10% of 80 is 8; 30% is 24.
- 5% is half of 10%, so it is 4.
- 35% is 24 + 4 = 28.
Find percents with mental math
Build a useful percentage from benchmarks.
Start with friendly benchmarks
10% is one tenth, so divide by 10. 1% is one hundredth, so divide by 100. 50% is half, 25% is one quarter, and 75% is three quarters. These connections make an estimate before any calculator work and offer an independent check.
Scale the whole by a percent.
Predict first. Change one value, then explain what stays the same and what changes. All bars use the same scale within a model.
Compose and scale percentages
Find 15% as 10% + 5%, and find 5% by halving 10%. Find 30% by tripling 10%, or 12% as 10% + 2%. Each percent must be taken from the same reference whole before the amounts are added. Choose a decomposition that suits the number.
Estimate without pretending it is exact
19.8% of 51 is close to 20% of 50, or 10. The exact product is 10.098. State which result is an estimate. In a shopping context, a sensible estimate should help you catch an error such as moving the decimal the wrong direction.
Worked examples
Find 12.5% of 64
- 12.5% = 1/8.
- 64 ÷ 8 = 8.
- Check: 25% is 16, and half of that is 8.
Guided Practice
Find 17% of 200 without a calculator.
A first hint
Build 17% from 10%, 5% and 2%.
Compare your reasoning
10% = 20, 5% = 10, 2% = 4. The total is 34.
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Connections
Find 48% of 75 in two ways: 50% minus 2%, and a decimal product. Explain which you prefer.
Use it in Extreme Couponing
Record the whole, the percent multiplier and the result with units. For each coupon, use the eligible amount at that step. State whether a resale percentage means percent of cost or markup on cost.