TARA percentages: no-calculator methods
Build any percentage from 10% and 1%. Chain successive changes as multipliers instead of adding the percentages, and reverse a change by dividing, never by taking the percentage off again.
No-calculator moves
| Move | Example |
|---|---|
| Build from 10% and 1% | 17% of 340 = 34 + 3.4 × 7 = 57.8 |
| Swap the numbers | 8% of 25 = 25% of 8 = 2 |
| Chain changes | Up 10% then down 10%: 1.1 × 0.9 = 0.99, a 1% fall |
| Reverse a change | After a 25% rise to 150: 150 ÷ 1.25 = 120 |
Two discounts
Worked example A sale, then money off at the till
A coat is reduced by 20% in a sale. A further 15% is then taken off the sale price at the till. The final price is £68. What was the original price?
Multipliers: . So original, and the original price is £100.
Why this works: Two reductions multiply: the coat ends at 68% of its original price.
Why the tempting route fails: Adding the discounts to 35% and dividing 68 by 0.65 gives about £104.62.
A percentage of a percentage
Worked example Walkers who live close
A school has 1,250 pupils. 36% walk to school, and 40% of the walkers live within a mile. How many pupils walk and live within a mile, and what percentage of the school is that?
Walkers: of 1,250 is 125, so is . Within a mile: of 450 is 180. As a share of the school: , so .
Why this works: The second percentage applies to the walkers only, so the shares multiply: 180 pupils, 14.4%.
Why the tempting route fails: Adding 36% and 40% gives 76%: the 40% is of the walkers, not of the school.