A percent change is measured from the amount before the change: the base. Name the base first.
1One multiplier carries the whole change
up 15%
down 20%
up 100%
down 5%
× 1.15
× 0.80
× 2.00
× 0.95
Start from 100%: 100% + 15% = 115% = ×1.15. 100% − 20% = 80% = ×0.80. Tax, tip, and markup go up; discount goes down.
2Undo by dividing
Taking 8% off $54 gives $49.68, which is wrong. To undo ×1.08, divide by 1.08.
3Two discounts do not add
$100−10% ($10)→$90−10% ($9)→$81
The first 10% takes $10 off $100. The second takes $9 off the new base of $90. Total off: $19, which is 19%, not 20%.
Repeated percents multiply: × 0.90 × 0.90 = × 0.81. They do not add.
4Name the base before you compute
discount% of the original price, never the sale pricetax% of the pre-tax totaltip% of the bill before the tipmarkup% of what the store paid, the costcommission% of the amount sold
Different words, one habit: point at the number the percent is measured against, then multiply.
