Unit Rates & Better Percents
Grades 6–8 Ratios Percents
A unit rate sets the bottom of the ratio to 1: "60 miles per 1 hour." Divide the top by the bottom and every comparison becomes apples-to-apples.
240 km in 3 h → 240 ÷ 3 = 80 km/h
$4.80 for 6 cans → 4.80 ÷ 6 = $0.80 per can
The better deal test
12 oz for $3.60 → $0.30 per oz
18 oz for $4.50 → $0.25 per oz ← the better deal
Percent is a unit rate — per hundred
"Per cent" literally means per hundred. 35% = 35/100 = 0.35. That's why percent problems are unit-rate problems:
What is 15% of 80?
15% × 80 = 0.15 × 80 = 12
Faster: 10% of 80 = 8, 5% = 4, so 15% = 12.
The 10% anchor
Mentally anchor every percent to 10%: 20% is double it, 5% is
half, 1% is a tenth of it. 13% of 60 ≈ 6 + 2 ≈ 8 (real: 7.8) —
instant sanity check without a calculator.
Practice
325 km in 5 hours = ___ km/h
Better deal: 500 g for $4 or 750 g for $5.25?
15% of 120 = ___
$300 with 20% off costs $___
Next: statistics basics · Back: ratios & proportions