Ratios and Proportional Relationships
What this domain tests
Ratios and Proportional Relationships asks you to compare quantities multiplicatively, find unit rates, and recognize when two variables are proportional. Expect tables, graphs, equations, and percent word problems.
Core rules
- A ratio compares two quantities. A unit rate rewrites the ratio with a denominator of 1: 12 miles in 3 hours is 4 miles per hour.
- Two quantities are proportional only if the ratio y/x is constant for every pair, and the graph is a straight line through the origin. That constant is k, and the relationship is y = kx.
- Percent problems use part = percent × whole. For percent change, divide the change by the original amount.
- For successive percent changes, multiply by each multiplier in order.
Worked example
A 3.5-pound bag of almonds costs $8.75. The unit rate is 8.75 ÷ 3.5 = $2.50 per pound, so y = 2.50x gives the cost of x pounds. A 6.4-pound bag should cost 2.50 × 6.4 = $16.00.
Percent version: a $48 jacket is 25% off, then 8% tax is added. Discounted price: 48 × 0.75 = $36. Final: 36 × 1.08 = $38.88. The multipliers 0.75 and 1.08 are applied in sequence, not added.
Traps that cost marks
- Writing the unit rate upside down, such as $0.40 per pound instead of $2.50.
- Calling a table proportional when y increases by a constant amount rather than by a constant multiplier.
- Treating 25% off followed by 8% tax as a single 17% change.
- Computing percent error with the wrong base: use the exact value in the denominator.