Solve and Simplify Ratios
Simplify ratios, find missing values, and scale proportions. Solve A:B = C:? problems instantly.
Understanding Ratios
A ratio compares two quantities. 12:8 simplified = 3:2 (divide both by their GCD of 4). Ratios appear everywhere: recipes (2:1 flour to sugar), maps (1:50,000 scale), screens (16:9 aspect ratio), and mixing (3:1 concrete mix). To solve proportions: if A:B = C:?, then ? = B×C÷A.
Scaling Ratios
To scale a ratio, multiply both sides by the same number. 3:2 scaled by 5 = 15:10. This is how recipes work — a 2:1 ratio of flour to sugar for 12 cookies becomes 4:2 for 24 cookies. The ratio stays the same; the quantities change proportionally.
Ratio questions dominate standardized tests (SAT, GRE, ACT). The most common mistake: confusing "ratio of A to B" with "fraction A/B." A 3:2 ratio means 3 parts A and 2 parts B out of 5 total parts — so A is 3/5 of the total, not 3/2.
