Ratios & Proportions — Cross-Multiply
Ratio: A comparison of two quantities. 3:5 means for every 3 of A, there are 5 of B.
Proportion: Two equal ratios. a/b = c/d, so ad = bc (cross-multiply).
SAT ratio problems:
"The ratio of boys to girls is 3:5. If there are 40 students total..."
3 + 5 = 8 parts. Each part = 40/8 = 5. Boys = 15, Girls = 25.
Unit conversion: Treat units like fractions and cancel.
60 miles/hour x 1 hour/60 minutes = 1 mile/minute
Direct proportion: y = kx (as x doubles, y doubles)
Inverse proportion: y = k/x (as x doubles, y halves)
Strategy: Set up the proportion with matching units. Label everything. Cross-multiply. Solve.
Reference:
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