📝 Ratios Proportions

Part 1 of 7 — Ratios and Proportions

Ratio: comparison of two quantities (a:b or a/b).

Proportion: two equal ratios, a/b = c/d.

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Key Insight: Cross-multiply to solve: ad = bc.

SAT Tip: Part-to-whole vs. part-to-part ratios: context matters on the SAT.

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Percentages

Part 2 of 7 — Percentages

Percent = (part/whole) × 100.

Percent change = ((new - old)/old) × 100.

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Key Insight: Successive percent changes: multiply the multipliers (1 + r₁)(1 + r₂)....

SAT Tip: Common SAT trap: 20% increase then 20% decrease ≠ original (it is 96% of original).

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Unit Conversion

Part 3 of 7 — Unit Conversion

Multiply by conversion factors as fractions.

Units should cancel: (mi/hr) × (hr/min) → mi/min.

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Key Insight: Dimensional analysis: track units through the calculation.

SAT Tip: SAT often uses unit conversion in multi-step problems.

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Direct & Inverse Variation

Part 4 of 7 — Direct & Inverse Variation

Direct variation: y = kx (y increases as x increases proportionally).

Inverse variation: y = k/x (y decreases as x increases).

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Key Insight: k is the constant of variation.

SAT Tip: Find k from one data point, then use it to find unknowns.

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Rate Problems

Part 5 of 7 — Rate Problems

Rate = distance/time or work/time.

Combined rates: add rates when working together.

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Key Insight: d = rt (distance = rate × time).

SAT Tip: Average speed = total distance / total time (NOT average of speeds).

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Rate = distance/time or work/time.

Combined rates: add rates when working together.

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Key Insight: d = rt (distance = rate × time).

SAT Tip: Average speed = total distance / total time (NOT average of speeds).

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Review & Applications

Part 7 of 7 — Review & Applications

Rate = distance/time or work/time.

Combined rates: add rates when working together.

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Key Insight: d = rt (distance = rate × time).

SAT Tip: Average speed = total distance / total time (NOT average of speeds).

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