Ratio, Proportion and Rates of Change

This lesson deepens your understanding of ratio and proportion, introducing algebraic expressions for direct and inverse proportion, exponential growth and decay, and rates of change in context.

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Ratio — Advanced Problems

Combining Ratios

If A : B = 2 : 3 and B : C = 4 : 5, find A : B : C. Make B the same in both: A : B = 8 : 12, B : C = 12 : 15 → A : B : C = 8 : 12 : 15

Ratio and Algebraic Equations

Example: A and B share £720 in the ratio (x + 1) : (2x − 1). A receives £270. Find x. A's fraction = (x + 1)/(3x) = 270/720 = 3/8 8(x + 1) = 3(3x) → 8x + 8 = 9x → x = 8

Proportion in Geometry

In similar shapes:

• The ratio of areas = (ratio of lengths)²
• The ratio of volumes = (ratio of lengths)³

Example: Two similar cones have heights in the ratio 2 : 3.