Comparing Ratios of Two or Three Variables A ratio compares the sizes of two or more quantities in a similar way. It tells us how much one quantity is of a...
A ratio compares the sizes of two or more quantities in a similar way. It tells us how much one quantity is of another. Ratios are often expressed as a fraction, where the numerator represents the part of the whole and the denominator represents the whole.
Similarities between ratios:
Equal ratios: If the ratios of two quantities are equal, then the two quantities are in the same relative size. For example, if ratio A/B = 2/3, then A and B are in a ratio of 2:3.
Unequal ratios: If the ratios of two quantities are unequal, then the two quantities are in different relative sizes. For example, if ratio A/B = 4:5, then A and B are in a ratio of 4:5.
How to compare ratios:
Identify the quantities: Determine the two or three quantities you want to compare.
Set up the ratios: Write two or three ratios comparing the two or three quantities. For example:
A/B = C/D
E/F = G/H
A/B = C/D => A = (C/D)B
E/F = G/H => E = (G/H)F
Examples:
If ratio A/B = 2/3, and ratio C/D = 4/6, then:
A/C = B/D
The sizes of A, B, and C are in the same relative order: 2:4:6
If ratio E/F = 2:3, and ratio G/H = 4:9, then:
E/G = F/H
The sizes of E, F, and G are in the same relative order: 2:4:9
By comparing ratios, we can understand the relative sizes of different quantities and make predictions about the values of those quantities based on the values of other quantities