Ratios, rates, and proportions

Ratios are another way to write fractions/division, as the "ratio sign", which is ':', is the slash, or fraction divider. Ratios are usually used to describe the relationship between two or more values, and two ore more ratios can be put together into a proportion, which is a way of showing that (some) ratios are equal to each other, such as, 1:2 = 2:4 = 3:6, and so on. Variables (unknown values) can also be put in as a value into a ratio, like, x:2 = 2:4. Rates are, well, the definition of rates, as in the "rate" something is changing or the rate of speed, etc.

To solve proportions:

To solve proportions, we need to make both sides of the proportion equal, and we'll take this as an example:

SOLVE FOR X: X:3 = 9:27

To find x, we need to turn the 3 into 27, and to do that, we need to multiply the first ratio by 9, turning x:3 into 9x:27 = 9:27, and solving 9x = 9 would be easy, giving us x = 1. 

Ratio and Proportion Problems:

Find x.

3x:5=27:5x=3:(5/3)

2.5x:5 = 8:8

Word Problem: