### 17.1. Ratio and Proportion

#### 17.1.1. Ratio

In our work so far, we have often dealt with expressions of the form

There are several different ways of looking at such an expression. We can say that a/b is

A fraction, with a numerator a and a denominator b

A quotient, where a is divided by b

The ratio of a to b

Thus a ratio can be thought of as a fraction or as the quotient of two quantities. Another way to write a ratio is to use a colon (:) instead of a fraction line. Thus the ratio a/b can also be written

- a:b

#### 17.1.2. Dimensionless Ratios

For a ratio of two physical quantities, it is usual to express the numerator and denominator in the same units, so that they cancel and leave the ratio dimensionless.

## Example 1:A corridor is 8 ft wide and 12 yd long. Find the ratio of length to width. Solution: We first express the length and width in the same units, say, feet. - 12 yd = 36 ft
So the ratio of length to width is Note that this ratio carries no units. |

Dimensionless ratios are handy because you do not have to worry about units. For this reason they are often used in technology.

## Example 2:The fuel-air ratio is the ratio of the mass of fuel to air in a combustion chamber. The turns ratio is the ratio of turns of wire in the secondary winding of a transformer to the number of turns in ... |

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