RATIOS, RATES AND PROPORTIONS

Ratios:- A comparison of two quantities measured in the

same units. {i.e. wins: losses (unit – games), apples: oranges (unit - fruit) ]

- Ratios can be written as two (or more) numbers separated by a colon (:), or in a fraction form (first number in the ratio expressed over the second)

- This ratio…42:12

is said as “forty-two TO twelve”and can be written like this in lowest terms: 21:6

RATIOS, RATES AND PROPORTIONS

Rates:- A rate is a comparison or relation between two

quantities measured in different units (i.e. kilometres and hours)

- A rate is expressed as the quantity of one unit, for 1 of the other unit. (i.e. 8 km/hr means that the object travels 8 kilometers in every 1 hour)

- Rates are expressed using both units combined with a /, which means “per”, as in m/s (metres PER second)

RATIOS, RATES AND PROPORTIONS

Equivalent ratios are ratios that can be converted to each other through multiplication or division. (i.e. 1:3 is equivalent with 3:9, because by multiplying by or dividing by 3, one ratio becomes the other)

A proportion is simply a pair of equivalent ratios, that represent the same units.

18 males = 72 males21 females 84 females(one can be changed to the other by

multiplying/diving by 4)

RATIOS, RATES AND PROPORTIONS

Any missing term in a proportion can be solved…- if three of the four terms are known- through CROSS MULTIPLICATION

In order to solve using cross multiplication…- set the terms equal in fraction form

3 = x9 378

- multiply the numbers that are diagonally across from each other, in this case 3 x 378 = 1134- divide the answer by the remaining known term ( 1134 divided by 9 = 126)

RATIOS, RATES AND PROPORTIONS

A scale is a ratio which always contains a 1, and is used for enlarging or reducing the size of an image in relation to an actual object.We use scales so that we can draw very small objects at a size where we can see more detail, or to make very large objects small enough to fit in a drawing.- A scale which makes a small object bigger is always

written with 1 as the second term. (i.e. 40:1)- A scale which makes a large object smaller is always

written with 1 as the first term (i.e. 1:350)- The drawing size is always the first term in a scale

ration, and the actual size is always the second term.

RATIOS, RATES AND PROPORTIONS

We can solve scale questions using the same method as solving for missing terms in a proportion.- For example:

The scale drawing of an ant is 12 cm. The scale is 40:1. What is the actual size of the ant?

40 = 12 1 x

12 x 1 = 12 divide by 40 = 0.3The ant is actually 0.3 cm long

NOTE: Scales are always in centimetres!