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 males 21 females84 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=x3=x multiply the numbers that are diagonally across from each other, in this case 3 x 378 = 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 = 0.3 The ant is actually 0.3 cm long NOTE: Scales are always in centimetres!