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RATIOS, RATES AND PROPORTIONS

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) ]

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RATIOS, RATES AND PROPORTIONS

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  1. 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

  2. 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)

  3. 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 females 84 females (one can be changed to the other by multiplying/diving by 4)

  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 = x 9 378 - 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)

  5. 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.

  6. 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!

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