[ dividing by ratio ][ proportional change ]

Simple Ratios - A ratio is a way of comparing the relative magnitude of different quantities.

A, B, C             20 : 30 : 50

Simplification of Ratios - Division by a common factor or factors reduces the size of numbers used in a ratio.

20 : 30 : 50       becomes       2 : 3 : 5

examples:

Dividing by Ratio - This is the method to follow:

Example #1 - Divide 90 in the ratio 3 : 2

total of ratio numbers = 3 + 2 = 5

Therefore 90 shared in the ratio 3 : 2 is 54 and 36

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Example #2 - Divide 132 in the ratio 6 : 5

total of ratio numbers = 6 + 5 = 11

Therefore 132 shared in the ratio 6 : 5 is 72 and 60

Example #3 - Divide 288 in the ratio 2 : 6 : 4

total of ratio numbers = 2 + 6 + 4 = 12

Therefore 288 shared in the ratio 2 : 6 : 4 is 48, 144 and 96

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Proportional Change is when a quantity is increased or decreased by multiplication with the numbers of a ratio expressed as a fraction.

The first number of the ratio becomes the numerator, while the second becomes the denominator.

Example #1 - increase 56 in the ratio 3 : 2

Example #2 - decrease 72 in the ratio 4 : 9

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