Coursework Notes - Number

Ratio & Proportion

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:

 20 : 55       becomes       4 : 11 (dividing by 5)   39 : 12       becomes       13 : 4 (dividing by 3)   56 : 24       becomes       7 : 3 (dividing by 8)

Dividing by Ratio - This is the method to follow:

 Add up the numbers of the ratio to give the total number of 'parts'.   Make fractions of each ratio number divided by the number total.   In turn, multiply each fraction by the number that is to be divided up.

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

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

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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