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Coursework Notes - Number

 

Ratio & Proportion

 

[ 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:

 

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

 

ratio #1

 

 

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

ratio #2

 

 

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

 

ratio #3

 

 

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

 

proportion #1

 

 

 

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

 

proportion #2

 

 

 

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