Arithmetic Grade Six

Lesson One Hundred Seventy-one: Proportions


There is often more than one way to solve a problem and this is certainly the case with proportions. The second method used to solve proportions is called cross-multiply-and-divide. Here's an example: 


	  N		  6
	 ---	=	 ---
	  10		  20

  STEP ONE: CROSS MULTIPLY (denominator one * numerator two)

	10 * 6 = 60

  STEP TWO: DIVIDE (denominator two ÷ product from step one)

	60 ÷ 20 = 3

  N = 3
Both methods involve two steps and so there is not a big advantage to using one method over the other. (However, when we are solving proportions which involve quotients which don't happen to be whole numbers, method two may be easier.)

Here's an example done both ways: 


	 N		 9
	---	=	---
	 7		 21

  METHOD ONE:
	1. divide (21 ÷ 7 = 3)
	2  divide (9 ÷ 3 = 3)

  METHOD TWO:
	1. multiply (7 * 9 = 63)
	2. divide   (63 ÷ 21 = 3)

  ANSWER:

	N = 3

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