Section 4.2 Proportion

Property of Proportions:

In a proportion, the product of the extremes is equal to the product of the means. That is,

if and only if ad = bc

Examples: Exercises from page 207

2. Identify the means and extremes of

4:2.5 = 8:5

The means are 2.5 and 8, and the extremes are 4 and 5.

10. Find the value of the variable that will satisfy the proportion:

; 12(18) = 9x; 216 = 9x; 24 = x

18. Determine whether the fractions are equivalent.

Using the property of proportions, 5(12) must equal 4(15).

5(12) = 60 4(15) = 60

So the fractions are equivalent.

22. A dieter loses 2 kg in three weeks. If he continues to lose at this rate, how many weeks (to the nearest week) will it take him to lose 25 kg?

Let w = the number of weeks.

; 2w = 75; w = 37.5 38 weeks

30. A factory finds that it averages 0.75 defective per 1000 items shipped. How many defectives are expected in a shipment of 6000?

Let d = the number of defectives

0.75(6000) = 1000d

4500 = 1000d

4.5 = d

4 or 5