Question

Which ratios form a proportion? Use cross products to test each pair.

A. 15/40, 35/90
B. 18/22, 45/55
C. 15/55, 33/121
D. 17/31, 32/45

Answer 1

B. 18/22, 45/55

C. 15/55, 33/121

Explanation:

Cross products are ...

A. 15×90 = 1350 ≠ 1400 = 40×35 . . . . not a proportion

B. 18×55 = 990 = 22×45 . . . . ratios are a proportion

C. 15×121 = 1815 = 55×33 . . . . ratios are a proportion

D. 17×45 = 765 ≠ 992 = 31×32 . . . . not a proportion

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Comment on the solution

When looking at cross products, it can work well to look at the factors of the numbers involved:

... 18×55 = 2·9·5·11 . . . . . . 22·45 = 2·11·9·5 . . . . the same list of factors

You don't actually need to multiply it out to see that the products will be equal.

In pair D, you may recognize that 31 is a prime number, so the other ratio will only be proportional if the denominator is a multiple of 31, which it is not.