Question

In which of the following sets are the numbers in proportion?

(1) 28, 16, 21, 12
(2) 12, 32, 15, 35
(3) 39, 26, 57, 38

Answer 1

A set of numbers are said to be in proportion if the simplest form of the ratios are equal .
Or we can say that if a, b, c, d are in proportion, then:
$\frac{a}{b}=\frac{c}{d}$

(1) For the set of numbers 28, 16, 21, 12:
The simplest form of the ratio of 28 : 16 is 7 : 4 .
The simplest form of the ratio of 21: 12 is 7: 4 .
Since the simplest forms of the ratios are equal, they are in proportion.

(2) For the set of numbers 12, 32, 15, 35:
The simplest form of the ratio of 12 : 32 is 3 : 8 .
The simplest form of the ratio of 15 : 35 is 3 : 7 .
Since, the simplest forms of the ratios are not equal, they are not in proportion.

(3) For the set of numbers 39, 26, 57, 38:
The simplest form of the ratio of 39 : 26 is 3 : 2 .
The simplest form of the ratio of 57 : 38 is 3 : 2 .
Since, the simplest forms of the ratios are equal, they are in proportion.