Question

Determine if the following numbers are in proportion:
(i) 4, 6, 8, 12
(ii) 7, 42, 13, 78
(iii) 33, 121, 9, 96
(iv) 22, 33, 42, 63
(v) 32, 48, 70, 210
(vi) 150, 200, 250, 300

Answer 1

(i) 4, 6, 8, 12
4 = 4 ​÷ 2 = 2 ; 8 = 8 ​÷ 4 = 2
6 6 ​÷ 2 3 12 12 ​÷ 4 3
Hence, 4:9::8:12 are in proportion.

(ii) 7, 42, 13, 78
7 = 7 ​÷ 7 = 1 ; 13 = 13 ​÷ 13 = 1
42 42 ​÷ 7 6 78 78 ​÷ 13 6
Hence, 7:42::13:78 are in proportion.

(iii) 33, 121, 9, 96
33 = 33 ​÷ 11 = 3 ; 9 = 9 ​÷ 3 = 3
121 121 ​÷ 11 11 96 96 ​÷ 3 32
Hence, 33:121::9:96 are not in proportion.

(iv) 22, 33, 42, 63

$\frac{22}{33}=\frac{22÷11}{33÷11}=\frac{2}{3}\mathrm{and}\frac{42}{63}=\frac{42÷21}{63÷21}=\frac{2}{3}$

Hence, 22:33 :: 42 : 63 are not in proportion.

(v) 32, 48, 70, 210
32 = 32 ​÷ 6 = 7 ; 70 = 70 ​÷ 70 = 1
48 48 ​÷ 6 8 210 210 ​÷ 70 3
Hence, 32:48::70:210 are not in proportion.


(vi) 150, 200, 250, 300
150 = 150 ​÷ 50 = 3; 250 = 250 ​÷ 50 = 5
200 200 ​÷ 50 4 300 300 ​÷ 50 6
Hence, 150:200::250:300 are not in proportion.