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

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Solution

(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

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

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.

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