Question

Determine if the following are in proportion.
(a) 15, 45, 40, 120
(b) 33, 121, 9,96
(c) 24, 28, 36, 48
(d) 32, 48, 70, 210
(e) 4, 6, 8, 12
(f) 33, 44, 75, 100

Answer 1

(a) 15,45,40,120
\(= 15:45 = \frac{15}{45}\)
\(= \frac{1}{3}\)
\(= 1:3\)
\(40:120 = \frac{40}{120}\)
\(=\frac{ 1}{3}\)
\(= 1:3\)
Since \(15: 45 = 40: 120\)
Therefore 15, 45, 40, 120 are in proportion.

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(b) 33,121,9,96
\(= 33:121\)
\(= \frac{33}{121}\)

\(= \frac{3}{11}\)
\(= 3:11\)
\(9:96 =\frac{ 9}{96}\)
\(= \frac{3}{32}\)
\(= 3:32\)
Since \(33 : 121 ≠ 9 : 96\)
Therefore, 33, 121, 9, 96 are not in proportion.

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(c) 24,28,36,48
\(= 24:28\)
\(= \frac{24}{28}\)

\(= \frac{6}{7}\)
\(= 6:7\)
\(36:48\)
\(= \frac{36}{48}\)

\(= \frac{3}{4}\)
\(= 3:4\)
Since \(24 : 28 ≠ 36 : 48\)
Therefore 24, 28, 36, 48 are not in proportion. 

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(d) 32,48,70,210
\(= 32:48\)
\(=\frac{ 32}{48}\)

\(= \frac{3}{4}\)
\(70:210\)
\(=\frac{ 70}{210}\)

\(=\frac{ 1}{3}\)
\(= 1:3\)
Since \(32 : 48 ≠ 70 : 210\)
Therefore 32, 48, 70, 210 are not in proportion. 

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(e) 4,6,8,12
\(= 4:6\)
\(=\frac{ 4}{6}\)

\(= \frac{2}{3}\)
\(= 2:3\)
\(8:12\)
\(=\frac{ 8}{12}\)

\(=\frac{ 2}{3}\)
\(= 2:3\)
Since \(4 : 6 = 8 : 12\)
Therefore 4, 6, 8, 12 are in proportion.

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(f) 33,44,75,100
\(= 33:44\)
\(= \frac{33}{44}\)

\(=\frac{ 3}{4}\)
\(= 3:4\)
\(75:100\)
\(= \frac{75}{100}\)

\(= \frac{3}{4}\)
\(= 3:4\)
Since \(33 : 44 = 75 : 100\)
Therefore 33, 44, 75, 100 are in ratio.