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
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

Updated On: Jun 26, 2024
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Solution and Explanation

(a) 15,45,40,120
=15:45=1545= 15:45 = \frac{15}{45}
=13= \frac{1}{3}
=1:3= 1:3
40:120=4012040:120 = \frac{40}{120}
=13=\frac{ 1}{3}
=1:3= 1:3
Since 15:45=40:12015: 45 = 40: 120
Therefore 15, 45, 40, 120 are in proportion.


(b) 33,121,9,96
=33:121= 33:121
=33121= \frac{33}{121}

=311= \frac{3}{11}
=3:11= 3:11
9:96=9969:96 =\frac{ 9}{96}
=332= \frac{3}{32}
=3:32= 3:32
Since 33:1219:9633 : 121 ≠ 9 : 96
Therefore, 33, 121, 9, 96 are not in proportion.


(c) 24,28,36,48
=24:28= 24:28
=2428= \frac{24}{28}

=67= \frac{6}{7}
=6:7= 6:7
36:4836:48
=3648= \frac{36}{48}

=34= \frac{3}{4}
=3:4= 3:4
Since 24:2836:4824 : 28 ≠ 36 : 48
Therefore 24, 28, 36, 48 are not in proportion. 


(d) 32,48,70,210
=32:48= 32:48
=3248=\frac{ 32}{48}

=34= \frac{3}{4}
70:21070:210
=70210=\frac{ 70}{210}

=13=\frac{ 1}{3}
=1:3= 1:3
Since 32:4870:21032 : 48 ≠ 70 : 210
Therefore 32, 48, 70, 210 are not in proportion. 


(e) 4,6,8,12
=4:6= 4:6
=46=\frac{ 4}{6}

=23= \frac{2}{3}
=2:3= 2:3
8:128:12
=812=\frac{ 8}{12}

=23=\frac{ 2}{3}
=2:3= 2:3
Since 4:6=8:124 : 6 = 8 : 12
Therefore 4, 6, 8, 12 are in proportion.


(f) 33,44,75,100
=33:44= 33:44
=3344= \frac{33}{44}

=34=\frac{ 3}{4}
=3:4= 3:4
75:10075:100
=75100= \frac{75}{100}

=34= \frac{3}{4}
=3:4= 3:4
Since 33:44=75:10033 : 44 = 75 : 100
Therefore 33, 44, 75, 100 are in ratio.

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