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:
(a) We have, \[15:45=\frac{15}{45}=\frac{1}{3}\] and \[40:120=\frac{40}{120}=\frac{1}{3}\] Since, \[15:45=40:120\] So, 15, 45, 40, 120 are in proportion. Other method: We have, Product of extremes \[=15\times 120=1800\] Product of middle terms \[=45\times 40=1800\] Product of extremes = Product of middle terms Hence, 15, 45, 40, 120 are in proportion. (b) We have \[33:121=\frac{33}{121}=\frac{3}{11}\] and \[9:96=\frac{9}{96}=\frac{3}{32}\] Therefore, \[\frac{3}{11}\ne \frac{3}{32}\] So, \[~33:121\ne 9:96\] Thus, 33, 121, 9, 96 are not in proportion. Other method: We have, Product of extremes \[=33\times 96=3168\] Product of middle terms \[=121\times 9=1089\] Product of extremes \[\ne \] Product of middle terms Hence, 33, 121, 9, 96 are not in proportion. (c) We have, \[~24:28=\frac{24}{28}=\frac{6}{7}\] and \[36:48=\frac{36}{48}=\frac{3}{4}\] Since, \[\frac{6}{7}\ne \frac{3}{4}\] Therefore, \[24:28\ne 36:48\] They, 24, 28, 36, 48 are not in proportion. (d) We have, \[32:48=\frac{32}{48}=\frac{2}{3}\] and \[70:210=\frac{70}{210}\text{=}\frac{1}{3}\text{ }\] Since, \[\frac{2}{3}\ne \frac{1}{3}\] Therefore, \[32:48\ne 70:210\] Hence, 32, 48, 70, 210 are not in proportion. (e) We have, \[4:6=\frac{4}{6}=\frac{2}{3}\] and \[8:12=\frac{8}{12}=\frac{2}{3}\] So, \[4:6=8:12\] Therefore, 4, 6, 8, 12 are in proportion. Other method : We have Product of extremes \[=4\times 12=48\] Product of middle terms \[=6\times 8=48\] Product of extremes = product of middle terms Hence, 4, 6, 8, 12 are in proportion. (f) We have, \[33:44=\frac{33}{44}=\frac{3}{4}\] and \[75:100=\frac{75}{100}=\frac{3}{4}\] So, \[33:44=75:100\] Therefore, 33, 44, 75, 100 are in proportion.
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