Chapter 4: Problem 4

Express the following ratios in their simplest \(\begin{array}{llll}\text { form: (a) } 6: 3 & \text { (b) } 5: 15 & \text { (c) } 8: 6: 10 & \text { (d) } \frac{1}{2}: \frac{1}{4}\end{array}\) (e) \(\frac{1}{2}: \frac{1}{3}: 1\)

Short Answer

Expert verified

Answer: 2:1

Step by step solution

Part (a): Simplify the ratio 6:3

To simplify the ratio 6:3, we have to find the GCD of 6 and 3, which is 3. Divide both numbers by the GCD and get the simplified ratio as \(\frac{6}{3}:\frac{3}{3}=2:1\).

Part (b): Simplify the ratio 5:15

To simplify the ratio 5:15, we have to find the GCD of 5 and 15, which is 5. Divide both numbers by the GCD and get the simplified ratio as \(\frac{5}{5}:\frac{15}{5}=1:3\).

Part (c): Simplify the ratio 8:6:10

To simplify the ratio 8:6:10, we have to find the GCD of 8, 6, and 10, which is 2. Divide all three numbers by the GCD and get the simplified ratio as \(\frac{8}{2}:\frac{6}{2}:\frac{10}{2}=4:3:5\).

Part (d): Simplify the ratio \(\frac{1}{2}:\frac{1}{4}\)

First, we need to convert the given fractions to have the same denominator, which is 4 in this case. Rewrite the ratio with the same denominator: \(\frac{2}{4}:\frac{1}{4}\). To simplify, find the GCD of the numerators, which is 1. Divide both numerators by the GCD and we get the simplified ratio as \(\frac{2}{1}:\frac{1}{1}=2:1\).

Part (e): Simplify the ratio \(\frac{1}{2}:\frac{1}{3}:1\)

First, we need to convert the given fractions (and the whole number) to a common denominator, which is 6 in this case. Rewrite the ratio with the same denominator: \(\frac{3}{6}:\frac{2}{6}:\frac{6}{6}\). To simplify, find the GCD of the numerators, which is 1. Divide all numerators by the GCD and we get the simplified ratio as \(\frac{3}{1}:\frac{2}{1}:\frac{6}{1}=3:2:6\).

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Express the following ratios in their simplest \(\begin{array}{llll}\text { form: (a) } 6: 3 & \text { (b) } 5: 15 & \text { (c) } 8: 6: 10 & \text { (d) } \frac{1}{2}: \frac{1}{4}\end{array}\) (e) \(\frac{1}{2}: \frac{1}{3}: 1\)

Short Answer

Step by step solution

Part (a): Simplify the ratio 6:3

Part (b): Simplify the ratio 5:15

Part (c): Simplify the ratio 8:6:10

Part (d): Simplify the ratio \(\frac{1}{2}:\frac{1}{4}\)

Part (e): Simplify the ratio \(\frac{1}{2}:\frac{1}{3}:1\)

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