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Do the ratios 6 : 3 and 4 : 2 form a proportion?

Question:

Do the ratios 6 : 3 and 4 : 2 form a proportion?

Proportions:

A comparison of two similar quantities is said to be a ratio. The ratio of {eq}a {/eq} by {eq}b {/eq} is represented as {eq}a:b = \frac{a}{b} {/eq}

When two ratios are equal, they are said to be in proportion.

The symbol used to represent the proportion is {eq}:: {/eq}

Answer and Explanation:

Given ratios are {eq}6:3,\ 4:2 {/eq}

Lets simplify each ratio into simplest terms and then compare them.

First ratio: {eq}\displaystyle 6:3=\frac{6}{3} \\ \displaystyle =\frac{2}{1} = 2:1 {/eq}

Second ratio: {eq}\displaystyle 4:2 = \frac{4}{2}\\ \displaystyle =\frac{2}{1} = 2:1 {/eq}

We can see that two ratios are equal. So, the given ratios are in proportion.


Learn more about this topic:

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What is a Proportion in Math? - Definition & Practice Problems

from High School Algebra I: Help and Review

Chapter 23 / Lesson 15
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