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Are dfrac{4}{6} and dfrac{14}{21} equivalent ratios?

Question:

Are {eq}\dfrac{4}{6} {/eq} and {eq}\dfrac{14}{21} {/eq} equivalent ratios?

Equivalent Ratios:

Equivalent ratios are ratios that are basically equivalent fractions. One ratio is an equivalent if they are multiples of each other, such that {eq}\dfrac{m}{n}= \dfrac{2m}{2n} {/eq}. The two are then equivalent ratios or fractions.

Answer and Explanation:

Yes, the fractions are equivalent ratios because their simplified firms are the same.

To illustrate:

{eq}\dfrac{4}{6} = \dfrac{2 \cdot 2}{2 \cdot 3} = \dfrac{2}{3} {/eq}

For the other ratio or fraction:

{eq}\dfrac{14}{21} = \dfrac{7 \cdot 2}{7 \cdot 3} = \dfrac{2}{3} {/eq}

{eq}\dfrac{4}{6} {/eq} is a multiple of 2 while {eq}\dfrac{14}{21} {/eq} is a multiple of 7. They both simplify into {eq}\dfrac{2}{3} {/eq} making them equivalent to each other.


Learn more about this topic:

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Equivalent Ratios: Definition & Examples

from High School Algebra I: Homework Help Resource

Chapter 23 / Lesson 18
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