# Which ratios are equal to each other? a. 1 : 16 and 2 : 8 b. 2 : 32 and 4 : 8 c. 1 : 64 and 4...

## Question:

Which ratios are equal to each other?

a. 1 : 16 and 2 : 8

b. 2 : 32 and 4 : 8

c. 1 : 64 and 4 : 16

d. 1 : 16 and 4 : 64

## Ratio:

The ratio denotes the comparable values of two numerical or physical quantities. The ratio is denoted using the rational number (consisting of numerator and denominator). It shows how many times a quantity is larger or less than the other.

## Answer and Explanation:

**Consider the first set of ratios:-**

Simplify the ratios into lowest form as,

{eq}\dfrac{1}{{16}} {/eq} and {eq}\dfrac{2}{8} = \dfrac{1}{4} {/eq}

Thus, the both ratios are not equal to each other.

**Consider the second set of ratios:-**

Simplify the ratios into lowest form as,

{eq}\dfrac{2}{{32}} = \dfrac{1}{{16}} {/eq} and {eq}\dfrac{4}{8} = \dfrac{1}{2} {/eq}

Thus, the both ratios are not equal to each other.

**Consider the third set of ratios:-**

Simplify the ratios into lowest form as,

{eq}\dfrac{1}{{64}} {/eq} and {eq}\dfrac{4}{{16}} = \dfrac{1}{4} {/eq}

Thus, the both ratios are not equal to each other.

**Consider the fourth set of ratios:-**

Simplify the ratios into lowest form as,

{eq}\dfrac{1}{{16}} {/eq} and {eq}\dfrac{4}{{64}} = \dfrac{1}{{16}} {/eq}

Thus, the both ratios are equal to each other.

Therefore, the option **d** is correct.

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from CAHSEE Math Exam: Help and Review

Chapter 10 / Lesson 14