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

Answer 1

Answer:

D. 1:16 and 4:64

Step-by-step explanation:

a ratio in the form $A:B$ is the same as $\frac{A}{B}$, we can simplify the quantities to a fraction that has a numerator of one and thus compare if they are equal or not:

• A. 1:16 and 2:8

$\frac{1}{16}$ already has a numerator of one, and $\frac{2}{8}$ if you divide numerator and denominator by two, you get  $\frac{1}{4}$, and since

$\frac{1}{16}$ ≠  $\frac{1}{4}$, these two ratios are not equal.

• B. 2:32 and 4:8

We divide the numerator and denominator of $\frac{2}{32}$ by two to get a numerator of one: $\frac{1}{16}$ and for the second ratio $\frac{4}{8}$ we divide by four: $\frac{1}{2}$ and since

$\frac{1}{16}$ ≠  $\frac{1}{2}$, these two ratios are not equal.

• C. 1:64 and 4:16

$\frac{1}{64}$ already has a numerator of one, and $\frac{4}{16}$ if you divide numerator and denominator by four, you get  $\frac{1}{4}$, and since

$\frac{1}{64}$ ≠  $\frac{1}{4}$, these two ratios are not equal.

• D. 1:16 and 4:64

$\frac{1}{16}$ already has a numerator of one, and $\frac{4}{64}$ if you divide numerator and denominator by four, you get  $\frac{1}{16}$, and since

$\frac{1}{16}$ =  $\frac{1}{16}$, these two ratios are equal.

the answer is D. 1:16 and 4:64

Answer 2

The answer to the question is d