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

a ratio in the form [tex]A:B[/tex] is the same as [tex]\frac{A}{B}[/tex], 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

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

[tex]\frac{1}{16}[/tex] ≠ [tex]\frac{1}{4}[/tex], these two ratios are not equal.

B. 2:32 and 4:8

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

[tex]\frac{1}{16}[/tex] ≠ [tex]\frac{1}{2}[/tex], these two ratios are not equal.

C. 1:64 and 4:16

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

[tex]\frac{1}{64}[/tex] ≠ [tex]\frac{1}{4}[/tex], these two ratios are not equal.

D. 1:16 and 4:64

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

[tex]\frac{1}{16}[/tex] = [tex]\frac{1}{16}[/tex], these two ratios are equal.

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