Which pair of ratios forms a proportion?
A. 5/12,7/15
B. 12/16,15/20
C. 8/32,1/3
D. 9/16,3/8
To determine which pair of ratios forms a proportion, we need to check if the ratios are equal. This can be done by simplifying both ratios to lowest terms and then comparing them.
Let's evaluate each pair of ratios:
A. 5/12, 7/15
To simplify 5/12 and 7/15, we find the greatest common factor (GCF) of the numerator and denominator of each ratio:
For 5/12, the GCF is 1, so the simplified ratio is 5/12.
For 7/15, the GCF is 1, so the simplified ratio is 7/15.
Since the simplified ratios are both different, A does not form a proportion.
B. 12/16, 15/20
To simplify 12/16 and 15/20, we find the GCF of the numerator and denominator of each ratio:
For 12/16, the GCF is 4, so the simplified ratio is 3/4.
For 15/20, the GCF is 5, so the simplified ratio is 3/4.
Since the simplified ratios are both the same (3/4), B forms a proportion.
C. 8/32, 1/3
To simplify 8/32 and 1/3, we find the GCF of the numerator and denominator of each ratio:
For 8/32, the GCF is 8, so the simplified ratio is 1/4.
For 1/3, the GCF is 1, so the simplified ratio is 1/3.
Since the simplified ratios are different, C does not form a proportion.
D. 9/16, 3/8
To simplify 9/16 and 3/8, we find the GCF of the numerator and denominator of each ratio:
For 9/16, the GCF is 1, so the simplified ratio is 9/16.
For 3/8, the GCF is 1, so the simplified ratio is 3/8.
Since the simplified ratios are both different, D does not form a proportion.
Therefore, the pair of ratios that forms a proportion is B: 12/16, 15/20.