Question

Choose the pairs of ratios below that represent equivalent rates. Select all that apply.
A
12 ��� 36\frac{1}{2}\ and\ \frac{3}{6}
2
1
​
and
6
3
​

B
34 ��� 920\frac{3}{4}\ and\ \frac{9}{20}
4
3
​
and
20
9
​

C
12 ��� 1020\frac{1}{2}\ and\ \frac{10}{20}
2
1
​
and
20
10
​

D
14 ��� 516\frac{1}{4}\ and\ \frac{5}{16}
4
1
​
and
16
5
​

Answer 1

To determine which pairs of ratios represent equivalent rates, we can simplify each ratio and see if any of those ratios are equal.

**A:**
- \( \frac{12}{36.5} \) can be simplified:
\( \frac{12}{36.5} = \frac{12 \div 12}{36.5 \div 12} = \frac{1}{3.04167} \approx \frac{3}{9.125} \)
- \( \frac{3}{6} = \frac{1}{2} \)

**B:**
- \( \frac{34}{920.75} \) can be simplified:
\( \frac{34}{920.75} = \frac{34 \div 34}{920.75 \div 34} = \frac{1}{27.1} \)
- \( \frac{9}{20} = 0.45 \)

This does not show equivalent rates.

**C:**
- \( \frac{12}{1020.5} \) can be simplified:
\( \frac{12}{1020.5} = 0.01176 \) and does not equal other rates.
- \( \frac{10}{20} = \frac{1}{2} \)

**D:**
- \( \frac{14}{516.25} \) can be simplified:
\( \frac{14}{516.25} \) doesn’t yield ratios equal to others.

Let's summarize the checks:
- From A, B, C and D, we do not find any pairs of ratios that are equal.

None of the pairs provide equivalent rates after evaluation. However, if you would provide detailed measurements, we could validate further with exact calculations.