Question

Which ratios have a unit rate of 3? Choose all that apply.
1 cup : 1.4 cup
2/3 cup : 1 cup
3 3/4 cups : 2 cups
15/2 cups : 2 1/2 cups
2 cups : 2/3 cup
2 1/2 : 5/6 cup

Answer 1

To find which ratios have a unit rate of 3, we need to calculate the rate for each ratio. A ratio has a unit rate of 3 if the value of the first quantity divided by the second quantity equals 3.

Let's calculate each ratio:

1. **1 cup : 1.4 cup**
\[
\frac{1}{1.4} \approx 0.714 \quad (\text{not 3})
\]

2. **2/3 cup : 1 cup**
\[
\frac{2/3}{1} = \frac{2}{3} \approx 0.667 \quad (\text{not 3})
\]

3. **3 3/4 cups : 2 cups**
\[
3 \frac{3}{4} = \frac{15}{4}, \text{ so }
\frac{15/4}{2} = \frac{15/4}{4/2} = \frac{15}{8} = 1.875 \quad (\text{not 3})
\]

4. **15/2 cups : 2 1/2 cups**
\[
2 \frac{1}{2} = \frac{5}{2}, \text{ so }
\frac{15/2}{5/2} = \frac{15}{2} \times \frac{2}{5} = \frac{15 \times 2}{2 \times 5} = \frac{15}{5} = 3 \quad (\text{this is 3})
\]

5. **2 cups : 2/3 cup**
\[
\frac{2}{2/3} = 2 \times \frac{3}{2} = 3 \quad (\text{this is 3})
\]

6. **2 1/2 : 5/6 cup**
\[
2 \frac{1}{2} = \frac{5}{2}, \text{ so }
\frac{5/2}{5/6} = \frac{5}{2} \times \frac{6}{5} = \frac{5 \times 6}{2 \times 5} = \frac{6}{2} = 3 \quad (\text{this is 3})
\]

Based on the calculations above, the ratios that have a unit rate of 3 are:

- **15/2 cups : 2 1/2 cups**
- **2 cups : 2/3 cup**
- **2 1/2 : 5/6 cup**