Question

A cake mix calls for these ingredients.

2 cups of sugar
7 cups of flour
3 cups of milk
1 cup of oil

Write the ratios of sugar to flour and milk to oil. Which correctly compares the ratios?
StartFraction 3 Over 7 EndFraction greater-than StartFraction 2 Over 1 EndFraction
StartFraction 2 Over 7 EndFraction less-than StartFraction 3 Over 1 EndFraction
StartFraction 7 Over 1 EndFraction less-than two-thirds
Three-halves greater-than StartFraction 1 Over 7 EndFraction

Answer 1

To solve this, let's first write down the ratios:

1. **Ratio of sugar to flour**:
- Sugar: 2 cups
- Flour: 7 cups
- Therefore, the ratio of sugar to flour is \( \frac{2}{7} \).

2. **Ratio of milk to oil**:
- Milk: 3 cups
- Oil: 1 cup
- Therefore, the ratio of milk to oil is \( \frac{3}{1} \).

Next, we will evaluate the comparisons given:

1. \( \frac{3}{7} > \frac{2}{1} \):
- This is false because \( \frac{3}{7} \approx 0.42857 < 2 \).

2. \( \frac{2}{7} < \frac{3}{1} \):
- This is true because \( \frac{2}{7} \approx 0.28571 < 3 \).

3. \( \frac{7}{1} < \frac{2}{3} \):
- This is false since \( 7 > \frac{2}{3} \).

4. \( \frac{3}{2} > \frac{1}{7} \):
- This is true because \( \frac{3}{2} = 1.5 \) which is indeed greater than \( \frac{1}{7} \approx 0.142857 \).

So, the correct comparisons are:
- \( \frac{2}{7} < \frac{3}{1} \)
- \( \frac{3}{2} > \frac{1}{7} \)

The statements that are true are:
- \( \frac{2}{7} < \frac{3}{1} \)
- \( \frac{3}{2} > \frac{1}{7} \)