Question

Which is a true statement about the given ratios?

StartFraction 9 Over 14 EndFraction, StartFraction 22 Over 28 EndFraction, StartFraction 5 Over 7 EndFraction, StartFraction 12 Over 14 EndFraction
StartFraction 9 Over 14 EndFraction greater-than StartFraction 5 Over 7 EndFraction
StartFraction 5 Over 7 EndFraction greater-than StartFraction 22 Over 28 EndFraction
StartFraction 12 Over 14 EndFraction greater-than StartFraction 22 Over 28 EndFraction
StartFraction 9 Over 14 EndFraction greater-than StartFraction 12 Over 14 EndFraction

Answer 1

To determine which statement about the given fractions is true, we first convert all the fractions to decimal form or analyze them by cross-multiplication.

1. **StartFraction 9 Over 14 EndFraction**:
- Decimal: \( \frac{9}{14} \approx 0.642857 \)

2. **StartFraction 22 Over 28 EndFraction**:
- Simplifies to \( \frac{11}{14} \) (both numerator and denominator divided by 2)
- Thus, Decimal: \( \frac{11}{14} \approx 0.785714 \)

3. **StartFraction 5 Over 7 EndFraction**:
- Decimal: \( \frac{5}{7} \approx 0.714286 \)

4. **StartFraction 12 Over 14 EndFraction**:
- Simplifies to \( \frac{6}{7} \) (both numerator and denominator divided by 2)
- Thus, Decimal: \( \frac{6}{7} \approx 0.857143 \)

Now we can compare the fractions:

- **Comparing \( \frac{9}{14} \) and \( \frac{5}{7} \)**:
- \( 0.642857 < 0.714286 \)
- Thus, \( \frac{9}{14} < \frac{5}{7} \)

- **Comparing \( \frac{5}{7} \) and \( \frac{11}{14} \)** (or \( \frac{22}{28} \)):
- \( 0.714286 < 0.785714 \)
- Thus, \( \frac{5}{7} < \frac{22}{28} \)

- **Comparing \( \frac{12}{14} \) and \( \frac{22}{28} \)**:
- \( 0.857143 > 0.785714 \)
- Thus, \( \frac{12}{14} > \frac{22}{28} \)

- **Comparing \( \frac{9}{14} \) and \( \frac{12}{14} \)**:
- \( 0.642857 < 0.857143 \)
- Thus, \( \frac{9}{14} < \frac{12}{14} \)

Putting it all together, the true statements are:
- \( \frac{12}{14} > \frac{22}{28} \)

So, the correct statement from the list provided is:
- **StartFraction 12 Over 14 EndFraction greater-than StartFraction 22 Over 28 EndFraction**.