Question

Which statements are TRUE? select TWO that apply.
A. 2/6 > 7/8
B. 2/11 < 5/7
C. 7/10 < 5/12
D. 6/10 > 4/9
E. 4/9 > 11/20

Answer 1

To determine which statements are true, we can compare the fractions. Let's analyze each statement:

A. \( \frac{2}{6} > \frac{7}{8} \)
- Converting \( \frac{2}{6} \) to its simplest form gives us \( \frac{1}{3} \).
- \( \frac{1}{3} \approx 0.333 \) and \( \frac{7}{8} = 0.875 \).
- Thus, \( \frac{1}{3} < \frac{7}{8} \) → False

B. \( \frac{2}{11} < \frac{5}{7} \)
- Cross-multiplying gives \( 2 \times 7 = 14 \) and \( 11 \times 5 = 55 \).
- Thus, \( 14 < 55 \) → True

C. \( \frac{7}{10} < \frac{5}{12} \)
- Cross-multiplying gives \( 7 \times 12 = 84 \) and \( 10 \times 5 = 50 \).
- Thus, \( 84 > 50 \) → False

D. \( \frac{6}{10} > \frac{4}{9} \)
- Converting \( \frac{6}{10} \) to its simplest form gives us \( \frac{3}{5} \).
- Cross-multiplying gives \( 3 \times 9 = 27 \) and \( 5 \times 4 = 20 \).
- Thus, \( 27 > 20 \) → True

E. \( \frac{4}{9} > \frac{11}{20} \)
- Cross-multiplying gives \( 4 \times 20 = 80 \) and \( 9 \times 11 = 99 \).
- Thus, \( 80 < 99 \) → False

The true statements are:
- **B. \( \frac{2}{11} < \frac{5}{7} \)**
- **D. \( \frac{6}{10} > \frac{4}{9} \)**

So the final answer is **B and D.**