Are the following fractions equivalent? Write Yes or No in the answers. a. 2/3 and 3/4 b. 4/7 and 9/8 c. 6/10 and 9/15 d. 2/10 and 3/15 e. 12/5 and 4/10 f. 2/5 and 2/5

Steps to Solve

1. Check the first pair: $ \frac{2}{3}$ and $ \frac{3}{4}$ To determine if these fractions are equivalent, cross-multiply. We need to check if: $$ 2 \times 4 \quad \text{is equal to} \quad 3 \times 3 $$ This simplifies to: $$ 8 \neq 9 $$ So, they are not equivalent.

2. Check the second pair: $ \frac{4}{7}$ and $ \frac{9}{8}$ Cross-multiply again: $$ 4 \times 8 \quad \text{versus} \quad 7 \times 9 $$ This simplifies to: $$ 32 \neq 63 $$ So, they are not equivalent.

3. Check the third pair: $ \frac{6}{10}$ and $ \frac{9}{15}$ Cross-multiply: $$ 6 \times 15 \quad \text{and} \quad 10 \times 9 $$ This simplifies to: $$ 90 = 90 $$ So, they are equivalent.

4. Check the fourth pair: $ \frac{2}{10}$ and $ \frac{3}{15}$ Cross-multiply: $$ 2 \times 15 \quad \text{and} \quad 10 \times 3 $$ This simplifies to: $$ 30 = 30 $$ So, they are equivalent.

5. Check the fifth pair: $ \frac{12}{5}$ and $ \frac{4}{10}$ Cross-multiply: $$ 12 \times 10 \quad \text{and} \quad 5 \times 4 $$ This simplifies to: $$ 120 \neq 20 $$ So, they are not equivalent.

6. Check the sixth pair: $ \frac{4}{10}$ and $ \frac{2}{5}$ Cross-multiply: $$ 4 \times 5 \quad \text{and} \quad 10 \times 2 $$ This simplifies to: $$ 20 = 20 $$ So, they are equivalent.