Are the pairs of fractions equivalent?(4 points)

Question

Yes No
1 over 2= 4 over 8

2 over 3 = 6 over 9

6 over 10 = 3 over 5

2 over 3 = 5 over 6

Answer 1

Let's evaluate each pair of fractions to see if they are equivalent.

1. \( \frac{1}{2} = \frac{4}{8} \)

   • To determine if these are equivalent, we can simplify \( \frac{4}{8} \).
   • \( \frac{4}{8} = \frac{1}{2} \).
   • Yes (they are equivalent).

2. \( \frac{2}{3} = \frac{6}{9} \)

   • Simplifying \( \frac{6}{9} \):
   • \( \frac{6}{9} = \frac{2}{3} \).
   • Yes (they are equivalent).

3. \( \frac{6}{10} = \frac{3}{5} \)

   • Simplifying \( \frac{6}{10} \):
   • \( \frac{6}{10} = \frac{3}{5} \).
   • Yes (they are equivalent).

4. \( \frac{2}{3} = \frac{5}{6} \)

   • To check if these are equivalent, we can cross-multiply:
   • \( 2 \times 6 = 12 \) and \( 3 \times 5 = 15 \).
   • Since \( 12 \neq 15 \), they are not equivalent.
   • No (they are not equivalent).

Summary of answers:

1. Yes
2. Yes
3. Yes
4. No