To determine if the pairs of fractions are equivalent, we can simplify each pair and see if they are equal.
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1/2 and 4/8: \[ \frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2} \] These fractions are equivalent.
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2/3 and 6/9: \[ \frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3} \] These fractions are equivalent.
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6/10 and 3/5: \[ \frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \] These fractions are equivalent.
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2/3 and 5/6: \[ \text{To compare these fractions, we can cross-multiply: } 2 \times 6 \text{ and } 3 \times 5: \] \[ 2 \times 6 = 12 \quad \text{and} \quad 3 \times 5 = 15 \] Since 12 is not equal to 15, these fractions are not equivalent.
In summary:
- 1/2 = 4/8 (Equivalent)
- 2/3 = 6/9 (Equivalent)
- 6/10 = 3/5 (Equivalent)
- 2/3 = 5/6 (Not Equivalent)