To determine if the fractions are equivalent, we'll cross-multiply and compare:
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For \( \frac{13}{25} = \frac{5}{12} \):
- Cross-multiply: \( 13 \times 12 \) and \( 25 \times 5 \)
- \( 13 \times 12 = 156 \)
- \( 25 \times 5 = 125 \)
- Not equivalent (156 ≠ 125)
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For \( \frac{5}{12} = \frac{4}{10} \):
- Cross-multiply: \( 5 \times 10 \) and \( 12 \times 4 \)
- \( 5 \times 10 = 50 \)
- \( 12 \times 4 = 48 \)
- Not equivalent (50 ≠ 48)
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For \( \frac{5}{12} = \frac{15}{36} \):
- Cross-multiply: \( 5 \times 36 \) and \( 12 \times 15 \)
- \( 5 \times 36 = 180 \)
- \( 12 \times 15 = 180 \)
- Equivalent (both equal 180)
- Both the numerator and denominator were multiplied by \( 3 \) to arrive at \( \frac{15}{36} \).
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For \( \frac{2}{11} = \frac{8}{44} \):
- Cross-multiply: \( 2 \times 44 \) and \( 11 \times 8 \)
- \( 2 \times 44 = 88 \)
- \( 11 \times 8 = 88 \)
- Equivalent (both equal 88)
- Both the numerator and denominator were multiplied by \( 4 \) to arrive at \( \frac{8}{44} \).
Summary:
- Fractions \( \frac{5}{12} = \frac{15}{36} \) are equivalent (multiplied by \( 3 \)).
- Fractions \( \frac{2}{11} = \frac{8}{44} \) are equivalent (multiplied by \( 4 \)).
- The other two fractions are not equivalent.
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