To determine if the fractions are equivalent, we will check if their cross products are equal.
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For \( \frac{1}{3} \) and \( \frac{5}{12} \):
- Cross products: \( 1 \times 12 = 12 \) and \( 3 \times 5 = 15 \)
- Since \( 12 \neq 15 \), these fractions are not equivalent.
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For \( \frac{2}{5} \) and \( \frac{4}{10} \):
- Cross products: \( 2 \times 10 = 20 \) and \( 5 \times 4 = 20 \)
- Since \( 20 = 20 \), these fractions are equivalent.
- To find the multiplier, \( \frac{4}{2} = 2 \) and \( \frac{10}{5} = 2 \). Thus, both the numerator and denominator are multiplied by 2.
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For \( \frac{5}{12} \) and \( \frac{15}{36} \):
- Cross products: \( 5 \times 36 = 180 \) and \( 12 \times 15 = 180 \)
- Since \( 180 = 180 \), these fractions are equivalent.
- To find the multiplier, \( \frac{15}{5} = 3 \) and \( \frac{36}{12} = 3 \). Thus, both the numerator and denominator are multiplied by 3.
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For \( \frac{2}{11} \) and \( \frac{8}{44} \):
- Cross products: \( 2 \times 44 = 88 \) and \( 11 \times 8 = 88 \)
- Since \( 88 = 88 \), these fractions are equivalent.
- To find the multiplier, \( \frac{8}{2} = 4 \) and \( \frac{44}{11} = 4 \). Thus, both the numerator and denominator are multiplied by 4.
Summary:
- Fractions \( \frac{2}{5} \) and \( \frac{4}{10} \) are equivalent (multiplier: 2).
- Fractions \( \frac{5}{12} \) and \( \frac{15}{36} \) are equivalent (multiplier: 3).
- Fractions \( \frac{2}{11} \) and \( \frac{8}{44} \) are equivalent (multiplier: 4).
The fractions \( \frac{1}{3} \) and \( \frac{5}{12} \) are not equivalent.