To determine if the fractions are equivalent, we can cross-multiply and see if the cross products are equal, or we can simplify both fractions and see if they are equal.
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Fractions: \( \frac{1}{3} \) and \( \frac{5}{12} \)
Cross-multiply: \( 1 \times 12 = 12 \) and \( 5 \times 3 = 15 \)
Since \( 12 \neq 15 \), these fractions are not equivalent.
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Fractions: \( \frac{2}{5} \) and \( \frac{4}{10} \)
Cross-multiply: \( 2 \times 10 = 20 \) and \( 4 \times 5 = 20 \)
Since \( 20 = 20 \), these fractions are equivalent.
The fraction \( \frac{4}{10} \) can be simplified by multiplying the numerator and denominator of \( \frac{2}{5} \) by \( 2 \) (since \( \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \)).
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Fractions: \( \frac{5}{12} \) and \( \frac{15}{36} \)
Cross-multiply: \( 5 \times 36 = 180 \) and \( 15 \times 12 = 180 \)
Since \( 180 = 180 \), these fractions are equivalent.
The fraction \( \frac{15}{36} \) can be obtained by multiplying both the numerator and denominator of \( \frac{5}{12} \) by \( 3 \) (since \( \frac{5 \times 3}{12 \times 3} = \frac{15}{36} \)).
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Fractions: \( \frac{2}{11} \) and \( \frac{8}{44} \)
Cross-multiply: \( 2 \times 44 = 88 \) and \( 8 \times 11 = 88 \)
Since \( 88 = 88 \), these fractions are equivalent.
The fraction \( \frac{8}{44} \) can be obtained by multiplying both the numerator and denominator of \( \frac{2}{11} \) by \( 4 \) (since \( \frac{2 \times 4}{11 \times 4} = \frac{8}{44} \)).
Summary of Results:
- \( \frac{1}{3} \) and \( \frac{5}{12} \) - Not Equivalent
- \( \frac{2}{5} \) and \( \frac{4}{10} \) - Equivalent (multiplied by \( 2 \))
- \( \frac{5}{12} \) and \( \frac{15}{36} \) - Equivalent (multiplied by \( 3 \))
- \( \frac{2}{11} \) and \( \frac{8}{44} \) - Equivalent (multiplied by \( 4 \))
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