To determine if the fractions are equivalent, we can cross-multiply or analyze them directly.
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1/3 = 5/12:
- Cross-multiplying gives us \(1 \cdot 12 = 12\) and \(3 \cdot 5 = 15\). Since \(12 \neq 15\), these fractions are not equivalent.
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2/5 = 4/10:
- Cross-multiplying gives us \(2 \cdot 10 = 20\) and \(5 \cdot 4 = 20\). Since both products are equal, these fractions are equivalent.
- To find the number both the numerator and denominator were multiplied by, we can see that \(2 \cdot 2 = 4\) (numerator), and \(5 \cdot 2 = 10\) (denominator), so they were both multiplied by 2.
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5/12 = 15/36:
- Cross-multiplying gives us \(5 \cdot 36 = 180\) and \(12 \cdot 15 = 180\). Since both products are equal, these fractions are equivalent.
- The first fraction multiplied by \(3\) gives the second fraction: \(5 \cdot 3 = 15\) (numerator) and \(12 \cdot 3 = 36\) (denominator), so they were both multiplied by 3.
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2/11 = 8/44:
- Cross-multiplying gives us \(2 \cdot 44 = 88\) and \(11 \cdot 8 = 88\). Since both products are equal, these fractions are equivalent.
- The first fraction multiplied by \(4\) gives the second fraction: \(2 \cdot 4 = 8\) (numerator) and \(11 \cdot 4 = 44\) (denominator), so they were both multiplied by 4.
In summary:
- 1/3 and 5/12: Not equivalent
- 2/5 and 4/10: Equivalent (multiplied by 2)
- 5/12 and 15/36: Equivalent (multiplied by 3)
- 2/11 and 8/44: Equivalent (multiplied by 4)
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