To multiply \( \frac{5}{6} \) by \( 2\left(\frac{3}{4}\right) \), we first convert \( 2\left(\frac{3}{4}\right) \) into an improper fraction.
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Convert the whole number \( 2 \) into a fraction: \[ 2 = \frac{2 \times 4}{4} = \frac{8}{4} \]
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Now, add \( \frac{8}{4} \) and \( \frac{3}{4} \): \[ 2\left(\frac{3}{4}\right) = \frac{8}{4} + \frac{3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \]
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Now we multiply \( \frac{5}{6} \) by \( \frac{11}{4} \): \[ \frac{5}{6} \times \frac{11}{4} = \frac{5 \times 11}{6 \times 4} = \frac{55}{24} \]
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Next, we convert \( \frac{55}{24} \) into a mixed number. To do this, we divide 55 by 24:
- \( 55 \div 24 = 2 \) with a remainder of \( 7 \) (since \( 24 \times 2 = 48 \)).
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Thus, we can express \( \frac{55}{24} \) as: \[ 2 \frac{7}{24} \]
Therefore, the product of \( \frac{5}{6} \) and \( 2\left(\frac{3}{4}\right) \) is \( 2 \frac{7}{24} \).
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