To multiply \( \frac{7}{10} \) by \( 1 \frac{1}{4} \), we first convert the mixed number \( 1 \frac{1}{4} \) into an improper fraction.
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Convert \( 1 \frac{1}{4} \) to an improper fraction: \[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \]
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Now, multiply the fractions: \[ \frac{7}{10} \times \frac{5}{4} = \frac{7 \times 5}{10 \times 4} = \frac{35}{40} \]
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Simplify \( \frac{35}{40} \):
- Find the greatest common divisor (GCD) of 35 and 40, which is 5. \[ \frac{35 \div 5}{40 \div 5} = \frac{7}{8} \]
Therefore, the result of multiplying \( \frac{7}{10} \) by \( 1 \frac{1}{4} \) in simplest form is \( \frac{7}{8} \).