To multiply \( \frac{7}{10} \) by \( 1\frac{1}{4} \), first, we need to convert \( 1\frac{1}{4} \) into an improper fraction.
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Convert \( 1\frac{1}{4} \): \[ 1\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \]
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Now multiply \( \frac{7}{10} \) by \( \frac{5}{4} \): \[ \frac{7}{10} \times \frac{5}{4} = \frac{7 \times 5}{10 \times 4} = \frac{35}{40} \]
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Next, simplify \( \frac{35}{40} \): \[ \frac{35}{40} = \frac{7}{8} \quad (\text{dividing both numerator and denominator by 5}) \]
So, the result in simplest form is \( \frac{7}{8} \).
The correct answer is: \[ \frac{7}{8} \]