To find out how much time Lara spends doing stretching exercises, we first need to convert the total time she spends working out into an improper fraction.
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Convert \(1 \frac{3}{4}\) hours to an improper fraction: \[ 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ hours} \]
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Next, calculate \( \frac{2}{5} \) of the time she spends working out: \[ \text{Time spent on stretching} = \frac{2}{5} \times \frac{7}{4} \]
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Multiplying the fractions: \[ = \frac{2 \times 7}{5 \times 4} = \frac{14}{20} \]
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Now, simplify \(\frac{14}{20}\):
- The greatest common divisor of 14 and 20 is 2.
- Therefore, divide both the numerator and denominator by 2: \[ \frac{14 \div 2}{20 \div 2} = \frac{7}{10} \]
Lara spends \(\frac{7}{10}\) hours doing stretching exercises.