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$1 \frac{1}{4}$ DIVIDED BY $1 \frac{2}{5}$

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Convert between improper fractions and mixed numbers

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Q.

1 \frac{1}{4}

DIVIDED BY

1 \frac{2}{5}

Convert to Improper Fractions: Convert the mixed numbers to improper fractions. $\newline$ $1 \frac{1}{4}$ is the same as $\frac{5}{4}$ because $1 \times 4 + 1 = 5$ . $\newline$ $1 \frac{2}{5}$ is the same as $\frac{7}{5}$ because $1 \times 5 + 2 = 7$ .
Set Up Division: Set up the division of the two improper fractions. $\newline$ We need to divide $\frac{5}{4}$ by $\frac{7}{5}$ .
Convert to Multiplication: Convert the division of fractions to multiplication by the reciprocal of the divisor. $\newline$ To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{7}{5}$ is $\frac{5}{7}$ . $\newline$ So, we need to multiply $\frac{5}{4}$ by $\frac{5}{7}$ .
Multiply Numerators and Denominators: Multiply the numerators and then the denominators. $\newline$ $(\frac{5}{4}) \times (\frac{5}{7}) = (\frac{5 \times 5}{4 \times 7}) = \frac{25}{28}$
Simplify Fraction: Simplify the fraction if possible. $\frac{25}{28}$ cannot be simplified further as there are no common factors between $25$ and $28$ .

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