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2021-11-16

Find the difference by converting the mixed numbers to improper fractions:
$4\frac{4}{7}-2\frac{6}{7}$

Troy Lesure

Calculation:
Given: $4\frac{4}{7}-2\frac{6}{7}$,
Writing the mixed numbers as improper functions,
$4\frac{4}{7}-2\frac{6}{7}=\frac{7\left(4\right)+4}{7}-\frac{7\left(2\right)+6}{7}$
$4\frac{4}{7}-2\frac{6}{7}=\frac{28+4}{7}-\frac{14+6}{7}$
$4\frac{4}{7}-2\frac{6}{7}=\frac{32}{7}-\frac{20}{7}$
To add or subtract rational numbers the denominators need to be equal.
When the denominators are equal, the numerators can be added or subtracted as per the operation.
Hence, $4\frac{4}{7}-2\frac{6}{7}=\frac{32-20}{7}$
$4\frac{4}{7}-2\frac{6}{7}=\frac{12}{7}$
To convert the improper fraction to mixed fraction, the numerator is written as sum of a multiple of denominator and the remainder.
$4\frac{4}{7}-2\frac{6}{7}=\frac{7+5}{7}$
$4\frac{4}{7}-2\frac{6}{7}=\frac{7}{7}+\frac{5}{7}$
$4\frac{4}{7}-2\frac{6}{7}=1+\frac{5}{7}$
$4\frac{4}{7}-2\frac{6}{7}=1\frac{5}{7}$
Therefore, $4\frac{4}{7}-2\frac{6}{7}=1\frac{5}{7}$

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