Question

5 2/5 - 6 5/7$.$$5 \frac{2}{5} - 6 \frac{5}{7}$

Answer 1

Given

$5\frac{2}{5}-6\frac{5}{7}$

To subtract both fractions, the first step is to express the mixed fractions as improper fractions.

$5\frac{2}{5}=\frac{5\cdot5}{5}+\frac{2}{5}=\frac{25}{5}+\frac{2}{5}=\frac{27}{5}$$6\frac{5}{7}=6+\frac{5}{7}=\frac{6\cdot7}{7}+\frac{5}{7}=\frac{42}{7}+\frac{5}{7}=\frac{47}{7}$

The subtraction expressed as improper fractions are

$\frac{27}{5}-\frac{47}{7}$

Second, you have to find the common denominator between 5 and 7 and express both fractions under said the common denominator. The common denominator for 5 and 7 is 35

To express the first fraction with denominator 35 you have to multiply both the numerator and denominator by 7

To express the second fraction with denominator 35, you have to multiply both the numerator and denominator by 5

$\begin{gathered} \frac{27\cdot7}{5\cdot7}-\frac{47\cdot5}{7\cdot5}=\frac{189}{35}-\frac{235}{35} \\ \frac{189-235}{35} \\ \frac{-46}{35} \end{gathered}$

The result of the calculation is

$-\frac{46}{35}$

Expressed as a mixed fraction the result is

$-1\frac{11}{35}$