5 2/5 - 6 5/7.5 (2)/(5) - 6 (5)/(7)

Question

5 2/5 - 6 5/7
`.`
`5 (2)/(5) - 6 (5)/(7)`

Answer 1

Given

`5(2)/(5)-6(5)/(7)`

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

`5(2)/(5)=(5\cdot5)/(5)+(2)/(5)=(25)/(5)+(2)/(5)=(27)/(5)`
`6(5)/(7)=6+(5)/(7)=(6\cdot7)/(7)+(5)/(7)=(42)/(7)+(5)/(7)=(47)/(7)`

The subtraction expressed as improper fractions are

`(27)/(5)-(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} (27\cdot7)/(5\cdot7)-(47\cdot5)/(7\cdot5)=(189)/(35)-(235)/(35) \\ (189-235)/(35) \\ (-46)/(35) \end{gathered}`

The result of the calculation is

`-(46)/(35)`

Expressed as a mixed fraction the result is

`-1(11)/(35)`