Subtract. Write answer as mixed number in simplest form. 5 (1)/(4) - 2 (7)/(10)

Question

Subtract. Write answer as mixed number in simplest form.


`5 (1)/(4) - 2 (7)/(10)`

Answer 1

`(102)/(40) = (51)/(20)`

Explanation:

`5(1)/(4) - 2(7)/(10) =`

simplify

`(21)/(4) - (27)/(10) =`

common denominator

`(210)/(40) - (108)/(40) = (102)/(40)`

simplify

`(102)/(40) = (51)/(20)`

Answer 2

2
`(11)/(20)`

Explanation:

one way is to change the mixed numbers to improper fractions

5
`(1)/(4)` =
`(21)/(4)` and 2
`(7)/(10)` =
`(27)/(10)`

now we have

`(21)/(4)` -
`(27)/(10)`

We require the fractions to have a common denominator before we can subtract them.

the lowest common multiple of 4 and 10 is 20

multiply the numerator/denominator of the first fraction by 5 and the numerator/denominator of the second fraction by 2

=
`(21(5))/(4(5))` -
`(27(2))/(10(2))`

=
`(105)/(20)` -
`(54)/(20)`

now subtract the numerators leaving the denominator

=
`(51)/(20)` = 2
`(11)/(20)` ← in simplest form