Question

Can someone explain this to me with a answer and work that is shown?

Answer 1

`1(19)/(30)`

Explanation:

To operate between mixed numbers is always better to write then in fraction form first (as improper fractions), and then operate using the rules to combine fractions.

For the first mixed number :

`4(5)/(6) = 4+(5)/(6) =(24)/(6) +(5)/(6)=(29)/(6)`

For the second mixed number:

`3(1)/(5) =3+(1)/(5)=(15)/(5)+(1)/(5)=(16)/(5)`

So now we have to subtract these two fractions, so we need to write them with the same common denominator (6 x 5 = 30):

`(29)/(6)-(16)/(5)=(145)/(30) -(96)/(30)=(49)/(30)`

and finally we write the obtained answer in mixed number form:

`(49)/(30) =1+(19)/(30) =1(19)/(30)`