Question

How do you solve this problem?3 7/3+2 5/6=

Answer 1

49/6

Step-by-step explanation:

In order to add the mixed numbers given, we first convert the mixed numbers to improper fractions.

Now,

`3(7)/(3)=3+(7)/(3)`

The number 3 can be rewritten as

`7=3\cdot(3)/(3)`

which helps us rewrite our mixed fraction as

`3+(7)/(3)=3\cdot(3)/(3)+(7)/(3)`
`=(9)/(3)+(7)/(3)`

adding the numerators gives

`(16)/(3)`

Hence,

`3(7)/(3)=(16)/(3)`

Similarly,

`2(5)/(6)=2+(5)/(6)`

the number 2 can be rewritten as

`2=2\cdot(6)/(6)=(12)/(6)`

therefore, the mixed number becomes

`2+(5)/(6)=(12)/(6)+(5)/(6)`
`=(17)/(6)`

Hence,

`2(5)/(6)=(17)/(6)`

Now with mixed numbers rewritten as improper fractions, we are ready to add

`3(7)/(3)+2(5)/(6)=(16)/(3)+(17)/(6)`

rewriting 16/3 as 16/3 * 2/2 gives

`(16)/(3)=(32)/(6)`

therefore, we have

`(16)/(3)+(17)/(6)=(32)/(6)+(17)/(6)`

and now we just add the denominators to get

`(32)/(6)+(17)/(6)=(49)/(6)`

Hence,

`3(7)/(3)+2(5)/(6)=(49)/(6)`

which is our answer!