Question

A. How many 1/3s are in 2 2/3?

Answer 1

To find the number of 1/3 s in 2 2 /3 , we divide 2 2 /3 by 1/3

`2(2)/(3)/(1)/(3)`

to perform this division, we first convert the mixed number to an improper fraction.

`2(2)/(3)=2+(2)/(3)`

which can be written as

`2+(2)/(3)=(2\cdot3)/(3)+(2)/(3)`
`\begin{gathered} =(6)/(3)+(2)/(3) \\ \end{gathered}`
`=(8)/(3)`

Now our division becomes

`(8)/(3)/(1)/(3)`

To perform the above division, we convert it to multiplication by taking the reciprocal of the fraction on the right. This gives

`(8)/(3)*3`

which simplifies to

`(8)/(3)*3=8`

Hence, there are 8 1/3s in 2 2 /3 .