Question

Adam wants to compare the fractions 3/12, 1/6, and 1/3. He wants to order them from least to greatest and rewrite them so they all have the same denominator. Explain how adam can rewrite the fractions.

Answer 1

He can change 1/6 and 1/3 to make their denominators 12, so it would be 2/12 and 4/12

Answer 2

`(1)/(6),(3)/(12),(1)/(3)`

or

`(2)/(12),(3)/(12),(4)/(12)`

Explanation:

we have

`(3)/(12) , (1)/(6) , (1)/(3)`

Remember that

To make the comparison of fractions of different denominators easier, multiply each fraction by a unit fraction such that the denominator will be the same in all fractions

Step 1

Multiply
`(1)/(6)` by
`(2)/(2)`

`(1)/(6)*(2)/(2)=(2)/(12)`

Step 2

Multiply
`(1)/(3)` by
`(4)/(4)`

`(1)/(3)*(4)/(4)=(4)/(12)`

Step 3

Compare the fractions

`(3)/(12)`

`(1)/(6)=(2)/(12)`

`(1)/(3)=(4)/(12)`

Order them from least to greatest

`(2)/(12),(3)/(12),(4)/(12)`

`(1)/(6),(3)/(12),(1)/(3)`