Question

The sum of 2 fractions is 5/6. Their difference is 1/2. Their least common denominator is 6. The denominator of one is twice the size of the other. The sum of their numerators is 3. Find both fractions.

Answer 1

2/3 and 1/6

Explanation:

Hope this helps

Answer 2

Explanation:

Alright, lets get started.

Suppose the first fraction is :
`(a)/(b)`

Suppose the second fraction is :
`(c)/(d)`

The sum of both fraction is given as :
`(5)/(6)`

`(a)/(b)+(c)/(d)=(5)/(6)` .......................equation (1)

The difference of both fraction is given as :
`(1)/(2)`

`(a)/(b)-(c)/(d)=(1)/(2)` .........................equation (2)

Adding equation (1) and equation (2)

`(c)/(d) \ will \ be \ cancelled`

`(2a)/(b)=(5)/(6)+(1)/(2)`

making common denominator

`(2a)/(b)=(5)/(6)+ (3)/(6)`

`(2a)/(b)=(8)/(6)`

Hence,

`(a)/(b)=(2)/(3)`

Plugging the value of
`(a)/(b)` in equation (1)

`(2)/(3)+(c)/(d)=(5)/(6)`

Subtracting
`(2)/(3)` in both sides

`(c)/(d)=(5)/(6)-(2)/(3)`

`(c)/(d)=(1)/(6)`

Hence both fractions are
`(2)/(3) \ and \ (1)/(6)` ...................Answer

Hope it will help :)