Question

What should the following equation be multiplied by in order to eliminate the fractions? x/3+x/6=11/9

Answer 1

Multiply by 18

Explanation:

Given

`(x)/(3) + (x)/(6) = (11)/(9)`

Required

Eliminate the fraction

To eliminate the fraction, we first determine the LCM of the denominators (3, 6 and 9)

This is show below:

List out the multiplies of 3, 6 and 9

`3 = 3,6,9,12,15,18,21,24,27,30...`

`6 = 6,12,18,24,30...`

`9 = 9,18,27...`

The least common multiple is 18.

Hence, when both sides of the equation is multiplied by 18, the fraction is eliminated;

See proof

`18 * ((x)/(3) + (x)/(6)) = (11)/(9) * 18`

`(18x)/(3) + (18x)/(6) = (11*18)/(9)`

`6x + 3x = 11 * 2`

`6x + 3x = 22`

The fraction is eliminated