Question

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

Answer 1

Answer:

Multiply by 18

Step-by-step explanation:

Given

$\frac{x}{3} + \frac{x}{6} = \frac{11}{9}$

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

$18 * (\frac{x}{3} + \frac{x}{6}) = \frac{11}{9} * 18$

$\frac{18x}{3} + \frac{18x}{6} = \frac{11*18}{9}$

$6x + 3x = 11 * 2$

$6x + 3x = 22$

The fraction is eliminated