Two Denominators

The equation x/2 + x/3 = 10 says that half a number plus a third of it is 10. It has two denominators, 2 and 3. To clear both, multiply every term by a number that both 2 and 3 divide into. The smallest such number is their least common multiple, which is 6:

6 × x/2 + 6 × x/3 = 6 × 10

3x + 2x = 60

5x = 60

x = 12

One multiplication by 6 removed both fractions. Check the answer: 12/2 + 12/3 = 6 + 4 = 10.

Any common multiple of the denominators clears the fractions, as long as it is not zero. The least common multiple keeps the numbers small. You can also add the two fractions first: x/2 + x/3 is 5/6 x, so the equation becomes 5/6 x = 10. Then divide both sides by 5/6. Both methods give x = 12.