Question

How do you solve `\frac { 4} { 6} + \frac { 4} { 7}`?

Answer 1

`26/21 = 1 5/21`

Explanation:

Given: `4/6 + 4/7`

To add these fractions we need to find a common denominator. We want to find the least common multiple (LCM) of the two denominators.

Find the LCM by finding the smallest multiple that is common:
`6: 6, 12, 18, 24, 30, 36, color(red)(42), ...`

`7: 7, 14, 21, 28, 35, color(red)(42), ...`

The LCM is `42`.

Multiply each fraction by a fraction that is `1` that = `42`(LCM) in the denominator:

`4/6 xx 7/7 = 28/42`

`4/7 xx 6/6 = 24/42`

`4/6 + 4/7 = 28/42 + 24/42 = 52/42`

Since both numerator and denominator are divisible by `2`, reduce the fraction: `52/42 -: 2/2 = 26/21`

Put answer in mixed numbers: `26/21 = 1 5/21`