Question

How do you simplify `1/3+1/2+1/5`?

Answer 1

`=31/30`

Explanation:

`1/3+1/2+1/5`
`=(10+15+6)/30`
`=31/30`

Answer 2

To add fractions, you must have common denominators. So, you need to get the bottom numbers to be the same.

The least common multiple of `3`, `2`, and `5` is `30`, since `3xx2xx5 = 30`, and `3`, `2`, and `5` are all prime numbers.

Therefore, you just need to get `30` in the denominators by multiplying by unit fractions. i.e. `x/x = y/y = z/z = 1`.

`1/3*stackrel(= 1)overbrace(10/10) + 1/2*stackrel(= 1)overbrace(15/15) + 1/5*stackrel(= 1)overbrace(6/6)`

`= 10/30 + 15/30 + 6/30`

`= color(blue)(31/30)`

Or, if you know your decimals...

`1/3 + 1/2 + 1/5`

`= 0.bar(33) + 0.5 + 0.2`

`= 1.0bar(33)`.

Since `0.0bar(33) = (0.bar(33))/10 = 1/3*1/10 = 1/30`,

`1.0bar(33) = 1/30 + 30/30 = color(blue)(31/30)`.