Question

What is the simplified value of `1/7 + 3/14 + 2/3 + 2/5 + 5/6` ?

Answer 1

`1/7+3/14+2/3+2/5+5/6=2 27/105`

Explanation:

To add `1/7+3/14+2/3+2/5+5/6`, firs convert all denominators to Lease Common Denominator (LCD), which is nothing but Least common multiple of `7`, `14`, `3`, `5` and `6`.

LCD of `7`, `14`, `3`, `5` and `6` is

`14xx6xx5=420` (as `7` is a factor of `14` and `3` is a factor of `5`).

Hence, converting each denominator of `1/7+3/14+2/3+2/5+5/6` to `420`,

`1/7+3/14+2/3+2/5+5/6`

= `(1xx60)/(7xx60)+(3xx30)/(14xx30)+(2xx140)/(3xx140)+(2xx84)/(5xx84)+(5xx70)/(6xx70)`

= `60/420+90/420+280/420+168/420+350/420`

= `(60+90+280+168+350)/420`

= `948/420=(237cancel948)/(105cancel420)=237/105=2 27/105`

(We have divided `948` and `420` by `4` here to simplify.)