Question

The sum of numerrator and the denomenator of a fraction is 14 if 1is subtracted from the neomerator and 3 is added to denominator the fraction is 1/3 find fraction ?

Answer 1

`5/9`

Explanation:

There are ways to work this using Algebra, but let's see if we can do it without it.

We're told that after operations take place, we have a fraction that is equivalent to `1/3`.

At the start of the question we're told that the numerator and denominator summed up equal 14. We're also told that when we subtract 1 from the numerator and add 3 to the denominator, we'll end up with that `1/3` equivalent fraction. So in all we have two numbers that sum to 14, we're adding 2 (in total, `3-1`) and so the sum after we're done equals 16.

Now we can find the fraction by observation:

`1/3=>1+3=4`

`2/6=>2+6=8`

`4/12=4+12=16`

We got `4/12` by subtracting 1 from the numerator and adding 3 to the denominator, so let's reverse those operations to find our starting fraction:

`(4+1)/(12-3)=5/9`

~~~~~

And just to show it, here's how to do it with Algebra:

Set `n` as the numerator and `d` as the denominator:

`n+d=14`

and

`(n-1)/(d+3)=1/3`

`3(n-1)=d+3`

`3n-3=d+3`

`d=3n-6`

Substitute into the first equation:

`n+3n-6=14`

`4n=20`

`n=5`

`:. d=3(5)-6=15-6=9`