Question

the denominator of a certain number was 147 greater than its numerator. What was the denominator of this fraction, if after the fraction was reduced it became 5/12

Answer 1

Let
`x` be the denominator of the number. Since we know that the denominator of the number was 147 greater than its numerator, the denominator of the number was
`x+147`, so our number was
`(x)/(x+147)`. We also know that after the fraction was reduced it became 5/12, so we can equate both fractions and solve for
`x`:

`(x)/(x+147) = (5)/(12)`

`12x=5(x+147)`

`12x=5x+735`

`7x=735`

`x= (735)/(7)`

`x=105`

Now we can replace 105 in our original fraction to get our number:

`(x)/(x+147)`

`(105)/(105+147) = (105)/(252)`

We can conclude that the original number was
`(105)/(252)`