Let [tex]x[/tex] 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 [tex]x+147[/tex], so our number was [tex] \frac{x}{x+147} [/tex]. We also know that after the fraction was reduced it became 5/12, so we can equate both fractions and solve for [tex]x[/tex]:
[tex] \frac{x}{x+147} = \frac{5}{12} [/tex]
[tex]12x=5(x+147)[/tex]
[tex]12x=5x+735[/tex]
[tex]7x=735[/tex]
[tex]x= \frac{735}{7} [/tex]
[tex]x=105[/tex]
Now we can replace 105 in our original fraction to get our number:
[tex] \frac{x}{x+147} [/tex]
[tex] \frac{105}{105+147} = \frac{105}{252} [/tex]
We can conclude that the original number was [tex]\frac{105}{252} [/tex]
