Tell me, how would you figure tthis out?

Question

The numerator of a fraction is 1 less than the denominator.If the numeraor and denominator are both increased by 4, the new fraction will be 1/8 more than the orginal fraction. Find the original fraction -

Answer 1

2/6=1/3

Answer 2

The original fraction is 3/4. If you increase by 4, you get 7/8, which is 1/8th more than the original. I tried using calculations to figure this out, but it actually does not work. It's guess-and-check.

Answer 3

You could do a guess and check method, except this particular question has more than one answer.

Using algebra:

n = d - 1 (numerator = denominator minus 1)

So your fraction is:

d - 1

-------

d

When they are both increased by 4:

d - 1 + 4

------------

d + 4

= d+3

---------

d+4

Then we're told that this new fraction is 1/8 more than the original fraction. So:

(d-1)/d + 1/8 = (d+3)/(d+4)

Find a common denominator (8d) for the fractions on the left and rewrite with equivalent fractions:

(8d-8)/8d + d/8d = (d+3)/(d+4)

Simplify the left-hand side:

(9d - 8)/8d = (d+3)/(d+4)

Multiply out your denominators:

(9d-8)(d+4) = 8d(d+3)

Simplify:

9d^2 + 36d - 8d - 32 = 8d^2 + 24d

9d^2 + 28d - 32 = 8d^2 + 24d

Bring everything to the left side so that it equals 0 on the right side:

9d^2 + 28d - 32 - 8d^2 - 24d = 0

d^2 + 4d - 32 = 0

Then factor:

(d+8)(d-4)

This leaves you with -8 and 4 as answers for d.

Going back to the original fraction:

(d-1)/d

(-8-1)/-8 = -9/-8, or 9/8.

With 4:

(4-1)/4 = 3/4

Answer 4

This kind of stuff gives me a banging headache!