The denominator of a fraction is 1 less than 3 times it's numerator. If the numerator and denominator are increased by 3, the fraction becomes 1/2.

Question

I need to find the fraction. Tried everything I could think of. also this is 8th grade maths

 

Answer 1

Hello Talal. Hope all is well.

 

We know nothing about the numerator, so

THAT is where we assign the variable.

 

Let N be the numerator of the fraction.

Then the denominator is 3N-1 <--- it is 1 less than 3 times the numerator.

 

So the fraction looks like this:

 

       N

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

   3N - 1

 

 

Now what happens next is if both the numerator and the denominator

are increased by 3, the fraction becomes 1/2

 

so the fraction becomes:

 

 

      N+3                1

------------   =    ------- 

  3N - 1+3             2

 

The denominator can be simplified:

 

  N+3             1

--------  =   ----------

 3N + 2          2

 

Cross multiplication :

 

2(N+3) = 1*(3N+2)

 

2N + 6 = 3N + 2  <---- distributive property

 

0 = 3N + 2 - 2N - 6 <---- moves everything to the right side

 

0 = N - 4  <--- combines like terms

 

N = 4 <--- solves for N

 

So the numerator is 4

Then the denominator is 3*4 - 1 = 11

 

So the original fraction is 4/11

 

When 3 is added to both the numerator and denominator,

the fraction becomes 7/14 which does reduce to 1/2.

 

The original fraction is 4/11