What number must be added to both, the numerator and the denominator of 11/19 to make the resulting fraction equal to 5/7

Question

How to find the new fraction 

Answer 1

Hi Breanna,

 

   What number must be added to both, the numerator and the denominator of 11/19 to make the resulting fraction equal to 5/7
How to find the new fraction

 

First we need to set up the equation:

Let x=the number

 

(11+x)= 5

-------   --

(19+x)   7

 

Now cross multiply:

7(11+x)=5(19+x)

 

Use the distributive property:

 

77+7x=95+5x

 

Add -5x to both sides:

77+2x=95

 

Add -77 to both sides:

2x=18

 

Divide both sides by 2:

x=9

 

ANSWER: x=9

 

But let's check to see whether our value is correct:

 

(11+x)= 5
-------   --
(19+x)    7

 

(11+9)= 5
-------    --
(19+9)   7

 

20 = 5

---    --

28     7

 

Reduce:

 

5  =  5

--    ---

7       7      It checks!

 

We're finished.