Question

When the number x is added to both the numerator and the denominator of the fraction 3/8 the result is the fraction 3/4. What is x equal to?

Answer 1

Answer:

If the same number is added to both the numerator and denominator of the fraction 6/9 and get a result of 2, what number is added?

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Let the number x to be added to both numerator and denominator as

=(6+x)/(9+x)

Now according to the condition this fraction is equal to 2

(6+x)/(9+x)=2 (1)

Multiplying (9+x) on both sides

(6+x)=2(9+x) (As (9+x) cancelled on the R.H.S)

6+x=18+2x (By distributive property)

subtracting 2x from both sides

6+x-2x=18+2x-2x

6-x=18

subtracting 6 from both sides

6-6-x=18-6

-x=12

Multiplying -1 on both sides

x=-12 (Answer)

Now You can check by putting back the value of x in equation (1) as

(6+x)/(9+x)=2

(6+(-12))/9+(-12)=2

(6-12)/(9-12)=2

-6/-3=2

2=2

Hence proved.