Question

The numerator of rational number is 6 less than its denominator if 3 is added to numerator the faction is equal to 2%3 find the original fraction.

Answer 1

Dear friend
I have a doubt whether the given fraction is 2/3 or 2%3. Any how I will solve for both the fractions.

If the fraction is 2/3,
Let the numerator be x
Then the denominator will be x+6
And the fraction is x / x+6
When 3 is added to the numerator, then the fraction = x+3 / x+6
According to the problem this equals 2/3
= x+3 / x+6 = 2/3
= 3(x+3) = 2(x+6) [cross multiplication]
= 3x+ 9 = 2x+12
=3x-2x = 12-9
=x = 3
Therefore, the fraction is 3/9
Proof:
= (3+3)/9 = 2/3
= 6/9 = 2/3
= 2/3 = 2/3
LHS = RHS
Thus proved.

If the fraction is 2%3,
Then the fraction is 2/100*3 = 3/50

-The remaining answer is in the photo-

Proof to the fraction in the photo
[(-132/47)+3] / (150/47) = 2%3
= [(-132+141)/47] / (150/47) = 2/100 * 3
= (9/47) / (150/47) = 3/50
=9/150 = 3/50
=3/50 = 3/50
LHS = RHS
Thus proved.

Hope this helps you