Question

The numerator of a fraction is 5 less than its denominator. If 1 is added ti the number and to the denominator, the new is 2/3. Find the fraction ​

Answer 1

Answer:

Step-by-step explanation:

Suppose the denominator is x,

then the numerator is x-5, since numerator is 5 less than denominator.

And the required fraction is (x-5)/x

If we use the given scenario, when 1 is added to the numerator and denominator , the fraction becomes 2/3

Adding 1 to both numerator and denominator:

(x-5+1)/(x+1) = 2/3

or 3 (x-4) = 2(x+1)

or 3x-12 = 2x+2

or 3x-2x = 2+12     that is x =14 and x-5 = 9

Thus the required fraction (x-5)/x = 9/14.

check: adding 1 to both numerator and denominator, we get (9+1)/(14+1) = 1015 = 2/3, which is given in the question .

Thus the answer is 9/14.

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Answer 2

Answer:

9/14

Step-by-step explanation:

Let fraction be (x-5)/x

(x-5+1)/(x+1)=2/3

(x-4)/(x+1)=2/3

3(x-4)=2(x+1)

3x-12=2x+2

x=14

Fraction=9/14