Question

the numerator of a fraction is 4 less than its denominator if 2 is added to the numerator then the fraction becomes 5 by 7 find the fraction

Answer 1

Let the denominator be x.
Then numerator =x-4.
According to question
(X-4+2)/x=5/7
5x=7x-14
-2x=-14
X=7
Therefore fraction becomes 3/7

Answer 2

The complete fraction is 3/7.

Step-by-step explanation:

According to the given information, it is given that the numerator of a fraction is 4 less than its denominator and if 2 is added to the numerator then the fraction becomes 5 by 7 .

Now, let the numerator of the fraction be x and let the denominator of the fraction be y.

Now, according to the given information, the numerator of the fraction is 4 less than its denominator. Then, we have,

x = y - 4.

Again, according to the given information, if 2 is added to the numerator then the fraction becomes 5 by 7.

Then, we get,

(x+2)/y = 5/7

Simplifying this equation, we get,

Cross multiplying, we get,

7(x+2) = 5y

Or, 7x + 14 = 5y

Or, 7x = 5y - 14.

Now, we already have got one relation between x and y initially that is,

x = y - 4...(1)

Multiplying both sides with 7, we get,

7x = 7y - 28.

Subtracting the above equation from the recently got equation, we get,

7x = 5y - 14.

7x = 7y - 28.

-     -  +

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

0 = -2y +14

Or, 2y = 14

Or, y = 7.

Now, substituting this value in (1) , we get,

x = 7 - 4 = 3

Thus, the complete fraction is 3/7.

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