Question

the denomintaor of a fraction is 4 more than the numerator if the denominator is increased by 1 and numerator is decreased by 1 the fraction become 4/7 find the fraction

Answer 1

Step-by-step explanation:

Given :-

The denomintaor of a fraction is 4 more than the numerator if the denominator is increased by 1 and numerator is decreased by 1 the fraction become 4/7 .

To find :-

Find the fraction ?

Solution :-

Let the numerator in the fraction be X

Then, the denominator = Numerator +4

=> X+4

If the numerator is decreased by 1 then it becomes X-1

If the denominator is increased by 1 then it becomes X+4+1 = X+5

Then, the new fraction = (X-1)/(X+5)

According to the given problem

The new fraction = 4/7

=> (X-1)/(X+5) = 4/7

On applying cross multiplication then

=> 7(X-1) = 4(X+5)

=> 7X-7 = 4X+20

=> 7X-4X = 20+7

=> 3X = 27

=> X = 27/3

=> X = 9

The numerator = 9

The denominator = 9+4 = 13

The fraction = 9/13

Answer:-

The required fraction for the given problem is 9/13

Check:-

The fraction = 9/13

The numerator = 9

The denominator = 9+4 = 13

Denominator is 4 more than the numerator

if the denominator is increased by 1 and numerator is decreased by 1 the fraction becomes

=> (9-1)/(13+1)

=> 8/14

=> 4/7

Verified the given relations in the given problem.