Question

The denominator of a rational number is 7 more than the numerator. If 1 is added to the numerator and 1 is subtracted from denominator the new number is 1/2. Find the rational number ?​

Answer 1

Step-by-step explanation:

Given :-

The denominator of a rational number is 7 more than the numerator.

If 1 is added to the numerator and 1 is subtracted from denominator the new number is 1/2.

To find :-

The rational number

Solution :-

Let the numerator of a rational number be X

Then, The denominator of the rational number

= Numerator + 7

= X+7

Then, the fraction = X/(X+7)

On adding 1 to the numerator then it becomes X+1

On subtracting 1 from the denominator then it becomes X+7-1 = X+6

Then, the new rational number = (X+1)/(X+6)

According to the given problem

The new rational number = 1/2

Therefore, (X+1)/(X+6) = 1/2

On applying cross multiplication then

=> 2(X+1) = 1(X+6)

=> 2X+2 = X+6

=> 2X-X = 6-2

=> X = 4

Therefore, X = 4

Numerator = 4

Denominator = X+7 = 4+7 = 11

Therefore, The rational number = 4/11

Answer :-

The required rational number = 4/11

Check :-

The rational number = 4/11

Denominator = 11 = 4+7

Denominator = Numerator+7

If 1 is added to the numerator and 1 is subtracted from the denominator then it becomes

(4+1)/(11-1)

= 5/10

= 1/2

Verified the given relations in the given problem.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Given :-

The denominator of a rational number is 7 more than the numerator.

If 1 is added to the numerator and 1 is subtracted from denominator the new number is 1/2.

To find :-

The rational number

Solution :-

Let the numerator of a rational number be X

Then, The denominator of the rational number

= Numerator + 7

= X+7

Then, the fraction = X/(X+7)

On adding 1 to the numerator then it becomes X+1

On subtracting 1 from the denominator then it becomes X+7-1 = X+6

Then, the new rational number = (X+1)/(X+6)

According to the given problem

The new rational number = 1/2

Therefore, (X+1)/(X+6) = 1/2

On applying cross multiplication then

=> 2(X+1) = 1(X+6)

=> 2X+2 = X+6

=> 2X-X = 6-2

=> X = 4

Therefore, X = 4

Numerator = 4

Denominator = X+7 = 4+7 = 11

Therefore, The rational number = 4/11

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