Question

The sum of the numerator and the denominator
of a fraction is 9. If one is added to the numerator
and one is subtracted from the denominator, it

reduces to 1/2 Find the fraction.
​

Answer 1

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf x+y= 9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition :-

$\longrightarrow\sf \dfrac{x+1}{y-1}=\dfrac{1}{2} \\\\\longrightarrow 2(x+1)=y-1 \\\\\longrightarrow 2x+2 = y - 1 \\\\\longrightarrow 2x-y = -3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Equation (2) + Equation (1) :-

$\longrightarrow \sf 3x = 6 \\\\\longrightarrow \bf x=2$

Substitute the value of x in eq (1) :-

$\longrightarrow \sf 2+y = 9 \\\\\longrightarrow \bf y = 7$

$\bf FRACTION = \dfrac{2}{7}$

Answer 2

Step-by-step explanation:

Given :

• The sum of the numerator and the denominator of a fraction is 9.

• If one is added to the numerator and one is subtracted from the denominator,

To find :

• it reduces to 1/2 Find the fraction.

Solution :

Concept

• A denominator can be defined as the bottom number in a fraction that shows the number of equal parts an item is divided into. It is the divisor of a fraction.

Example= In the fraction 2/3 the numerator is 2 and the denominator is 3.

• Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).

• Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.

• Then add (or subtract) the fractions, as we wish!

Let the numerator be x and the denominator be y.

So the fraction will be x/y.

✪ According to the Question. ✪

sum of the numerator and the denominator of a fraction is 9.

x + y = 9

x = 9 - y    ......... ( 1 )

One is added to the numerator and one is subtracted from the denominator, it reduces to 1/2.

➪ (x + 1)/(y - 1) = 1/2

➭ 2(x + 1) = y - 1

➪ 2x + 2 = y - 1

☯ Substitute the Value of x

➭ 2 ( 9 - y ) + 2 = y - 1

➭ 18 - 2y + 2 = y - 1

➭ 20 - 2y = y - 1

➭ 20 + 1 = y + 2y

➭ 21 = 3y

➭ y = 21/3y

➭ y = 7

• ☯ Putting the Value of x in Equ. ( 1 )

➭ x = 9 - y

➭ x = 9 - 7

➭ x = 2

Therefore,

• Fraction = 2/7

Hence the fraction. is 2/7