# A fraction becomes 9/11 if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 5/6, find the fraction by substitution method.

Fractions are the numerical values that are a part of the whole. A whole can be an object or a group of objects. If a number or a thing is divided into equal parts, then each part will be a fraction of the whole. A fraction is denoted as a/b, where a is the numerator and b is the denominator. The 3 types of fractions in Maths are
• Proper fractions
• Improper fractions
• Mixed fractions
Example:
1. If a watermelon is divided into four equal parts, then each part is a fraction of ¼.
2. If a pizza is divided into three equal parts, then each part shows 1/3rd of pizza.

### Solution

• Let the Numerator of the fraction to be identified be x
• Let the Denominator of the fraction to be identified be y

Hence the fraction will be= x/y

According to the given data, we note that

If 2 is added to both numerator and denominator the fraction becomes 9/11.

In equation we can represent it as

⇒ (x + 2)/y + 2 = 9/11

On Cross multiplying ,

⇒ 11x + 22 = 9y + 18

Subtracting 22 from both sides,

⇒ 11x = 9y – 4

Dividing by 11, we get

⇒ x = 9y – 4/11 … (i)

Then, another given condition f 3 is added to both numerator and denominator it becomes 5/6,

The equation can be written as

⇒ (x+3)/y +3 = 5/6 … (ii)

On Cross multiplying ,

⇒ 6x + 18 = 5y + 15

Subtracting the value of x, we get

⇒ 6(9y – 4 )/11 + 18 = 5y + 15

Subtracting 18 from both the sides

⇒ 6(9y – 4 )/11 = 5y – 3

⇒ 54 – 24 = 55y – 33

⇒ –y = – 9

⇒ y = 9

Putting this value of y in equation (i), we get

⇒ x = 9y – 4

⇒ x = (81 – 4)/77

⇒ x = 77/11

⇒ x = 7

Hence, the fraction is 7/9.

Check out the video given below to know more about fractions.