Formula For Adding Fractions

Before learning the formula for adding fractions, let us recall what are fractions. In mathematics, fractions can be defined as the parts of a whole. A fraction can be a portion or section of any quantity out of a whole, where, the whole can be any number, a specific value, or a thing. Examples are 1/2, 3/7,4/5, 6/6, etc. There are different types of fractions depending upon their form. These are 

• Proper Fraction
• Improper Fraction
• Unit Fraction
• Mixed Fraction
• Equivalent Fractions
• Like Fractions, and
• Unlike Fractions.

What Is Formula for Adding Fractions?

The formulas for adding fractions vary in each of the following situations:  Adding fractions with whole numbers, adding fractions with like denominators, adding fractions with different denominators, and adding fractions with variables. These formulas are:

• Adding fractions with whole numbers
  \(\left(a+\dfrac{b}{c}\right)\) = \(\dfrac{({a×c})+b}{c}\)

• Adding fractions with like denominators
  \(\left(\dfrac{a}{b} + \dfrac{d}{b}\right)\)=\(\dfrac{(a+d)}{b}\)

• Adding fractions with different denominators
  \(\left(\dfrac{a}{b} + \dfrac{c}{d}\right)\)=\(\left(\dfrac{a×d+b×c}{b×d}\right)\)

• Adding fractions with variables
  \(\dfrac {a}{b} x + \dfrac{ c}{b} x = \left( \dfrac{a}{b} +  \dfrac{c}{b} \right) x = \left(\dfrac{a+c}{b}\right) x\)

where

• a, b, c, and, d are constants 
• x is variable.

Let us see the applications of formula for adding fractions in the solved examples below.

Examples Using Formula for Adding Fractions

Example 1: Using the formula for adding fractions, add 3/2 and 5. 

Solution:   

To find: addition of 3/2 and 5.

We have

\(\left(a+\dfrac{b}{c}\right)\) = \(\dfrac{({a×c})+b}{c}\)

Adding Fractions = \(\dfrac{({2×5})+3}{2}\)

= (10+3)/2

= 13/2

Answer:  The addition of 3/2 and 5 is 13/2.

Example 2: If the difference between two fractions is 2/3 and one fraction is 6/5, find the original fraction.

Solution: 

To find: The original fraction.                 

Using formula for adding fractions,

Adding Fractions = \(\dfrac{a×d+b×c}{b×d}\)

Adding Fractions = \(\dfrac{2×5+6×3}{3×5}\)

= (10+18)/15

= 28/15

Answer: The original fraction is 28/15.