Unit Fraction

A fraction is a type of number that represents a part of a whole and is written in the form p/q. A unit fraction is a type of fraction where the numerator is always 1 and the denominator can be any natural number. The word ‘unit’ means one, which is why the fraction with 1 as the numerator is called a unit fraction. For example, 1/4, 1/23, and 1/45.

The fractions can be classified into unit fractions and non-unit fractions based on the numerator and denominator. Let’s understand the difference between unit fractions and non-unit fractions.

The multiplication of a unit fraction follows the same rules as fractions. We can multiply a unit fraction with a whole number, another unit fraction, or a non-unit fraction. When multiplying two unit fractions, we first multiply the numerators and then the denominators.  It can be expressed as 1/a × 1/b = (1 × 1)/(a × b), 


For example, 
1/5 × 1/7 = (1 × 1)/(5 × 7) = 1/35
 

When adding unit fractions, there are two cases based on the denominator. That is, whether the denominators are the same or not. 
 

• Adding unit fractions with the same denominators:
  
  When the denominator is the same, we add the numerators and the denominator is kept unchanged; then the answer is simplified if necessary. 
  
  For example, 1/5 + 1/5 = (1 + 1)/5 = 2/5.
  
   
• Adding unit fractions with different denominators:
  
  When adding unit fractions with different denominators, convert the fractions to equivalent fractions. First, we need to find the least common multiple of the denominators. If the fractions have the same denominators, then just by adding the numerators, the result is obtained. 
  
  For example, 1/8 + 1/6
  
  The least common denominator of 8 and 6 is 24.
  Multiplying 1/8 with 3/3, 1/8 × 3/3 = 3/24
  Multiplying 1/6 with 4/4, 1/6 ×4/4 = 4/24
  So adding 3/24 and 4/24, 3/24 + 4/24 
  = (3 + 4)/24 = 7/24.

The subtraction of a unit fraction is similar to the addition, and instead of adding, we subtract. For example, subtract 1/5 from 1/2
1/2 - 1/5, as the fractions have different denominators, we find the least common denominator of 2 and 5
The LCM of 2 and 5 is 10

To convert the fraction to equivalent fractions, 
we multiply 1/2 with 5/5, that is 1/2 × 5/5 = 5/10
we multiply 1/5 with 2/2, that is 1/5 × 2/2 = 2/10
5/10 - 2/10 = (5 - 2)/10 = 3/10
 

Dividing a unit fraction by a whole number is done by multiplying the fraction by the reciprocal of the whole number. By following these steps, you can divide a unit fraction by a whole number.



Step 1: Take the reciprocal of the whole number

Step 2: Change the division to the multiplication of the first fraction by the reciprocal of the whole number

For example, 1/5 ÷ 4

To divide ⅕ by 4, we multiply ⅕ by the reciprocal of 4. 
The reciprocal of 4 is 1/4
That is 1/5 ÷ 1/4 = 1/5 × 1/4 
= 1/20 
 

In real life, we use unit fractions in different fields such as cooking, shopping, math, physics, and so on. Here are the applications of unit fractions:
 

• We use fractions when dividing an object among a group. For example, to cut a cake into equal slices, such as 1/4, 1/6, etc.
   
• In cooking and baking, to measure the ingredients, we mostly use unit fractions, for example, 1/2 cup of sugar, 1/4 teaspoon, etc.
   
• To calculate the discount in shopping, we use unit fractions, for example, ½ off.