Unit Fraction

A fraction represents a part of a whole and is written as p/q, where p is the numerator and q is the denominator. When the numerator is always 1 for a fraction, and the denominator is any natural number, it is known as a unit fraction. It means that any fraction in the form 1/q is termed a unit fraction. Since ‘unit’ means one, a unit fraction shows one part out of the total number of equal parts. Fractions such as \(\frac{1}{4}\), \(\frac{1}{10}\), \(\frac{1}{25}\), etc., are examples of unit fractions. 

Definition of Unit Fraction
 

A unit fraction is a fraction in which the numerator is 1 and the denominator is any natural number greater than 1. It represents one equal part of a whole that is divided into 'q' equal parts, and is written in the form \(\frac{1}{q}\). 

Unit Fraction Example: 
Imagine you cut a pizza into 8 equal slices. If you take one slice, you have to take 1 out of 8 parts, which is the unit fraction ⅛. This shows how a unit fraction represents one equal part of a whole.

Fractions are classified as unit or non-unit fractions based on the numerator. Let’s understand the difference between unit fractions and non-unit fractions.

Multiplying unit fractions is the same as multiplying any fractions. We can multiply a unit fraction with a whole number, another unit fraction, or a non-unit fraction.

Multiplying Unit Fractions with Unit Fractions

When multiplying two unit fractions, multiply the numerators and denominators.

\(\frac{1}{a} × \frac{1}{b} = \frac{1 × 1} {a × b} = \frac{1}{ab}\).

For example, 

\(\frac{1}{5} × \frac{1}{7} = \frac{1 × 1}{5 × 7}\) 

\(= \frac{1}{35}\). 


Multiplying Unit Fractions with Non-unit Fractions

To multiply a unit fraction by a non-unit fraction, multiply the numerators and denominators in the same way.

\(\frac{1}{a} × \frac{p}{q} = \frac{1 × p}{a × q} = \frac{p}{aq}\)

For example, 

\(\frac{1}{4} ×\frac{3}{8} = \frac{1 × 3}{4 × 8} = \frac{3}{32}\)

When adding unit fractions, there are two cases based on the denominator. This depends on whether the denominators are the same or different.

 

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, \(\frac{1}{5} + \frac{1}{5} = \frac{(1 + 1)}{5} = \frac{2}{5}\).

 

Adding unit fractions with different denominators: When adding unit fractions with different denominators, convert the fractions to equivalent fractions. For converting fractions to equivalent fractions, follow the steps given below:


Step 1: 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, \(\frac{1}{8} + \frac{1}{6}\).
 

Step 2: The least common denominator of 8 and 6 is 24.

Step 3: Multiplying \(\frac{1}{8}\) with \(\frac{3}{3}\), \(\frac{1}{8} × \frac{3}{3} = \frac{3}{24}\)

Step 4: Multiplying \(\frac{1}{6}\) with \(\frac{4}{4}\), \(\frac{1}{6} × \frac{4}{4} = \frac{4}{24}\)

Step 5: So adding \(\frac{3}{24}\) and \(\frac{4}{24}\), \(\frac{3}{24} + \frac{4}{24} \)

\(= \frac{(3 + 4)}{24} = \frac{7}{24}.\)

The subtraction of a unit fraction is similar to the addition, and instead of adding, we subtract.

For example, subtract \(\frac{1}{5}\) from \(\frac{1}{2}\).
 

Step 1: \(\frac{1}{2} - \frac{1}{5}\), as the fractions have different denominators, we find the least common denominator of 2 and 5
 

Step 2: The LCM of 2 and 5 is 10
 

Step 3: To convert the fraction to equivalent fractions, 

we multiply \(\frac{1}{2}\) with \(\frac{5}{5}\), that is \(\frac{1}{2} × \frac{5}{5} = \frac{5}{10}\)

Step 4: we multiply \(\frac{1}{5}\) with \(\frac{2}{2}\), that is \(\frac{1}{5} × \frac{2}{2} = \frac{2}{10}\)

\(\frac{5}{10} - \frac{2}{10} = \frac{(5 - 2)}{10} = \frac{3}{10}\)

To divide a unit fraction by a whole number, multiply it by the reciprocal of that 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: Convert the division into multiplication by using the reciprocal of the whole number.

For example, \(\frac{1}{5} ÷ 4\)

To divide \(\frac{1}{5}\) by 4, we multiply \(\frac{1}{5}\) by the reciprocal of 4. 

The reciprocal of 4 is \(\frac{1}{4}\)

That is \(\frac{1}{5} ÷ \frac{1}{4} = \frac{1}{5} × \frac{1}{4} \)

\(= \frac{1}{20} \)

Solving mathematical operations based on unit fractions can be difficult for students. Here are some quick tips and tricks to make it easy for students, parents, and teachers to guide students effectively. 

• To convert a whole number into a fraction, write it with a denominator 1.
   
• To find the reciprocal of a fraction, just flip the numerator and the denominator.
   
• Finding LCM of large numbers can be lengthy. Just multiply the first fraction with the denominator of the second fraction. Similarly, multiply the second fraction with the denominator of the first fraction.
   
• To add like fractions, just add the numerators, keeping the denominator the same.
   
• When converting unlike to like fraction, multiply both the numerator and the denominator by the same number.
   
• Parents and teachers can use compelling real-life examples, such as slices of fruit, pieces of chocolate, or paper cutouts, to visually show what 1 part of a whole looks like. 
   
• Encourage students to adopt visual learning techniques. Make them draw fraction bars or circles to represent 1/q, which helps them visualize how the size of a unit fraction changes as the denominator increases. 
   
• Before introducing operations on fractions to students, start with unit fractions. Their simple structure helps them build confidence with fractions before moving to more complex ones. 
   
• Provide them with exercises and practice problems to memorize concepts such as numerator, denominator, whole, and equal parts, often so they can easily connect these ideas to the concept of unit fractions. 
   
• Parents and teachers can show how unit fractions appear frequently in our daily lives, such as sharing food, dividing chores, or telling time, which will make learning more meaningful.

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.  
   
• To calculate time, unit fractions can be used. For example: 30 minutes is 1/2 hour.
   
• During designing a space into different zones, unit fractions are used. Like, 1/2 of the room should be the dining room, or 1/4 of the room is the closet area.