Fractions Class 6: Types, Comparison, Addition & Subtraction

A fraction represents a part of a whole. When you cut a pizza into 4 equal slices and eat 1 slice, you have eaten $\frac{1}{4}$ of the pizza.

A fraction is written as:

• The numerator (top number) tells you how many parts you have.
  - The denominator (bottom number) tells you how many equal parts the whole is divided into.

For example, in $\frac{3}{5}$: the numerator is $3$ (you have 3 parts) and the denominator is $5$ (the whole is divided into 5 equal parts).

Important: The denominator can never be zero. $\frac{3}{0}$ is undefined.

Just like whole numbers, fractions can be placed on a number line.

To plot $\frac{3}{4}$ on a number line:
1. The fraction is between $0$ and $1$ (since $\frac{3}{4} < 1$).
2. Divide the segment from $0$ to $1$ into $4$ equal parts.
3. Count $3$ parts from $0$. That point is $\frac{3}{4}$.

To plot $\frac{7}{4}$ on a number line:
1. $\frac{7}{4} = 1\frac{3}{4}$, so it is between $1$ and $2$.
2. Divide the segment from $1$ to $2$ into $4$ equal parts.
3. Count $3$ parts from $1$. That point is $\frac{7}{4}$.

The number line helps you see that fractions are not just "parts of things" but actual numbers with precise positions.

There are several ways to classify fractions.

Equivalent fractions are different fractions that represent the same value.

To get an equivalent fraction, multiply (or divide) both the numerator and denominator by the same non-zero number.

How to check if two fractions are equivalent: Cross multiply. If the cross products are equal, the fractions are equivalent.

Example: Are $\frac{3}{4}$ and $\frac{9}{12}$ equivalent?
$3 \times 12 = 36$ and $4 \times 9 = 36$. Yes, they are equivalent.

A fraction is in its simplest form (or lowest terms) when the numerator and denominator have no common factor other than $1$.

To reduce a fraction to its simplest form, divide both the numerator and the denominator by their HCF (Highest Common Factor).

Example: Simplify $\frac{12}{18}$.
- HCF of $12$ and $18$ is $6$.
- $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$

Example: Simplify $\frac{35}{49}$.
- HCF of $35$ and $49$ is $7$.
- $\frac{35}{49} = \frac{35 \div 7}{49 \div 7} = \frac{5}{7}$

Quick check: If the numerator and denominator are both even, you can definitely simplify by dividing by $2$. If both end in $0$ or $5$, divide by $5$. Keep dividing until no common factor remains.

There are several methods to compare fractions.

Adding and subtracting fractions is one of the most important skills in Class 6 Maths.

Fractions are one of those topics that come back again and again, in Class 7 (multiplication and division of fractions), Class 8 (rational numbers), and all the way through Class 10. Getting the basics right now will save you a lot of trouble later.

SparkEd has 60 practice questions on Fractions for Class 6 CBSE, covering every type discussed above. Each question has a detailed step-by-step solution.

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