CBSE Class 6 Maths — Fractions

What is a Fraction?

A fraction represents a part of a whole or a part of a collection. It consists of a top number called the numerator and a bottom number called the denominator.

• Numerator: Shows how many parts we have taken.
• Denominator: Shows how many equal parts the whole is divided into.

[ X | X | X |   |   ]  = 3 shaded out of 5 total = 3/5

Types of Fractions

1. Proper Fractions

Fractions where the numerator is less than the denominator. They are always less than 1. Examples: $\frac{1}{4}, \frac{5}{8}, \frac{99}{100}$.

2. Improper Fractions

Fractions where the numerator is greater than or equal to the denominator. They are $\ge 1$. Examples: $\frac{5}{4}, \frac{11}{8}, \frac{7}{7}$.

3. Mixed Fractions (Mixed Numbers)

A combination of a whole number and a proper fraction. They can be converted into improper fractions and vice versa. Example: $2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$.

Like and Unlike Fractions

• Like Fractions: Fractions with the same denominators. (e.g., $\frac{1}{7}, \frac{3}{7}, \frac{5}{7}$)
• Unlike Fractions: Fractions with different denominators. (e.g., $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$)

Equivalent Fractions

Fractions that represent the same value or part of a whole. For example, $\frac{1}{2}$ is the same as $\frac{2}{4}$, $\frac{3}{6}$, or $\frac{50}{100}$.

To find equivalent fractions, you either multiply or divide the numerator and denominator by the same non-zero number.

graph LR
    A["1 / 2"] -- "Multiply by 3" --> B["3 / 6"]
    B -- "Multiply by 2" --> C["6 / 12"]
    C -- "Divide by 6" --> A

Simplest Form: A fraction is in simplest form when the numerator and denominator have no common factor other than 1. (e.g., $\frac{15}{20} \rightarrow \text{divide by } 5 \rightarrow \frac{3}{4}$).

Comparing and Adding Fractions

Comparing Like Fractions

Just compare the numerators! The fraction with the greater numerator is larger. $\frac{4}{9} > \frac{2}{9}$

Adding and Subtracting

Rule 1: For Like Fractions, simply add/subtract the numerators and keep the denominator the same.

Rule 2: For Unlike Fractions, first convert them to like fractions using their Lowest Common Multiple (LCM), and then add/subtract.

Example: Add $\frac{1}{4} + \frac{2}{5}$

1. Denominators are 4 and 5. LCM of 4 and 5 is 20.
2. $\frac{1}{4} = \frac{5}{20}$
3. $\frac{2}{5} = \frac{8}{20}$
4. Add: $\frac{5}{20} + \frac{8}{20} = \frac{13}{20}$.