Fractions — Class 6 Maths (Ganita Prakash)

1. About This Chapter

Fractions are everywhere — dividing a pizza among friends, measuring half a cup of milk, or saying "quarter past three." Chapter 7 of Ganita Prakash builds a thorough understanding of fractions, starting from the basics and progressing through types, comparison, and arithmetic operations. By the end, students should see fractions not as abstract symbols but as practical tools for sharing, measuring, and comparing.

2. What Is a Fraction?

A fraction represents equal parts of a whole. It is written as:

$\boxed{\frac{\text{Numerator}}{\text{Denominator}}}$

• Numerator (top): The number of parts we have
• Denominator (bottom): The total number of equal parts the whole is divided into

Example: $\frac{3}{8}$ means the whole is divided into 8 equal parts, and we have 3 of them.

3. Types of Fractions

Like Fractions

Fractions with the same denominator.

Examples: $\frac{2}{7},\frac{3}{7},\frac{5}{7}$

Like fractions are easy to compare and add — just work with the numerators.

Unlike Fractions

Fractions with different denominators.

Examples: $\frac{1}{3},\frac{2}{5},\frac{3}{8}$

To compare or add unlike fractions, first convert them to like fractions.

Equivalent Fractions

Fractions that represent the same value even though they look different.

$\frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{50}{100}$

To find equivalent fractions: multiply or divide both numerator and denominator by the same number.

4. Comparing Fractions

Rule 1: Same Denominator

If denominators are the same, the fraction with the larger numerator is larger.

$\frac{5}{8}>\frac{3}{8}\text{(5 parts > 3 parts)}$

Rule 2: Same Numerator

If numerators are the same, the fraction with the smaller denominator is larger.

$\frac{1}{3}>\frac{1}{5}\text{(1 of 3 bigger pieces > 1 of 5 smaller pieces)}$

Rule 3: Different Numerators and Denominators

Convert to equivalent fractions with a common denominator (LCM of the denominators), then compare.

Compare $\frac{2}{5}$ and $\frac{1}{3}$:

• LCM of 5 and 3 = 15
• $\frac{2}{5}=\frac{6}{15}$, $\frac{1}{3}=\frac{5}{15}$
• $\frac{6}{15}>\frac{5}{15}$, so $\frac{2}{5}>\frac{1}{3}$

5. Ordering Fractions

Arrange $\frac{2}{3},\frac{5}{6},\frac{7}{12}$ in ascending order.

Solution:

• LCM of 3, 6, 12 = 12
• $\frac{2}{3}=\frac{8}{12}$, $\frac{5}{6}=\frac{10}{12}$, $\frac{7}{12}=\frac{7}{12}$
• Ascending: $\frac{7}{12},\frac{8}{12},\frac{10}{12}$
• Answer: $\frac{7}{12},\frac{2}{3},\frac{5}{6}$

6. Addition of Fractions

Like Fractions (Same Denominator)

Simply add the numerators, keep the denominator same.

$\frac{2}{7}+\frac{3}{7}=\frac{2+3}{7}=\frac{5}{7}$

Unlike Fractions (Different Denominators)

Step 1: Find LCM of denominators.
Step 2: Convert each fraction to an equivalent fraction with the LCM as denominator.
Step 3: Add the numerators, keep denominator same.
Step 4: Simplify if possible.

Example: $\frac{1}{2}+\frac{1}{3}$

• LCM of 2 and 3 = 6
• $\frac{1}{2}=\frac{3}{6}$, $\frac{1}{3}=\frac{2}{6}$
• $\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$

7. Subtraction of Fractions

Same rules as addition — just subtract instead.

Like Fractions:

$\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}=\frac{2}{8}=\frac{1}{4}$

Unlike Fractions:

$\frac{3}{4}-\frac{1}{3}$

• LCM of 4 and 3 = 12
• $\frac{3}{4}=\frac{9}{12}$, $\frac{1}{3}=\frac{4}{12}$
• $\frac{9}{12}-\frac{4}{12}=\frac{5}{12}$

8. Fractions in Daily Life

• Cooking: "Add $\frac{1}{2}$ cup of sugar and $\frac{1}{4}$ cup of oil"
• Time: "Quarter past three" = $\frac{15}{60}=\frac{1}{4}$ of an hour
• Money: "Half the price" = $\frac{1}{2}$
• Sharing: $\frac{3}{8}$ of a pizza each
• Measurement: $\frac{3}{4}$ metre of cloth

9. Key Concepts Summary

10. Worked Examples

Example 1: Equivalent fractions

Find two equivalent fractions for $\frac{3}{5}$.

Solution: Multiply by 2: $\frac{3\times 2}{5\times 2}=\frac{6}{10}$. Multiply by 3: $\frac{3\times 3}{5\times 3}=\frac{9}{15}$.

Example 2: Compare

Which is larger: $\frac{3}{4}$ or $\frac{5}{6}$?

Solution: LCM of 4 and 6 = 12. $\frac{3}{4}=\frac{9}{12}$, $\frac{5}{6}=\frac{10}{12}$. $\frac{10}{12}>\frac{9}{12}$, so $\frac{5}{6}>\frac{3}{4}$.

Example 3: Word problem

Riya ate $\frac{3}{8}$ of a chocolate bar and her friend ate $\frac{2}{8}$. How much did they eat together?

Solution: $\frac{3}{8}+\frac{2}{8}=\frac{5}{8}$. They ate $\frac{5}{8}$ of the chocolate bar together.

11. Conclusion

Fractions connects number sense with real-life sharing and measuring. Understanding fractions deeply — not just memorizing rules — is essential because fractions are the gateway to decimals, percentages, ratios, algebra, and virtually every advanced mathematical concept. The key is practice: comparing, converting, adding, and subtracting fractions until the LCM method becomes second nature.