Introduction to Class 6 Maths Chapter Fractions and Decimals
Fractions and Decimals is one of the most practical and important chapters in Class 6 Mathematics. This chapter introduces students to numbers that represent parts of a whole and quantities that are not always expressed as complete numbers. Students learn how to identify and write fractions, understand numerators and denominators, compare fractions, and recognize equivalent fractions. The chapter also explains proper fractions, improper fractions, and mixed numbers through simple examples from daily life.
The second part of the chapter focuses on decimals, helping students understand tenths, hundredths, and the relationship between fractions and decimals. Learners practice reading, writing, comparing, and using decimal numbers in different situations such as measuring length, weight, money, and distance. The chapter develops a strong foundation for advanced mathematical concepts that students will encounter in higher classes. Must-read Class 6 Maths Notes and NCERT Solutions for class 6, NCERT exemplar for class 6.
By studying Fractions and Decimals, students improve their numerical reasoning and problem-solving abilities. The concepts taught in this chapter are widely used in shopping, cooking, measurement, banking, and science. A clear understanding of fractions and decimals helps students perform calculations accurately and builds confidence in handling real-life mathematical situations. Mastering this chapter is essential for developing a strong base in mathematics and preparing for future topics involving percentages, ratios, algebra, and data handling.
Class 6 CBSE Maths Notes: Fractions and Decimals - Complete Guide with Example
What Are Fractions?
A fraction is a part of a whole and consists of a numerator (top number) and a denominator (bottom number). For example, in 3/4, 3 is the numerator, and 4 is the denominator.
Types of Fractions
- Proper Fractions: Numerator < Denominator (e.g. 2/5, 7/12).
- Improper Fractions: Numerator ≥ Denominator (e.g. 7/4, 9/5).
- Mixed Fractions: Combination of a whole number and a proper fraction (e.g. 2 3/4).
- Like Fractions: Same denominator (2/7, 6/7).
- Unlike Fractions: Different denominators (2/5, 3/7).
- Equivalent Fractions: Represent same value, e.g. 2/3 = 4/6 = 6/9.
Understanding Decimals
Decimals are numbers that use a decimal point, separating the whole and fractional parts. Fractions with denominators of 10, 100, 1000, etc. become decimal fractions and can be written in decimal notation.
Place Value in Decimals
| Position | Place Value | Fraction Equivalent |
| Tenths | 0.1 | 1/10 |
| Hundredths | 0.01 | 1/100 |
| Thousandths | 0.001 | 1/1000 |
Like and Unlike Decimals
- Like decimals: Same number of decimal places (e.g., 5.235, 17.567).
- Unlike decimals: Different decimal places (e.g., 2.576, 3.04).
How to Convert a Decimal to a Fraction Step by Step
- Write the decimal number without the decimal point as the numerator.
- For the denominator, write 1 followed by as many zeros as the number of decimal places.
- Simplify the fraction to its lowest terms using HCF.
Example 1: 0.75 = 75/100 = 3/4
Example 2: 2.6 = 26/10 = 13/5 (or 2 3/5)
How to Add and Subtract Fractions with Different Denominators
- Find the LCM of the denominators.
- Convert each fraction to an equivalent one with the common denominator.
- Add (or subtract) the numerators, keeping the denominator same.
- Simplify if possible.
Add: 2/3 + 5/6 = 4/6 + 5/6 = 9/6 = 3/2
Subtract: 5/6 - 2/3 = 5/6 - 4/6 = 1/6
How to Multiply and Divide Fractions with Examples
Multiplication of Fractions
Multiply numerators together and denominators together.
- Example: 2/5 × 3/7 = 6/35
- Example: 2 1/3 × 3/4 = 7/3 × 3/4 = 21/12 = 7/4 = 1 3/4
Division of Fractions
Multiply the first fraction by the reciprocal of the second.
- Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
- Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1 1/4
How to Convert Repeating Decimals to Fractions
- Identify repeating digits, set the decimal equals x.
- Multiply both sides by a power of 10 to move the decimal point.
- Subtract original equation from new equation.
- Solve for x and simplify.
Example 1: 0.333... = 1/3
Example 2: 0.121212... = 12/99 = 4/33
Formulas for Fractions and Decimals
| Formula Name | Mathematical Representation | Explanation |
|---|---|---|
| Equivalent Fractions | a/b = (a×c)/(b×c) | Multiply numerator & denominator by the same number |
| Add Like Fractions | a/c + b/c = (a+b)/c | Add numerators, keep denominator |
| Subtract Like Fractions | a/c - b/c = (a-b)/c | Subtract numerators, keep denominator |
| Multiply Fractions | (a/b) × (c/d) = (a×c)/(b×d) | Multiply numerators and denominators |
| Divide Fractions | (a/b) ÷ (c/d) = (a/b) × (d/c) | Multiply by reciprocal |
| Mixed to Improper | a b/c = (a×c + b)/c | Convert mixed to improper fraction |
| Decimal to Fraction | 0.abc = abc/1000 | Denominator based on decimals |
| Fraction to Decimal | a/b = a ÷ b | Divide numerator by denominator |
Practice Problems for Fractions and Decimals with Answers
Q1: Add 3/8 + 5/8
Answer: 8/8 = 1
Q2: Subtract 7/10 - 3/10
Answer: 4/10 = 2/5
Q3: Convert 3.75 to fraction
Answer: 375/100 = 15/4 or 3 3/4
Q4: Add 7.25 + 98.005 + 545.28
Answer: 650.535
Q5: Multiply 2/3 × 5/7
Answer: 10/21
Q6: Renu painted 2/5 of a wall and Meera 3/5. How much is left?
Answer: 2/5 + 3/5 = 1; Left = 0
Q7: Convert 7/25 to decimal
Answer: 0.28
Q8: Divide 5/6 ÷ 2/3
Answer: 5/4 or 1 1/4
Q9: Simplify 210/300
Answer: 7/10
Q10: Convert 0.666... to a fraction
Answer: 2/3