Class 6 CBSE Maths Notes: Fractions and Decimals - Complete Guide with Example
Introduction to Fractions and Decimals
Fractions and decimals are fundamental concepts in mathematics that represent parts of a whole. A fraction expresses a portion divided into equal parts, while decimals use a decimal point to express those same values. Understanding these concepts is essential for Class 6 CBSE students as they form the foundation for many mathematical operations.
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 fraction
Answer: 2/3
Conclusion
Mastering fractions and decimals is essential for Class 6 CBSE students as these concepts appear throughout mathematics. Regular practice with conversion methods, operations, and problem-solving will build strong foundational skills. Use this comprehensive guide to strengthen your understanding and excel in your examinations