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
Frequently Asked Questions
A proper fraction has a numerator smaller than its denominator (e.g., 3443), while an improper fraction has a numerator greater than or equal to its denominator (e.g., 7447).
Divide the numerator by the denominator using long division. For example, 34=3÷4=0.7543=3÷4=0.75. Alternatively, convert the fraction to an equivalent fraction with a denominator of 10, 100, or 1000.
Like fractions have the same denominator (2772, 5775), making them easy to add or subtract. Unlike fractions have different denominators (2552, 3773) and must be converted to like fractions before operations.
Multiply or divide both the numerator and denominator by the same non-zero number. For example, 23=2×43×4=81232=3×42×4=128.
No, fractions with zero in the denominator are undefined. Division by zero is not mathematically valid. However, zero in the numerator is acceptable and equals zero (e.g., 05=050=0).
Find the LCM of the denominators, convert all fractions to equivalent fractions with this common denominator, then add the numerators. Keep the common denominator and simplify if needed.
A mixed fraction combines a whole number with a proper fraction (e.g., 234243). To convert, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator: 234=(2×4)+34=114243=4(2×4)+3=411.
Multiply the numerators together and the denominators together, then simplify. For example, 23×45=2×43×5=81532×54=3×52×4=158.
The answer should have as many decimal places as the number with the most decimal places in the problem. Convert all decimals to like decimals before adding to avoid errors.
Use the algebraic method: let x equal the repeating decimal, multiply by an appropriate power of 10, subtract the equations, and solve for x. For example, 0.3‾=130.3=31.