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
FAQs on Fractions and Decimals Notes
A fraction is a number that represents a part of a whole. It consists of two parts: the numerator and the denominator. The numerator shows how many parts are taken, while the denominator shows the total number of equal parts. In Class 6 Maths, students learn different types of fractions such as proper fractions, improper fractions, and mixed fractions. Fractions are used in everyday life for sharing food, measuring quantities, and dividing objects equally. Understanding fractions helps students compare quantities, solve word problems, and prepare for advanced mathematical concepts taught in higher classes.
Fractions and decimals are two different ways of representing the same quantity. A fraction is written in the form of numerator and denominator, while a decimal is written using a decimal point. For example, one-half can be written as a fraction and also as a decimal. Decimals are commonly used in measurements, money calculations, and scientific data. Fractions are useful when dealing with equal parts of a whole. Learning the relationship between fractions and decimals helps students convert one form into another and solve mathematical problems more efficiently and accurately.
Comparing fractions means determining which fraction is greater, smaller, or equal. When fractions have the same denominator, students compare the numerators directly. If the denominators are different, equivalent fractions can be created to make comparison easier. Visual models such as fraction strips and diagrams also help students understand comparisons. This concept is important because it develops number sense and logical thinking. Comparing fractions is frequently tested in school examinations and forms the basis for fraction operations such as addition, subtraction, multiplication, and division in higher mathematics.
Equivalent fractions are fractions that represent the same value even though they appear different. They are obtained by multiplying or dividing both the numerator and denominator by the same non-zero number. For example, different fractions can represent the same portion of a whole. Understanding equivalent fractions helps students simplify fractions, compare fractions, and perform calculations more effectively. This topic is one of the most important concepts in the Fractions and Decimals chapter because it strengthens the understanding of numerical relationships and supports future learning in algebra and ratio concepts.
Decimals are used extensively in everyday activities. They are commonly seen in money transactions, measurements of length and weight, fuel quantities, sports statistics, and scientific calculations. For example, prices in shops often include decimal values, and measurements may require tenths or hundredths of a unit. Understanding decimals enables students to read and interpret real-world information accurately. The Class 6 chapter teaches students how to read, write, compare, and use decimals confidently. These skills are essential for practical mathematics and help students connect classroom learning with real-life situations.
Converting a fraction into a decimal involves dividing the numerator by the denominator. This process helps students understand that fractions and decimals can represent the same quantity in different forms. Some fractions convert into simple terminating decimals, while others may produce repeating patterns. Learning this conversion improves numerical flexibility and strengthens problem-solving skills. It is an important topic because many practical applications, such as money and measurement, use decimal notation. Class 6 students are introduced to basic fraction-to-decimal conversions to build a strong foundation for more advanced mathematical operations.
Fractions and Decimals is considered a foundational chapter because it introduces students to numbers beyond whole numbers. The concepts learned here are used throughout mathematics, including percentages, ratios, algebra, geometry, and statistics. This chapter develops logical reasoning, estimation skills, and numerical accuracy. It also helps students solve real-life problems involving measurements, money, and sharing quantities. A strong understanding of fractions and decimals makes future mathematical topics easier to learn. Students who master this chapter gain confidence in calculations and develop the skills necessary for academic success in mathematics.