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Mathematics Class 6 - Fractions Notes

Comprehensive study notes for Class 6 - Fractions olympiad preparation

Fractions

Welcome to the chapter on Fractions for Class 6. In this chapter, you will learn what fractions are, how to compare and simplify them, and how to add, subtract, multiply, and divide fractions. By the end of this chapter, you will be able to solve problems using fractions confidently!

Introduction

A fraction is a way to show a part of a whole. Fractions are written as a/b, where a is the numerator (top number) and b is the denominator (bottom number).

Types of Fractions

  • Proper Fraction: Numerator is less than denominator (e.g., 3/5).
  • Improper Fraction: Numerator is greater than or equal to denominator (e.g., 7/4).
  • Mixed Fraction: A whole number and a proper fraction together (e.g., 2 1⁄3).
  • Like Fractions: Fractions with the same denominator (e.g., 2/7, 5/7).
  • Unlike Fractions: Fractions with different denominators (e.g., 1/3, 2/5).

Comparing Fractions

To compare fractions, make their denominators the same or use cross multiplication.

  • Example: Which is greater, 3/8 or 5/8? (5/8 is greater)
  • Example: Compare 2/5 and 3/7 using cross multiplication.

Simplifying Fractions

To simplify a fraction, divide both numerator and denominator by their greatest common factor (GCF).

  • Example: 6/12 = 1/2 (divide both by 6)

Equivalent Fractions

Fractions that look different but have the same value are called equivalent fractions.

  • Example: 1/2 = 2/4 = 4/8

Operations with Fractions

  • Addition: Make denominators the same, then add numerators.
  • Subtraction: Make denominators the same, then subtract numerators.
  • Multiplication: Multiply numerators and denominators directly.
  • Division: Flip the second fraction and multiply.

Examples:
Addition: 1/4 + 2/4 = 3/4
Subtraction: 5/6 - 1/6 = 4/6 = 2/3
Multiplication: 2/3 × 3/5 = 6/15 = 2/5
Division: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8

Word Problems

Use fractions to solve real-life problems. Read the question, choose the correct operation, and solve.

  • Example: If you eat 2/5 of a cake and your friend eats 1/5, how much cake is eaten in total? (2/5 + 1/5 = 3/5)

Fun Activity: Fraction Pizza!

Draw a pizza and divide it into equal parts. Color some parts and write the fraction that shows how much is colored.

Summary

  • Fractions show parts of a whole.
  • Learn to compare, simplify, and find equivalent fractions.
  • You can add, subtract, multiply, and divide fractions.

Practice Questions

  1. Write two equivalent fractions for 1/3.
  2. Simplify: 8/12
  3. Add: 2/7 + 3/7
  4. Subtract: 5/8 - 3/8
  5. Multiply: 2/5 × 3/4
  6. Divide: 3/7 ÷ 2/5

Challenge Yourself

  • Make a word problem using fractions and solve it.
  • Find three pairs of equivalent fractions.

Did You Know?

  • Fractions are used in cooking, shopping, and sharing things every day!
  • Decimals and percentages are also ways to show parts of a whole.

Glossary

  • Fraction: A part of a whole, written as a/b.
  • Numerator: The top number in a fraction.
  • Denominator: The bottom number in a fraction.
  • Equivalent: Having the same value.

Answers to Practice Questions

  1. 2/6, 3/9
  2. 2/3
  3. 5/7
  4. 2/8 = 1/4
  5. 6/20 = 3/10
  6. 3/7 × 5/2 = 15/14

Practice fractions every day to become a math expert!

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