Class 6 Maths Fractions Notes

Introduction:
The chapter “Fractions” introduces students to a fundamental concept in mathematics—dividing a whole into smaller, equal parts. Fractions are used to represent parts of a whole or a set. This chapter lays the groundwork for understanding how fractions work, their types, and how to perform basic operations like addition, subtraction, and simplification with fractions.

Key Concepts Covered:

1. What is a Fraction?
   • A fraction represents a part of a whole. It consists of two parts:
     • Numerator: The number above the fraction bar, representing the number of parts taken.
     • Denominator: The number below the fraction bar, representing the total number of equal parts the whole is divided into.
   • Example: In the fraction $\frac{3}{4}$43​, 3 is the numerator, and 4 is the denominator.
2. Types of Fractions:
   • Proper Fractions: The numerator is smaller than the denominator (e.g., $\frac{3}{4}$43​).
   • Improper Fractions: The numerator is greater than or equal to the denominator (e.g., $\frac{5}{3}$35​).
   • Mixed Numbers: A whole number combined with a proper fraction (e.g., $1 \frac{1}{2}$121​).
   • Like Fractions: Fractions with the same denominator (e.g., $\frac{2}{5}$52​ and $\frac{3}{5}$53​).
   • Unlike Fractions: Fractions with different denominators (e.g., $\frac{2}{3}$32​ and $\frac{5}{4}$45​).
3. Equivalent Fractions:
   • Fractions that represent the same value but have different numerators and denominators (e.g., $\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$21​=42​=84​).
   • You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number.
4. Simplification of Fractions:
   • Fractions can be simplified by dividing both the numerator and denominator by their Greatest Common Divisor (GCD).
   • Example: $\frac{8}{12}$128​ can be simplified by dividing both the numerator and denominator by 4, resulting in $\frac{2}{3}$32​.
5. Addition and Subtraction of Fractions:
   • Like Fractions: Simply add or subtract the numerators and keep the denominator the same.
   • Unlike Fractions: Find the Least Common Denominator (LCD), convert the fractions to like fractions, and then add or subtract the numerators.
6. Multiplication and Division of Fractions:
   • Multiplication: Multiply the numerators and denominators.
     • Example: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$32​×54​=158​.
   • Division: Multiply the first fraction by the reciprocal of the second fraction.
     • Example: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$32​÷54​=32​×45​=1210​=65​.

Important Questions with Answers:

1. What is the fraction for the part of a pizza if 3 slices are eaten out of 8?
   • Answer: $\frac{3}{8}$83​.
2. Simplify 69\frac{6}{9}96​.
   • Answer: $\frac{2}{3}$32​ (dividing both the numerator and denominator by 3).
3. Convert 1141 \frac{1}{4}141​ into an improper fraction.
   • Answer: $\frac{5}{4}$45​.
4. What is the sum of 34+24\frac{3}{4} + \frac{2}{4}43​+42​?
   • Answer: $\frac{5}{4}$45​ or $1 \frac{1}{4}$141​.
5. Multiply 56×23\frac{5}{6} \times \frac{2}{3}65​×32​.
   • Answer: $\frac{10}{18} = \frac{5}{9}$1810​=95​ (simplified).
6. What is the difference between 78−38\frac{7}{8} – \frac{3}{8}87​−83​?
   • Answer: $\frac{4}{8} = \frac{1}{2}$84​=21​ (simplified).