📘 60-Minute Classwork: Fractions and Their Operations
📌 What is a Fraction?
A fraction represents a part of a whole. It is written as \( \frac{a}{b} \), where:
A fraction represents a part of a whole. It is written as \( \frac{a}{b} \), where:
- Numerator = a (number of parts taken)
- Denominator = b (total parts)
📐 Types of Fractions:
| Type | Example | Description |
|---|---|---|
| Proper Fraction | \( \frac{3}{5} \) | Numerator < Denominator |
| Improper Fraction | \( \frac{7}{4} \) | Numerator > Denominator |
| Mixed Fraction | \( 2 \frac{1}{3} \) | Whole number + proper fraction |
➕ Addition of Fractions (like denominators):
Example: \( \frac{2}{7} + \frac{3}{7} = \frac{5}{7} \)
Example: \( \frac{2}{7} + \frac{3}{7} = \frac{5}{7} \)
➕ Addition of Fractions (unlike denominators):
Example: \( \frac{2}{5} + \frac{1}{3} \)
LCM of 5 and 3 = 15 \( \Rightarrow \frac{6}{15} + \frac{5}{15} = \frac{11}{15} \)
Example: \( \frac{2}{5} + \frac{1}{3} \)
LCM of 5 and 3 = 15 \( \Rightarrow \frac{6}{15} + \frac{5}{15} = \frac{11}{15} \)
➖ Subtraction Example:
\( \frac{5}{6} - \frac{1}{4} \) LCM of 6 and 4 = 12 \( \Rightarrow \frac{10}{12} - \frac{3}{12} = \frac{7}{12} \)
\( \frac{5}{6} - \frac{1}{4} \) LCM of 6 and 4 = 12 \( \Rightarrow \frac{10}{12} - \frac{3}{12} = \frac{7}{12} \)
✖️ Multiplication of Fractions:
Multiply numerators and denominators: \( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \)
Multiply numerators and denominators: \( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \)
➗ Division of Fractions:
Multiply the first by the reciprocal of the second: \( \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} \)
Multiply the first by the reciprocal of the second: \( \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} \)
🎯 Important Questions & Answers:
Q1: Convert \( 2 \frac{1}{2} \) into an improper fraction.
A1: \( 2 \frac{1}{2} = \frac{5}{2} \)
Q2: Add \( \frac{3}{4} \) and \( \frac{2}{5} \).
A2: \( \frac{3}{4} + \frac{2}{5} = \frac{15}{20} + \frac{8}{20} = \frac{23}{20} \)
Q1: Convert \( 2 \frac{1}{2} \) into an improper fraction.
A1: \( 2 \frac{1}{2} = \frac{5}{2} \)
Q2: Add \( \frac{3}{4} \) and \( \frac{2}{5} \).
A2: \( \frac{3}{4} + \frac{2}{5} = \frac{15}{20} + \frac{8}{20} = \frac{23}{20} \)
📚 30-Minute Homework: Fractions Practice
1. Add \( \frac{5}{6} + \frac{1}{4} \)
2. Multiply \( \frac{2}{7} \times \frac{3}{5} \)
3. Divide \( \frac{4}{9} \div \frac{2}{3} \)
4. Subtract \( \frac{5}{8} - \frac{1}{3} \)
5. Convert the mixed fraction \( 3 \frac{2}{5} \) into an improper fraction.