Introduction

Fractions are numbers that represent a part of a whole. They consist of a numerator (top number) and a denominator (bottom number). Fractions are written in the form $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator.

Understanding Fractions

A fraction represents a part of a whole. For example, $\frac{1}{2}$ represents one out of two equal parts.

Example: If a pizza is divided into 8 equal slices, and you eat 3 slices, the fraction of the pizza you ate is $\frac{3}{8}$.

Types of Fractions

1. Proper Fractions: The numerator is less than the denominator.

   • Example: $\frac{2}{3}$

2. Improper Fractions: The numerator is greater than or equal to the denominator.

   • Example: $\frac{5}{4}$

3. Mixed Fractions: A whole number combined with a fraction.

   • Example: $1\frac{2}{5}$

Adding and Subtracting Fractions

When adding or subtracting fractions, ensure the denominators are the same. If not, find a common denominator before performing the operation.

Example: Add $\frac{1}{3} + \frac{1}{6}$. $$ \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} $$

Multiplying Fractions

To multiply fractions, simply multiply the numerators and denominators together.

Example: Multiply $\frac{2}{3} \times \frac{4}{5}$. $$ \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} $$

Common Mistakes

• Forgetting to simplify fractions to their simplest form.
• Adding or subtracting fractions without a common denominator.
• Misunderstanding the concept of mixed fractions.

Key Points

• Fractions represent parts of a whole.
• Proper fractions have numerators smaller than denominators.
• Improper fractions have numerators equal to or greater than denominators.
• Mixed fractions combine whole numbers and fractions.

Practice Questions

1. Add $\frac{2}{5} + \frac{3}{10}$.
2. Multiply $1\frac{1}{4} \times \frac{2}{3}$.
3. Subtract $2\frac{1}{3} - 1\frac{2}{5}$.