Topic: Fractions

Levels Supported

Primary: yes

Junior: yes

Intermediate: yes

Senior: yes

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Intermediate

A fraction is an expression of the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$. Fractions can be proper ($|a| < |b|$), improper ($|a| \geq |b|$), or mixed numbers (a whole number plus a fraction). Fractions can be simplified by dividing numerator and denominator by their greatest common divisor (GCD).

Important properties:

• Equivalent fractions: $\frac{a}{b} = \frac{ka}{kb}$ for any nonzero $k$.

• Addition and subtraction: $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$.

• Multiplication: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$.

• Division: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ (for $c \neq 0$).

• Fractions can represent rational numbers.

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Validation

Mathematical correctness: OK Age suitability: OK Progression between levels: OK