Fractions

Study Notes

Fractions represent parts of a whole and can be visualized by dividing shapes into equal parts. Equivalent Fractions — fractions that represent the same value even if they look different. Example: $\frac{2}{6} = \frac{1}{3}$. Mixed Numbers — a combination of a whole number and a fraction. Example: $7 \frac{1}{2}$. Improper Fractions — fractions where the numerator is greater than the denominator. Example: $\frac{7}{4}$. Express Mixed Numbers as Improper Fractions — convert by multiplying the whole number by the denominator, adding the numerator, and placing over the original denominator. Example: $3 \frac{1}{3} = \frac{10}{3}$. Express Improper Fractions as Mixed Numbers — divide the numerator by the denominator to find the whole number and remainder. Example: $\frac{11}{5} = 2 \frac{1}{5}$. Compare and Order Fractions — use common denominators or numerators to compare sizes. Example: $\frac{3}{5} > \frac{1}{5}$. Addition and Subtraction of Fractions — find a common denominator before performing operations. Example: $\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$.

Exam Tips

Key Definitions to Remember

• Equivalent Fractions
• Mixed Numbers
• Improper Fractions

Common Confusions

• Mixing up numerators and denominators when comparing fractions
• Forgetting to convert mixed numbers to improper fractions before operations

Typical Exam Questions

• What is an equivalent fraction for $\frac{2}{3}$? $\frac{4}{6}$
• Convert $4 \frac{1}{2}$ to an improper fraction. $\frac{9}{2}$
• Add $\frac{1}{4} + \frac{1}{2}$. $\frac{3}{4}$

What Examiners Usually Test

• Ability to convert between mixed numbers and improper fractions
• Comparing and ordering fractions
• Performing addition and subtraction with fractions