Study Notes
Fractions represent parts of a whole and can be illustrated by dividing a shape into equal parts and shading some of them.
- Equivalent Fractions — Fractions that represent the same value even if they look different. Example: Cutting a cake into six pieces and eating two is equivalent to cutting it into three pieces and eating one.
- Mixed Numbers — A combination of a whole number and a fraction. Example: 7 1/2 is a mixed number.
- Improper Fractions — Fractions where the numerator is greater than the denominator. Example: 7/4 is an improper fraction.
- 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 1/3 becomes 10/3.
- Express Improper Fractions as Mixed Numbers — Divide the numerator by the denominator to find the whole number and remainder. Example: 11/5 becomes 2 1/5.
- Compare and Order Fractions — Use equivalent fractions or compare numerators and denominators directly. Example: 3/5 is greater than 1/5.
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 performing operations
Typical Exam Questions
- What is an equivalent fraction for 1/2? 2/4
- Convert 5 3/4 to an improper fraction. 23/4
- Compare 3/4 and 2/3. Which is greater? 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