Learning Objectives
- Understand fractions as parts of a whole
- Identify equivalent fractions
- Compare and order fractions
- Add and subtract simple fractions with the same denominator
Key Concepts
Understanding Fractions
A fraction represents a part of a whole. When you cut a pizza into 8 equal slices and eat 3 slices, you have eaten 3/8 of the pizza. The top number (3) is the numerator and tells how many parts you have. The bottom number (8) is the denominator and tells how many equal parts the whole was divided into.
Equivalent Fractions
Equivalent fractions are different fractions that show the same amount. For example, 1/2 = 2/4 = 3/6 = 4/8. If you cut a cake into 2 equal pieces and take 1, or cut it into 4 equal pieces and take 2, you get the same amount of cake. To make equivalent fractions, multiply or divide both the numerator and denominator by the same number.
Comparing Fractions
When fractions have the same denominator, the one with the bigger numerator is bigger: 5/8 > 3/8. When fractions have the same numerator, the one with the smaller denominator is bigger: 1/3 > 1/5 (a third is bigger than a fifth). You can also compare by making the denominators the same using equivalent fractions.
Adding and Subtracting Fractions
When fractions have the same denominator, just add or subtract the numerators and keep the denominator the same. For example: 2/7 + 3/7 = 5/7. And 5/8 - 2/8 = 3/8. If the denominators are different, first find equivalent fractions with the same denominator, then add or subtract.
Important Terms
- Fraction: A number representing a part of a whole (like 3/4)
- Numerator: The top number in a fraction (how many parts you have)
- Denominator: The bottom number in a fraction (how many equal parts in the whole)
- Equivalent Fractions: Different fractions that represent the same amount
- Whole: The complete thing before it is divided into parts
Quick Revision
- Fractions show parts of a whole: numerator / denominator
- 1/2 = 2/4 = 3/6 (equivalent fractions)
- Same denominator: bigger numerator = bigger fraction
- Same numerator: smaller denominator = bigger fraction
- Add fractions with same denominator: add numerators, keep denominator
- Multiply both numerator and denominator by the same number to find equivalents