Multiplication of Fractions
Learn how to multiply fractions, whole numbers, and mixed numbers step by step!
What is Multiplying Fractions?
Finding a Fraction OF Something
When we multiply fractions, we're finding a part of a part or a fraction OF another number.
Example: ½ × 6 means "half of 6"
Think: What is half of 6? It's 3!
Example: ⅔ × ¾ means "two-thirds of three-fourths"
We're taking a fraction of another fraction!
Repeated Addition Connection
Multiplying a fraction by a whole number is like repeated addition:
⅖ × 3 = ⅖ + ⅖ + ⅖ = ⁶⁄₅
We're adding the fraction 3 times!
Scaling
Multiplying by a fraction scales (resizes) a quantity:
- Multiply by a fraction less than 1 → result is smaller
- Multiply by a fraction greater than 1 → result is larger
Three Types of Fraction Multiplication
Type 1
Fraction × Whole Number
⅔ × 5
A fraction multiplied by a counting number
Type 2
Fraction × Fraction
⅔ × ¾
Two fractions multiplied together
Type 3
Mixed Numbers
2½ × 1⅓
Mixed numbers multiplied together
Key Insight: All three types use the same basic principle — multiply numerators together and multiply denominators together!