Multiplying Fractions Calculator
Multiply fractions, mixed numbers, and whole numbers with step-by-step solutions
Multiply Fractions
Fraction 1
Fraction 2
Example Calculations
Simple Fractions: ³⁄₅ × ⁵⁄₈
Step 1: Multiply numerators: 3 × 5 = 15
Step 2: Multiply denominators: 5 × 8 = 40
Step 3: Result: ¹⁵⁄₄₀
Step 4: Simplify: GCD(15, 40) = 5 → ³⁄₈
Final Answer: ³⁄₅ × ⁵⁄₈ = ³⁄₈
Mixed Numbers: 2³⁄₅ × 1¹⁄₆
Step 1: Convert to improper fractions:
2³⁄₅ = (2×5+3)/5 = ¹³⁄₅
1¹⁄₆ = (1×6+1)/6 = ⁷⁄₆
Step 2: Multiply: ¹³⁄₅ × ⁷⁄₆ = (13×7)/(5×6) = ⁹¹⁄₃₀
Step 3: Convert back: ⁹¹⁄₃₀ = 3¹⁄₃₀
Final Answer: 2³⁄₅ × 1¹⁄₆ = 3¹⁄₃₀
Fraction × Whole Number: ⁷⁄₈ × 13
Step 1: Write whole number as fraction: 13 = ¹³⁄₁
Step 2: Multiply: ⁷⁄₈ × ¹³⁄₁ = (7×13)/(8×1) = ⁹¹⁄₈
Step 3: Convert to mixed number: ⁹¹⁄₈ = 11³⁄₈
Final Answer: ⁷⁄₈ × 13 = 11³⁄₈
Multiplication Rules
Multiply Straight Across
Numerator × Numerator
Denominator × Denominator
Convert Mixed Numbers
Change to improper fractions first
Simplify Result
Reduce to lowest terms using GCD
Quick Tips
Multiplication is easier than addition/subtraction
No need to find common denominators
Whole numbers = number over 1
Always simplify your final answer
Check your work by converting back
Understanding Fraction Multiplication
Why Multiply Fractions?
Multiplying fractions is used in many real-world situations, such as finding a fraction of a fraction, calculating portions of recipes, determining areas of rectangles with fractional dimensions, and solving proportion problems in science and engineering.
Basic Rules
- •Multiply numerators together to get the new numerator
- •Multiply denominators together to get the new denominator
- •Simplify the result by dividing by the greatest common divisor
- •Convert mixed numbers to improper fractions first
Multiplication Formula
a/b × c/d = (a × c)/(b × d)
For multiple fractions: multiply all numerators, then all denominators
Visual Understanding
Example: ½ × ⅓
Think of taking ½ of a ⅓ portion
Result: ⅙ (one-sixth of the whole)
This is smaller than either original fraction
Key Insight: Multiplying fractions usually results in a smaller value than either original fraction (unless multiplying by a whole number > 1)