Published 5/16/2025
How to Multiply Fractions: The Method, Shortcuts, and Mixed Numbers
Multiplying fractions is the simplest fraction operation once you know the rule. Here's how it works, why it works, and how to handle mixed numbers and whole numbers.
Multiplication is the one fraction operation where you don’t need a common denominator. You just multiply straight across.
The Rule
Multiply the numerators. Multiply the denominators. Simplify.
2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15
That’s it. No finding common denominators, no converting. Just two multiplications.
More examples:
1/2 × 1/4 = 1/83/5 × 2/7 = 6/355/6 × 3/4 = 15/24 = 5/8(simplified by dividing by 3)
Why Does Multiplying Across Work?
“2/3 of 4/5” means you take four-fifths of something and keep two-thirds of that.
Visually: draw a rectangle. Shade 4/5 of it horizontally (4 columns out of 5). Now shade 2/3 of that vertically (2 rows out of 3). The doubly-shaded region covers 8 out of 15 total cells. That’s 8/15.
The “multiply across” rule is just a shortcut for this overlapping region calculation.
Cross-Cancelling Before You Multiply
Rather than multiplying large numbers and then simplifying, you can simplify first. This is called cross-cancelling.
Look for common factors between any numerator and any denominator (including diagonally across the multiplication sign), then cancel before multiplying.
4/9 × 3/8
- 4 and 8 share a factor of 4: cancel to give 1 and 2
- 3 and 9 share a factor of 3: cancel to give 1 and 3
Result: 1/3 × 1/2 = 1/6
Compare this to multiplying first: 4/9 × 3/8 = 12/72 = 1/6. Same answer, but cross-cancelling kept the numbers small throughout.
Multiplying Fractions by Whole Numbers
Write the whole number as a fraction with 1 as the denominator, then multiply normally.
6 × 2/3 = 6/1 × 2/3 = 12/3 = 4
5 × 3/8 = 15/8 = 1 7/8
A quick mental shortcut: multiplying a fraction by a whole number just multiplies the numerator. 5 × 3/8 = 15/8. You only need the fraction form to simplify or convert at the end.
Multiplying Mixed Numbers
You must convert to improper fractions first. You cannot multiply mixed numbers directly by multiplying the whole parts and fraction parts separately.
2 1/2 × 1 3/4
Step 1: Convert.
2 1/2 = (2 × 2 + 1)/2 = 5/21 3/4 = (1 × 4 + 3)/4 = 7/4
Step 2: Multiply.
5/2 × 7/4 = 35/8
Step 3: Convert back.
35/8 = 4 3/8
The common mistake is trying to do (2 × 1) + (1/2 × 3/4) = 2 + 3/8 = 2 3/8. This is wrong because it ignores cross terms (2 × 3/4 and 1/2 × 1). Always convert first.
A Note on Fractions of Fractions
“1/2 of 3/4” and “1/2 × 3/4” mean the same thing. The word “of” in fraction problems signals multiplication.
So “what is 2/3 of 9?” = 2/3 × 9 = 18/3 = 6.
Use our Fraction Calculator for step-by-step working on any multiplication, or try the Practice Multiplication page for unlimited generated problems at three difficulty levels.