To multiply three fractions, multiply all three numerators together to get your new numerator, then multiply all three denominators together to get your new denominator. That’s the core of it. For example, 1/2 × 3/4 × 2/5 means multiplying 1 × 3 × 2 on top (giving you 6) and 2 × 4 × 5 on the bottom (giving you 40), for a result of 6/40, which simplifies to 3/20.
The Four Steps
Multiplying three fractions follows the same logic as multiplying two. You just extend the process across one more fraction.
- Step 1: Multiply the three numerators straight across. Write their product as the new numerator.
- Step 2: Multiply the three denominators straight across. Write their product as the new denominator.
- Step 3: Place the new numerator over the new denominator to form a single fraction.
- Step 4: Simplify the fraction to its lowest terms.
Here’s a full example: 2/3 × 5/7 × 1/4. Numerators: 2 × 5 × 1 = 10. Denominators: 3 × 7 × 4 = 84. The result is 10/84. Both 10 and 84 are divisible by 2, so divide each by 2 to get 5/42. That’s your final answer.
Simplify Before You Multiply
You can make the multiplication easier by canceling common factors before you do any multiplying. This technique, sometimes called cross canceling, lets you pair any numerator with any denominator across all three fractions and divide both by a shared factor.
Take 4/9 × 3/8 × 6/5. Before multiplying everything out, notice that the 4 in the first numerator and the 8 in the second denominator share a factor of 4. Divide the 4 by 4 (getting 1) and the 8 by 4 (getting 2). Now look at the 3 in the second numerator and the 9 in the first denominator. Both are divisible by 3, giving you 1 and 3. Finally, the 6 in the third numerator and the remaining 3 in the first denominator share a factor of 3, reducing them to 2 and 1.
After all that canceling, you’re left with 1/1 × 1/2 × 2/5. Multiply across: 1 × 1 × 2 = 2 on top, 1 × 2 × 5 = 10 on the bottom, giving you 2/10, which simplifies to 1/5. The answer is the same as if you had multiplied the original numbers (4 × 3 × 6 = 72, and 9 × 8 × 5 = 360, so 72/360 = 1/5), but the arithmetic along the way was much smaller.
To find factors to cancel, break each numerator and denominator into prime factors. Any prime that appears in both a numerator and a denominator (even if they belong to different fractions) can be crossed out from both spots.
When One of the Three Is a Whole Number
A whole number is just a fraction with 1 as the denominator. If you need to multiply 5 × 2/3 × 1/4, rewrite the 5 as 5/1. Now you have 5/1 × 2/3 × 1/4. Multiply the numerators: 5 × 2 × 1 = 10. Multiply the denominators: 1 × 3 × 4 = 12. The result is 10/12, which simplifies to 5/6.
When One of the Three Is a Mixed Number
A mixed number like 2 1/5 needs to become an improper fraction before you multiply. To convert it, multiply the whole number part by the denominator, add the numerator, and place that total over the original denominator. For 2 1/5: 5 × 2 + 1 = 11, so 2 1/5 becomes 11/5.
Suppose you need to solve 2 1/5 × 3/4 × 1/2. First convert: 11/5 × 3/4 × 1/2. Numerators: 11 × 3 × 1 = 33. Denominators: 5 × 4 × 2 = 40. The answer is 33/40. Since 33 and 40 share no common factors, that’s already in simplest form.
If your final answer is an improper fraction (the numerator is larger than the denominator), you can convert it back to a mixed number by dividing the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.
Two Errors That Trip People Up
The most common mistake is treating fraction multiplication like addition. When you add fractions, you need a common denominator. When you multiply, you don’t. Just multiply straight across, top times top and bottom times bottom, regardless of whether the denominators match.
The second frequent error is skipping simplification. Your answer isn’t wrong if you write 6/40 instead of 3/20, but most teachers, textbooks, and standardized tests expect the fraction in its lowest terms. After multiplying, check whether the numerator and denominator share any common factor greater than 1. Divide both by the greatest common factor to reduce the fraction fully.
Quick Practice Problem
Try 3/5 × 2/9 × 5/4. Before multiplying, notice the 3 in the first numerator and the 9 in the second denominator share a factor of 3 (reducing to 1 and 3). The 5 in the first denominator and the 5 in the third numerator cancel completely (both become 1). Now you have 1/1 × 2/3 × 1/4. Numerators: 1 × 2 × 1 = 2. Denominators: 1 × 3 × 4 = 12. That gives 2/12, which simplifies to 1/6.