With this multiplying fractions calculator, you'll quickly learn how to perform multiplication on fractions, be they simple fractions, improper fractions, or mixed numbers. You will also learn how to multiply fractions with whole numbers, and even multiplying three fractions won't be a hurdle anymore. Remember that in our tool you can multiply up to five fractions — awesome, isn't it? 😍
How to multiply fractions
Multiplying fractions is not rocket science, believe us. You only need to know how to multiply numbers, which you surely do, and how to simplify fractions.
Let's say you have two fractions, 3/5 and 5/8. How to multiply these fractions?
Multiply the numerator by the other numerator and the denominator by the other denominator:
- 3/5 × 5/8 = (3 × 5) / (5 × 8) = 15/40
If you had more fractions than two, the process would be analogous: multiply all numerators together to make a new numerator, and do the same with the denominators to get a new denominator.
If needed, simplify the fraction. To make a reduction, find the greatest common factor of the numerator and denominator, and divide them by that value:
- 15/40 = 3/8
How to multiply a fraction with whole numbers
When it comes to multiplying fractions by whole numbers, it's even easier! Why? Remember that you can write every whole number as a fraction, which is equal to that number over 1.
As a word problem, imagine seven people attending your Halloween party 🎃. You bought three pumpkin pies and cut each pie into six equal slices. Would it be enough if each guest ate two slices of pie 🥧?
One slice out of six pieces is written as the fraction 1/6, and each guest wants two slices — that's 2/6. With seven guests you need:
- 7 × 2/6 = 7/1 × 2/6 = (7 × 2) / (1 × 6) = 14/6 = 2 2/6 = 2 1/3
By multiplying a fraction by a whole number, we perform the same operation as with simple fractions: we multiply the numerators by the numerators and the denominators by the denominators, writing the whole number as its value over one. Lucky you 🍀 — three pies are more than enough!
How to multiply mixed fractions? Multiplying mixed numbers
Multiplication of mixed numbers is also a no-brainer if you know how to multiply simple fractions. It just needs one additional step at the beginning — a change from a mixed fraction to an improper fraction.
Let's say we want to multiply the mixed numbers 2 3/5 and 1 1/6.
- Turn 2 3/5 into an improper fraction: multiply the denominator by the whole number (2 × 5 = 10), add the numerator (10 + 3 = 13), and keep the denominator — you get 13/5.
- Repeat for 1 1/6: ((6 × 1) + 1) / 6 = 7/6.
- Multiply the fractions as usual: 13/5 × 7/6 = (13 × 7) / (5 × 6) = 91/30.
- Change the result back from an improper fraction to a mixed number: 91/30 = 3 1/30.
Multiplying fractions with mixed numbers
The problem of multiplying fractions with mixed numbers is very similar to multiplying mixed numbers. This time, one of your fractions is in its simple form and the other is in mixed-fraction form. The solution is simple: leave the simple fraction in its current form, change the mixed fraction to its improper form, and then follow the standard procedure to get the result. In this calculator, just fill in the whole-number box next to any fraction to enter a mixed number.
Example 1: multiplying three fractions
Multiply 1/2, 2/3, and 3/4:
- 1/2 × 2/3 × 3/4 = (1 × 2 × 3) / (2 × 3 × 4) = 6/24 = 1/4
Example 2: multiplying a fraction by a whole number
Multiply 4 by 3/8:
- 4 × 3/8 = 4/1 × 3/8 = (4 × 3) / (1 × 8) = 12/8 = 1 1/2
Practical contexts — Units & Currencies
Beyond pure numbers, this calculator supports three practical contexts:
- US Measurement — inches, feet, yards, miles, pounds, ounces, gallons, etc. Handy for carpentry, cooking, and everyday scaling of recipes or plans.
- Metric System — millimeters, centimeters, meters, kilometers, grams, kilograms, liters, etc. Used worldwide for science and engineering.
- Currency — multiply monetary fractions in USD ($), Russian Ruble (₽ RUB), Euro (€ EUR), British Pound (£ GBP), Japanese Yen (¥ JPY), Chinese Yuan (¥ CNY), Indian Rupee (₹ INR), Canadian Dollar (C$ CAD), Australian Dollar (A$ AUD), Swiss Franc (CHF), Brazilian Real (R$ BRL), Mexican Peso (MX$ MXN), Korean Won (₩ KRW), and more.
Reading the step-by-step solution
After calculating, the results panel shows:
- Result Fraction — the simplified answer (e.g., 3/8).
- Mixed Number — shown when the result is an improper fraction (e.g., 3 1/30).
- Decimal — the floating-point equivalent.
- Step-by-Step — the original expression, mixed-to-improper conversion, the numerator and denominator products, and the simplification.
Tips for multiplying fractions
- You can cancel common factors between any numerator and any denominator before multiplying to keep the numbers small.
- A whole number is just that number over 1 (e.g., 7 = 7/1).
- Always convert mixed numbers to improper fractions before multiplying.
- If you'd like to check how other operations on fractions work, take a peek at our versatile fraction calculators.