Multiplying Fractions Calculator
Enter two fractions or mixed numbers to find their product, simplified to lowest terms, with every step shown.
Updated
Multiplying Fractions Calculator
Our Multiplying Fractions Calculator multiplies two fractions or mixed numbers and gives the product in lowest terms. Type the numerators and denominators and the answer appears straight away as a simplified fraction, a mixed number and a decimal, with every step shown: the numerators multiplied, the denominators multiplied and the simplification. It works with negative fractions and very large numbers, always exactly.
Quick answer
To multiply fractions, multiply the numerators, multiply the denominators, then simplify. For example, 2/3 × 3/4 = 6/12 = 1/2. Enter any two fractions above and the calculator shows the product instantly.
- Formula: a/b × c/d = (a × c) / (b × d)
- No common denominator is needed, unlike adding
- Mixed numbers: change them to improper fractions first
- Whole numbers: write them over 1, so 7/8 × 4 = 7/8 × 4/1 = 7/2
How to Multiply Fractions
Multiplying is the simplest fraction operation. It takes three steps:
- Multiply the numerators (the top numbers).
- Multiply the denominators (the bottom numbers).
- Simplify by dividing the top and bottom by their greatest common divisor.
2/3 × 3/4 = (2 × 3)/(3 × 4)
= 6/12 = 1/2
Why Multiplying Across Works
Multiplying by a fraction means taking that part of something. 2/3 × 3/4 is two thirds of three quarters. Cut a bar into quarters and take 3 of them, then take 2/3 of that: you are left with 2 of the 3 quarters, which is 2/4 = 1/2 of the bar.
Because "of" means multiply, multiplying by a fraction smaller than 1 always makes a positive number smaller: 1/2 × 1/3 = 1/6.
Simplifying First by Cross Cancelling
You can simplify before multiplying by dividing any numerator and any denominator by a common factor. This keeps the numbers small. For 8/15 × 5/12:
5 and 15 share 5: 2/3 × 1/3
2/3 × 1/3 = 2/9
Multiplying first gives 40/180, which also simplifies to 2/9. The calculator multiplies first and then shows the simplification step.
Multiplying Mixed Numbers
Turn each mixed number into an improper fraction (whole × denominator + numerator) before multiplying. For 2 1/2 × 1 3/4:
5/2 × 7/4 = 35/8
= 4 3/8
Multiplying the whole numbers and the fractions separately (2 × 1 and 1/2 × 3/4) gives 2 3/8, which is wrong. Choose Mixed in the calculator to type a whole number for each fraction.
Multiplying Fractions by Whole Numbers
Write the whole number over 1, then multiply as usual. In the calculator, type the whole number as the numerator and 1 as the denominator.
= 28/8 = 7/2
2/3 × 24 = 48/3 = 16
Finding a fraction of an amount works the same way: 2/3 of 24 is 16.
Multiplying Negative Fractions
The sign rules are the same as for whole numbers: one negative gives a negative answer, two negatives give a positive one.
−1/2 × (−4/5) = 4/10 = 2/5
For a negative mixed number such as −1 1/2, the minus sign applies to the whole thing, so it is −3/2.
Common Fraction Products
| Product | Multiplied | Answer |
|---|---|---|
| 1/2 × 1/2 | 1/4 | 1/4 |
| 1/2 × 1/3 | 1/6 | 1/6 |
| 2/3 × 3/4 | 6/12 | 1/2 |
| 3/4 × 2/5 | 6/20 | 3/10 |
| 3/5 × 5/3 | 15/15 | 1 |
| 7/8 × 4 | 28/8 | 7/2 = 3 1/2 |
Common Mistakes
- Finding a common denominator. It is not needed for multiplying and only makes the numbers bigger.
- Cross multiplying. That is for comparing fractions or solving proportions; multiply straight across instead.
- Multiplying mixed numbers part by part. Convert them to improper fractions first.
- Forgetting to simplify. 6/12 is correct but not finished; it reduces to 1/2.
- Whole numbers on both lines. 4 is 4/1, so 7/8 × 4 is 28/8, not 28/32.
Key Terms
- Product
- The answer to a multiplication.
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction.
- Improper
- A fraction whose numerator is at least its denominator, such as 35/8.
- Mixed number
- A whole number and a fraction, such as 4 3/8.
- Cross cancel
- Divide a numerator and the other denominator by a common factor before multiplying.
How to Use the Multiplying Fractions Calculator
- Choose the fraction type. Pick Simple for fractions such as 3/4 or 7/2, or Mixed to add a whole-number box for mixed numbers such as 2 1/2.
- Enter the two fractions. Type the numerator in the top box and the denominator in the bottom box of each fraction. For a whole number, use 1 as the denominator. Negative numbers work; put the minus sign on the numerator, or on the whole number of a mixed number.
- Read and copy the product. The product appears as you type, in lowest terms. The table shows it as a fraction, a mixed number and a decimal, with the steps: the numerators multiplied, the denominators multiplied and the simplification. Press Copy to copy it, or Clear or Esc to start again.
Example: enter 2/3 and 3/4. The product is 1/2, with the working 2/3 × 3/4 = 6/12 = 1/2, the decimal 0.5 and the steps: numerators 2 × 3 = 6, denominators 3 × 4 = 12, then divide by 6.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you multiply fractions?
Multiply the numerators, multiply the denominators, then simplify. For example 2/3 × 3/4 = 6/12 = 1/2.
What is the formula for multiplying fractions?
a/b × c/d = (a × c) / (b × d). For example 3/4 × 2/5 = (3 × 2)/(4 × 5) = 6/20 = 3/10.
Do you need a common denominator to multiply fractions?
No. A common denominator is only needed to add or subtract fractions. To multiply, go straight across: 1/2 × 1/3 = 1/6.
How do you multiply mixed numbers?
Turn each mixed number into an improper fraction, multiply, then turn the answer back into a mixed number. 2 1/2 × 1 3/4 = 5/2 × 7/4 = 35/8 = 4 3/8.
How do you multiply a fraction by a whole number?
Write the whole number over 1 and multiply as usual, which is the same as multiplying only the numerator. 7/8 × 4 = 7/8 × 4/1 = 28/8 = 7/2, or 3 1/2.
What is 2/3 times 3/4?
2/3 × 3/4 = 6/12 = 1/2, or 0.5.
What is 1/2 times 1/3?
1/2 × 1/3 = 1/6, or about 0.1667. Half of a third is a sixth.
What is cross cancelling?
Dividing a numerator and the other fraction's denominator by a common factor before multiplying, so the numbers stay small. In 8/15 × 5/12, cancel 4 from 8 and 12 and 5 from 5 and 15 to get 2/3 × 1/3 = 2/9.
Why does multiplying fractions make the answer smaller?
Multiplying by a fraction less than 1 takes only part of a number, so a positive number gets smaller: 1/2 × 1/3 = 1/6. Multiplying by a fraction greater than 1, such as 3/2, makes it bigger.
Is the Multiplying Fractions Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Multiplying Fractions Calculator to multiply any two fractions or mixed numbers, with every step shown.