Divide Fractions Calculator
Enter two fractions or mixed numbers to find their quotient, simplified to lowest terms, with every step shown.
Updated
Divide Fractions Calculator
Our Divide Fractions Calculator divides one fraction or mixed number by another and gives the quotient 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 reciprocal, the multiplication and the simplification. It works with negative fractions and very large numbers, always exactly.
Quick answer
To divide fractions, keep the first fraction, change ÷ to ×, and flip the second fraction, then multiply and simplify. For example, 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2. Enter any two fractions above and the calculator shows the quotient instantly.
- Formula: a/b ÷ c/d = (a × d) / (b × c)
- Flip only the divisor, the second fraction, never the first
- Mixed numbers: change them to improper fractions first
- Dividing by a fraction below 1 gives a bigger answer: 2 ÷ 1/2 = 4
How to Divide Fractions
Dividing fractions takes three steps, often remembered as keep, change, flip:
- Keep the first fraction (the dividend) as it is.
- Change the division sign to a multiplication sign.
- Flip the second fraction (the divisor) to get its reciprocal, then multiply the numerators, multiply the denominators and simplify.
= (a × d)/(b × c)
2/3 ÷ 3/4 = 2/3 × 4/3
= 8/9
Why Flipping the Second Fraction Works
Division asks how many times the divisor fits into the dividend. Half fits into 3 six times, so 3 ÷ 1/2 = 6, which is the same as 3 × 2. Dividing by a number always equals multiplying by its reciprocal, because a number times its reciprocal is 1:
so dividing by c/d undoes
multiplying by c/d, just
like multiplying by d/c
This is also why dividing by a fraction smaller than 1 makes the answer bigger, and dividing by a fraction bigger than 1 makes it smaller.
Dividing Mixed Numbers
Turn each mixed number into an improper fraction (whole × denominator + numerator) before flipping. For 2 1/2 ÷ 1 1/4:
5/2 ÷ 5/4 = 5/2 × 4/5
= 20/10 = 2
Unlike adding, you cannot divide the whole numbers and the fractions separately. Choose Mixed in the calculator to type a whole number for each fraction.
Dividing Fractions and Whole Numbers
Write the whole number over 1, then divide as usual. In the calculator, type the whole number as the numerator and 1 as the denominator.
= 3/12 = 1/4
6 ÷ 1/2 = 6/1 × 2/1
= 12
Dividing a fraction by a whole number makes it smaller; dividing a whole number by a fraction less than 1 makes it bigger.
Dividing Negative Fractions
The sign rules are the same as for whole numbers: one negative gives a negative answer, two negatives give a positive one.
= −10/12 = −5/6
When a negative fraction is flipped it stays negative: the reciprocal of −3/4 is −4/3. 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 Quotients
| Division | Multiply by | Answer |
|---|---|---|
| 1/2 ÷ 1/4 | 4/1 | 2 |
| 3/4 ÷ 1/2 | 2/1 | 3/2 = 1 1/2 |
| 2/3 ÷ 3/4 | 4/3 | 8/9 |
| 3/4 ÷ 2/3 | 3/2 | 9/8 = 1 1/8 |
| 7/8 ÷ 1/4 | 4/1 | 7/2 = 3 1/2 |
| 1/2 ÷ 3 | 1/3 | 1/6 |
Common Mistakes
- Flipping the wrong fraction. Only the divisor is flipped: 3/4 ÷ 1/2 is 3/4 × 2/1, not 4/3 × 1/2.
- Forgetting to change ÷ to ×. Flipping without multiplying gives a wrong answer.
- Dividing mixed numbers part by part. Convert them to improper fractions first.
- Forgetting to simplify. 6/4 is correct but not finished; it reduces to 3/2.
- Dividing by zero. 0/5 has no reciprocal, so a fraction cannot be divided by 0.
Key Terms
- Dividend
- The fraction being divided, the first one.
- Divisor
- The fraction you divide by, the second one.
- Quotient
- The answer to a division.
- Reciprocal
- A fraction flipped upside down: 3/4 becomes 4/3.
- Mixed number
- A whole number and a fraction, such as 1 1/2.
- Simplify
- Divide the top and bottom by their GCD.
How to Use the Divide 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 dividend, the fraction being divided, on the left and the divisor on the right, with the numerator in the top box and the denominator in the bottom box. 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 quotient. The quotient appears as you type, in lowest terms. The table shows it as a fraction, a mixed number and a decimal, with the steps: the reciprocal of the divisor, the multiplication and the simplification. Press Copy to copy it, or Clear or Esc to start again.
Example: enter 3/4 and 1/2. The quotient is 3/2, with the working 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2, the mixed number 1 1/2, the decimal 1.5 and the steps: flip 1/2 to 2/1, multiply to get 6/4, then divide by 2.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you divide fractions?
Keep the first fraction, change ÷ to ×, and flip the second fraction, then multiply and simplify. For example 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.
What is the formula for dividing fractions?
a/b ÷ c/d = (a × d) / (b × c). Multiply the first numerator by the second denominator, and the first denominator by the second numerator: 2/3 ÷ 3/4 = (2 × 4)/(3 × 3) = 8/9.
Why do you flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal, because a number times its reciprocal is 1. Dividing by 1/2 asks how many halves fit, which is the same as multiplying by 2: 3 ÷ 1/2 = 3 × 2 = 6.
How do you divide mixed numbers?
Turn each mixed number into an improper fraction, then keep, change and flip. 2 1/2 ÷ 1 1/4 = 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2.
How do you divide a fraction by a whole number?
Write the whole number over 1 and flip it, so dividing by 3 is multiplying by 1/3. 3/4 ÷ 3 = 3/4 × 1/3 = 3/12 = 1/4.
What is 3/4 divided by 1/2?
3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2, which is 1 1/2 as a mixed number, or 1.5.
What is 1/2 divided by 1/4?
1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Two quarters fit into one half.
Why is the answer bigger when dividing by a fraction?
Dividing by a fraction smaller than 1 counts how many small pieces fit, so the answer is bigger than the starting number: 2 ÷ 1/2 = 4. Dividing by a fraction bigger than 1, such as 3/2, makes the answer smaller.
Can you divide a fraction by zero?
No. Zero has no reciprocal, so division by 0 (or by 0/5, which is 0) is undefined. The calculator shows a message instead of an answer.
Is the Divide Fractions Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Divide Fractions Calculator to divide any two fractions or mixed numbers, with every step shown.