Division of Fractions Calculator
This Division of Fractions Calculator helps you divide one fraction by another and shows the working clearly at every step. Dividing by a fraction is the same as multiplying by that fraction turned upside down. So keep the first fraction as it is, swap the top and bottom of the second one, and change the divide sign into a times sign. Then multiply as normal and check whether the answer can be written with smaller numbers. Following the same pattern every time is what makes dividing fractions easy to picture, check, and repeat on your own with any two fractions.
Step-by-step method
- Set up the problem.
- Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
- Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
- Do a simplifying of fractions at the end if you can.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the problem.
- Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
- Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
- Do a simplifying of fractions at the end if you can.
Step 1
Step 1 - Set up the problem.
In this problem: We are dividing \(\frac{3}{4}\) by \(\frac{1}{2}\).
Step 2
Step 2 - Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
In this problem: Swapping the top and bottom of \(\frac{1}{2}\) gives \(\frac{2}{1}\), because the top \(1\) moves down and the bottom \(2\) moves up.
Problem
Approach
Step-by-step method
- Set up the problem.
- Swap the top and bottom numbers over.
Step 1
Step 1 - Set up the problem.
In this problem: We are finding the reciprocal of \(\frac{1}{2}\).
Step 2
Step 2 - Swap the top and bottom numbers over.
In this problem: The top number \(1\) moves down and the bottom number \(2\) moves up, so \(\frac{1}{2}\) becomes \(\frac{2}{1}\).
Final Answer
Step 3
Step 3 - Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
In this problem: Now we change ÷ into × and multiply: \(3 \times 2 = 6\) and \(4 \times 1 = 4\).
Step 4
Step 4 - Do a simplifying of fractions at the end if you can.
In this problem: The biggest number that divides both \(6\) and \(4\) is \(2\). Dividing each by it gives \(6 \div 2 = 3\) and \(4 \div 2 = 2\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the top number, and the numbers that divide the bottom number. The biggest one on both lists is the one to use.
- Divide the top and the bottom by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{6}{4}\).
Step 2
Step 2 - List the numbers that divide the top number, and the numbers that divide the bottom number. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 2\). The biggest of those is \(2\), so \(2\) is the number to divide by.
Step 3
Step 3 - Divide the top and the bottom by that number.
In this problem: Divide both by \(2\): \(6 \div 2 = 3\) and \(4 \div 2 = 2\).
Final Answer
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the problem.
- Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
- Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
- Do a simplifying of fractions at the end if you can.
Step 1
Step 1 - Set up the problem.
In this problem: We are dividing \(\frac{2}{3}\) by \(\frac{4}{9}\).
Step 2
Step 2 - Keep the first fraction, and do a reciprocal of a fraction on the second one to flip it over.
In this problem: Swapping the top and bottom of \(\frac{4}{9}\) gives \(\frac{9}{4}\), because the top \(4\) moves down and the bottom \(9\) moves up.
Problem
Approach
Step-by-step method
- Set up the problem.
- Swap the top and bottom numbers over.
Step 1
Step 1 - Set up the problem.
In this problem: We are finding the reciprocal of \(\frac{4}{9}\).
Step 2
Step 2 - Swap the top and bottom numbers over.
In this problem: The top number \(4\) moves down and the bottom number \(9\) moves up, so \(\frac{4}{9}\) becomes \(\frac{9}{4}\).
Final Answer
Step 3
Step 3 - Change the divide sign into a times sign, then multiply the tops and multiply the bottoms.
In this problem: Now we change ÷ into × and multiply: \(2 \times 9 = 18\) and \(3 \times 4 = 12\).
Step 4
Step 4 - Do a simplifying of fractions at the end if you can.
In this problem: The biggest number that divides both \(18\) and \(12\) is \(6\). Dividing each by it gives \(18 \div 6 = 3\) and \(12 \div 6 = 2\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the top number, and the numbers that divide the bottom number. The biggest one on both lists is the one to use.
- Divide the top and the bottom by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{18}{12}\).
Step 2
Step 2 - List the numbers that divide the top number, and the numbers that divide the bottom number. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 2, 3, 6\). The biggest of those is \(6\), so \(6\) is the number to divide by.
Step 3
Step 3 - Divide the top and the bottom by that number.
In this problem: Divide both by \(6\): \(18 \div 6 = 3\) and \(12 \div 6 = 2\).
Final Answer
Final Answer
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