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 numerator and denominator 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 flip the second one over. This step is Reciprocal of a Fraction.
- Change the divide sign into a times sign, then multiply the numerators and multiply the denominators.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the problem.
- Keep the first fraction, and flip the second one over. This step is Reciprocal of a Fraction.
- Change the divide sign into a times sign, then multiply the numerators and multiply the denominators.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
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 flip the second one over. This step is Reciprocal of a Fraction.
In this problem: Swapping the numerator and denominator of \(\frac{1}{2}\) gives \(\frac{2}{1}\), because the numerator \(1\) moves down and the denominator \(2\) moves up.
Problem
Approach
Step-by-step method
- Set up the problem.
- Swap the numerator and denominator 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 numerator and denominator over.
In this problem: The numerator \(1\) moves down and the denominator \(2\) 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 numerators and multiply the denominators.
In this problem: Now we change ÷ into × and multiply: \(3 \times 2 = 6\) and \(4 \times 1 = 4\).
Step 4
Step 4 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.
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 numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator 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 numerator, and the numbers that divide the denominator. 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 numerator and the denominator 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 flip the second one over. This step is Reciprocal of a Fraction.
- Change the divide sign into a times sign, then multiply the numerators and multiply the denominators.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
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 flip the second one over. This step is Reciprocal of a Fraction.
In this problem: Swapping the numerator and denominator of \(\frac{4}{9}\) gives \(\frac{9}{4}\), because the numerator \(4\) moves down and the denominator \(9\) moves up.
Problem
Approach
Step-by-step method
- Set up the problem.
- Swap the numerator and denominator 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 numerator and denominator over.
In this problem: The numerator \(4\) moves down and the denominator \(9\) 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 numerators and multiply the denominators.
In this problem: Now we change ÷ into × and multiply: \(2 \times 9 = 18\) and \(3 \times 4 = 12\).
Step 4
Step 4 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.
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 numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator 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 numerator, and the numbers that divide the denominator. 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 numerator and the denominator 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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Example Problems
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