Divide Fractions Calculator – Fraction Division
Divide two fractions with step-by-step solutions
How to Use
- Enter the numerator and denominator for the first fraction
- Enter the numerator and denominator for the second fraction
- Click calculate to divide the fractions
- View the simplified result, decimal form, and solution steps
How to Divide Fractions
To divide fractions, follow these steps: Keep the first fraction the same, flip the second fraction (find its reciprocal), and multiply. This is often remembered as 'Keep, Change, Flip.'
For example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3
Why Does This Method Work?
Dividing by a fraction is the same as multiplying by its reciprocal. When you divide by 3/4, you're asking 'how many 3/4s fit into this number?' This is mathematically equivalent to multiplying by 4/3.
The reciprocal of a fraction is found by flipping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.
Simplifying Fractions
After dividing fractions, always simplify the result by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by this number.
For example, 4/6 can be simplified to 2/3 because both 4 and 6 are divisible by 2.
Converting to Mixed Numbers
If the result is an improper fraction (numerator larger than denominator), it can be converted to a mixed number by dividing the numerator by the denominator. The quotient becomes the whole number, and the remainder over the original denominator becomes the fraction part.
For example, 7/3 = 2 1/3 because 7 ÷ 3 = 2 with remainder 1.
Frequently Asked Questions
- How do you divide fractions?
- To divide fractions, keep the first fraction the same, change the division to multiplication, and flip the second fraction (use its reciprocal). Then multiply the fractions and simplify the result.
- What is the reciprocal of a fraction?
- The reciprocal of a fraction is obtained by swapping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3. Multiplying a fraction by its reciprocal always equals 1.
- Can I divide a fraction by a whole number?
- Yes. Convert the whole number to a fraction by placing it over 1. For example, to divide 1/2 by 3, rewrite it as 1/2 ÷ 3/1, then follow the normal division process: 1/2 × 1/3 = 1/6.
- Why do we flip and multiply when dividing fractions?
- Dividing by a fraction is the same as multiplying by its reciprocal. This method works because division is the inverse operation of multiplication, and using the reciprocal maintains this mathematical relationship.