How to Divide Fractions
While fraction division has one more step than fraction multiplication, it is still much easier than adding and subtracting fractions -- because there is no need to worry about the denominators being like or unlike.
Instead, all you need to do is invert (flip upside down) the divisor (second term in the division equation) and change the sign from division (÷) to multiplication (x), then multiply the dividend (first term in the division equation) by the inverted divisor.
To complete the fraction division, you simply multiply the numerators of each fraction to get a new numerator and then multiply the denominators of each fraction to get a new denominator -- regardless of whether the denominators are different or the same.
The following illustrates how you would divide a dividend of 1/2 by a divisor of 1/3:
| 1 | ÷ | 1 | = | 1 | x | 3 | ||
| 2 | 3 | 2 | 1 |
Step #2: Multiply Dividend by Inverted Divisor
| 1 | x | 3 | = | 3 | = | 1 | 1 | ||
| 2 | 1 | 2 | 2 |
How to Divide Fractions and Mixed Numbers
If you need to divide a fraction by a mixed number, you first need to convert the mixed number to an improper fraction. To do that, you simply multiply the denominator by the whole number and add that product to the value of the numerator. That result then becomes the numerator of the improper fraction, while the denominator remains the same.
To illustrate, here is how you would convert the mixed number 2 1/3 (two and one third) into an improper fraction:
| 2 | 1 | = | 3 x 2 + 1 | = | 7 | ||
| 3 | 3 | 3 |
Once you have converted the mixed number to an improper fraction, you simply divide the fractions as normal.
How to Divide Fractions By Whole Numbers
Here again, to divide a fraction by a whole number, you first need to convert the whole number into an improper fraction. To do that you simply place the whole number over the number 1 (any non-zero number divided by 1 is equal to the number), like this:
| 4 | = | 4 | ||
| 1 |
Once you have converted the whole number into an improper fraction, you simply divide the fractions as explained earlier.