How to Multiply Fractions
Multiplication is the easiest of all operations involving fractions -- because there is no need to worry about the denominators being like or unlike as in the case of adding and subtracting fractions.
Instead, all you need to do is 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, like this:
| 1 | x | 1 | = | 1 | ||
| 3 | 4 | 12 |
Multiplying Fractions and Mixed Numbers
If you need to multiply 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 multiply the numerators and denominators as usual.
Multiplying Fractions By Whole Numbers
Here again, to multiply 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 multiply the numerators and denominators as usual.