How to Multiply Fractions in Four Easy Steps
Easy Method for Multiplying Fractions
The good news is that multiplying and dividing fractions is far easier than adding or subtracting fractions. It would be logical to expect it to be harder. After all, when it comes to whole numbers you start with addition and subtraction and move onto multiplication and division. What makes multiplying (and dividing) fractions so much easier is that, unlike when you're adding or subtracting, you do NOT have to find the lowest common denominator. Despite this you still need to know a step by step method and there are just 4 simple steps to follow that will ensure you get the right answer every time.
This article will walk you through the four steps to multiply fractions and also includes a short video (only about 80 seconds long). For best results, I suggest you read through the article and then watch the video.
Video: How to Multiply Fractions in Four Easy Steps
As with many endeavors, you need to know some key definitions:-
Mixed Number = 3¾ - i.e a number that is made up of an integer combined with a fraction..
Improper number = 15/4 - i.e a fraction greater than 1. In other words, a fraction where the number above "fraction line" (the numerator) is greater than the number below the "fraction line" (the denominator).
Numerator and denominator: (see below)
Example 3¾ x 3/5
The best way to explain the 4 easy steps is with an example. This article and the video use the example of 3¾ x 3/5.
Step 1 Convert any Mixed Number to an Improper Fraction.
In our example of 3¾ x 3/5, 3¾ is a mixed number (remember from above that a mixed number is a number that consists of a whole number and a fraction). So we need to convert 3¾ into an improper fraction (check the definition of improper fraction above). First multiply the integer by the bottom number (the denominator) of the fraction (in this example; 3 x 4) and add to the top number of the fraction (in this example; 3). This gives a new top number (numerator) to place over the bottom number (denominator).
So convert 3¾ from a mixed number to an improper fraction:-
Numerator = (3 x 4) + 3 = 15.
Denominator = 4.
Improper fraction = 15/4.
Simplify and Cancel
The more you can simplify the easier it makes the next 2 steps. So again using our example we have:-
Step 3- Just Multiply!
Now we're ready to just multiply the numerators and denominators:
Step 4 Convert Improper Fraction to a Mixed Number
This step is not always required (because your answer may not be an improper fraction) but where your answer is an improper fraction (remember, where the numerator is greater than the denominator), you need to convert it to a mixed number. You may gain extra marks from your teacher or, perhaps more significantly, your examiner if you tidy up your answer by converting an improper fraction to a mixed number.
Recap the four easy steps to Multiply Fractions
Here are the 4 steps in one go:-
This article has shown that multiplying fractions is relatively straightforward (certainly simpler than adding or subtracting fractions in most cases). We have defined the terms, numerator and denominator. We have looked at mixed numbers and improper fractions and how to convert a mixed number into an improper fraction and vice versa.
We have walked through the four steps to multiply fractions.
- Convert mixed numbers to improper fractions
- Simplify and cancel
- Multiply the numerators and denominators
- Convert any improper fraction answer back to a mixed number