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Fractions & Decimals

Fractions & Decimals

At a Glance - Multiplying Fractions & Mixed Numbers



Multiplication of fractions is pretty simple compared to addition and subtraction. And guess what, you don't have to find a common denominator. Just follow these four easy steps:

  1. Convert all mixed numbers to improper fractions.
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Reduce your final answer. 

Multiplication Example 1


If you'd like, you could convert that into a mixed number


5/6 x 3 1/2First convert 3½ to an improper fraction3 1/2 = 7/2
5/6 = 7/2Next multiply the numerators, then multiply the denominators
35/12 =This is your answer
2 11/12

Multiplication Example 2


3/8 x 4/9 =Multiply the numerators, then multiply the denominators.
12/72 =Reduce the fraction (12 and 72 have a GCF of 12)
1/6

Cross-Canceling

Instead of reducing the fraction at the end of the problem, you can cross-cancel before you multiply

Cross-canceling means that when multiplying fractions you can reduce the numerator of one fraction with the denominator of another. In this example, 5 and 10 can both be divided by 5.

5/8 x 3/10 = 3/16

Let's look at the three examples again and see how to use this method.

Cross-Canceling Example 1


5/6 x 3 1/2
5/6 = 7/2In this first example, we cannot use cross-canceling, since 5 and 2 do not share a common factor, and neither do 7 and 6
35/12 =
2 11/12

Cross-Canceling Example 2


3/8 x 4/9 =
1/2 x 1/3Here we can reduce the 3 and 9 (by 3) and we can also reduce the 4 and 8 (by 4)
1/6

Cross-Canceling Example 3


4 2/3 x 1 3/7First convert each to an improper fraction
14/3 x 10/714 and 7 can each be reduced by 7
140/21 =Cross cancel
20/3 =Here's the answer
6 2/3If you'd like, you can turn it back into a mixed number

Multiplying a Whole Number by a Fraction

Well, remember that all real numbers can be written as fractions. With a whole number, all you need to do is place it over a denominator of 1.

Let's look at an example, shall we?

5 x 1/3 = 1 2/3

Exercise 1

2/9 x 3/4


Exercise 2

1 3/5 x 3/4


Exercise 3

3 1/2 x 4 2/7


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