Mathematics 4 Life and Beyond: Multiplying fractions and Mixed Numbers (3-9)

Multiplying fractions and Mixed Numbers

Vocabulary

Product - The answer to a multiplication problem.

Reduce - Replace the fraction with its simplest form

Greatest Common Factor (GCF) - The largest factor of two or more numbers.

Cross Canceling - When multiplying fractions you can reduce the numerator of one fraction with the denominator of another.

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:

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

Multiplication Example 1

	First convert 3½ to an improper fraction
	Next multiply the numerators, then multiply the denominators
	This is your answer
	If you'd like, you could convert that into a mixed number

Multiplication Example 2

	Multiply the numerators, then multiply the denominators.
	Reduce the fraction (12 and 72 have a GCF of 12)

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


	In this first example, we cannot use cross-canceling, since 5 and 2 do not share a common factor, and neither do 7 and 6

Cross-Canceling Example 2


	Here we can reduce the 3 and 9 (by 3) and we can also reduce the 4 and 8 (by 4)

Cross-Canceling Example 3

	First convert each to an improper fraction
	14 and 7 can each be reduced by 7
	Cross cancel
	Here's the answer
	If you'd like, you can turn it back in to 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