Multiplying mixed fractions can be a bit tricky, but with a few simple steps, you can easily master the process. In this blog post, we’ll explore the basic rules for multiplying mixed fractions and provide some helpful examples to guide you through the process.
What Are Mixed Fractions?
Mixed fractions, also known as mixed numbers, are numbers that contain both a whole number and a fraction. For example, 2 1/2 is a mixed fraction, as it includes the whole number 2 and the fraction 1/2.
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Multiplying Mixed Fractions: Step-by-Step
Multiplying mixed fractions involves multiplying the whole numbers and fractions separately and then adding the two results together. Outlined below are the steps that must be followed:
Step #1: Transform the mixed fractions into improper fractions.
To do this, you need to multiply the denominator by the whole number and add the numerator. For example, to convert the mixed fraction 2 1/2 to an improper fraction, you would multiply 2 by 2 and add 1, resulting in 5. So, 2 1/2 can be written as 5/2.
Step #2: Multiply the two improper fractions.
To multiply two fractions, you simply multiply the numerators together and the denominators together. For example, if you want to multiply 3/4 by 5/6, you would multiply 3 by 5 to get 15 for the numerator, and 4 by 6 to get 24 for the denominator. So, 3/4 x 5/6 = 15/24.
Step #3: Simplify the result.
If possible, simplify the result by dividing both the numerator and denominator by their greatest common factor. For example, if you have the fraction 15/24, you can simplify it by dividing both the numerator and denominator by 3. This gives you 5/8.
Step #4: Convert the result back to a mixed fraction.
If the answer is an improper fraction, you’ll need to convert it back to a mixed fraction. This can be achieved by dividing the numerator by the denominator. The whole number part of the result is the whole number of the mixed fraction, and the remainder is the numerator of the fraction. For example, if you have the improper fraction 13/4, you would divide 13 by 4 to get 3 with a remainder of 1. So, 13/4 can be written as 3 1/4.
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Multiplying Mixed Fractions: Example Problems
Let’s work through some example problems to help you understand the steps involved in multiplying mixed fractions.
Example 1:
What is 2 1/2 x 3 2/3?
Step #1: Transform the mixed fractions into improper fractions.
2 1/2 = 5/2
3 2/3 = 11/3
Step #2: Multiply the two improper fractions.
5/2 x 11/3 = 55/6
Step #3: Simplify the result.
55/6 cannot be simplified any further.
Step #4: Convert the result back to a mixed fraction.
To convert 55/6 to a mixed fraction, divide the numerator by the denominator.
55 ÷ 6 = 9 with a remainder of 1.
So, 55/6 can be written as 9 1/6.
Therefore, 2 1/2 x 3 2/3 = 9 1/6.
Example 2:
What is 4 3/4 x 1 2/5?
Step #1: Transform the mixed fractions into improper fractions.
4 3/4 =19/4
1 2/5 = 7/5
Step #2: Multiply the two improper fractions.
19/4 x 7/5 = 133/20
Step #3: Simplify the result.
133/20 cannot be simplified any further.
Step #4: Convert the result back to a mixed fraction.
To convert 133/20 to a mixed fraction, divide the numerator by the denominator.
133 ÷ 20 = 6 with a remainder of 13.
So, 133/20 can be written as 6 13/20.
Therefore, 4 3/4 x 1 2/5 = 6 13/20.
Find out what is 5/3 as a mixed number
Example 3:
What is 5 3/8 x 2 1/4?
Step #1: Transform the mixed fractions into improper fractions.
5 3/8 = 43/8
2 1/4 = 9/4
Step #2: Multiply the two improper fractions.
43/8 x 9/4 = 387/32
Step #3: Simplify the result.
387/32 cannot be simplified any further.
Step #4: Convert the result back to a mixed fraction.
To convert 387/32 to a mixed fraction, divide the numerator by the denominator.
387 ÷ 32 = 12 with a remainder of 3.
So, 387/32 can be written as 12 3/32.
Therefore, 5 3/8 x 2 1/4 = 12 3/32.
Summary
Multiplying mixed fractions may seem daunting at first, but with the right steps and practice, it can become much easier. Remember to convert the mixed fractions to improper fractions, multiply the two improper fractions, simplify the result if possible, and convert the result back to a mixed fraction if necessary. These steps will help you avoid mistakes and ensure that you arrive at the correct answer. With some practice and patience, you can master the art of multiplying mixed fractions and take on more complex math problems with confidence.
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