Multiplying Mixed Fractions

Mixed numbers are a combination of a whole number and a proper fraction. For example, 5 1/3, here 5 is the whole number and ⅓ is the fractional part of the mixed number. To perform the basic operations using mixed fractions, we convert mixed numbers to improper fractions. 

Conversion of mixed fractions to improper fractions includes multiplication and addition. The steps are explained below

1. Firstly, denominator is multiplied by the whole number

2. The result of the first step has to be added to the numerator

3. Then the sum is written over the original denominator 

Example: Convert 5 2/3 into an improper fraction.
Solution: 5  3 + 2 = 15 + 2 = 17
1 7/3 is the improper fraction of the given mixed fraction.
 

Multiplication is a basic mathematical operation; it is a way of finding the product of any numbers. Finding the product of two mixed numbers is multiplying mixed numbers. 

Example: Multiply  5 2/3  and  2 1/2
Solution: Converting the given mixed fractions to improper fractions,
 5 2/3  = 5  3 + 2 =  15 + 2 = 17 = 17/3
2 1/2 = 2  2 + 1 = 4 + 1 = 5 =  5/2
As we converted the mixed numbers to improper fractions, now we will multiply the improper fractions,
17/3 x 5/2 = 85/6
Converting this back to a mixed number: 
85/6 = 14 1/6 .

Multiplying mixed fractions with like denominators is the process of multiplying two mixed fractions with same denominators. Follow these steps to multiply the mixed fractions with like denominators:

• Mixed fractions are converted to improper fractions

• Multiply the numerators and the denominators

• If necessary, convert the result back to a mixed fraction.

Example: Multiply 3 3/2 and 4 5/2
Solution: Converting the given mixed fractions to improper fractions,
 3 3/2 = (3 x 2) + 3 = 9 / 2 = 9/2
4 5/2 = (4 x 2) + 5 = 13/2
Next is to multiply the improper fractions,
9/2 x 13/2 = 9x13/2x2 = 117/4
Converting this back to a mixed number,
117/4 = 29 1/4 .
 

The multiplication of mixed fractions with unlike denominators is the multiplication of two mixed fractions with different denominators. In this section, we learn how to multiply it step-by-step with an example.

 
Multiplying 2 1/2 and 3 2/5

Step 1:  Converting the given mixed fractions to improper fractions,
2 1/2 = 2  2 + 1 = 4 + 1 = 5 =  5/2
3 2/5 = 3 5 + 2 = 15 + 2 = 17 = 17/5

Step 2: Next, multiply the improper fractions,
 5/2 x 17/5 = 5x17/2x5 = 85/10

Step 3: Converting the result back to a mixed number,
 85/10 = 8 5/10 = 8 1/2 .
 

Now we learned how to multiply mixed numbers with like and unlike fractions. Now let’s see how to multiply mixed fractions and proper fractions. Here are the steps to multiply mixed fractions and proper fractions with an example,

Example: Multiply 4 5/2 and 2/3

Step 1:  Converting the given mixed fraction to an improper fraction,
4 5/2 = (4 x 2 + 5) = 13/2

Step 2: Next, multiply the improper fractions and the proper fraction.
13/2 x 2/3 = 13x2/2x3 = 26/6

Step 3: Converting the result back to a mixed number,
26/6 = 4 2/6 = 4 1/3 .
 

We can even multiply a mixed fraction by a whole number. To multiply mixed fractions with whole numbers, follow the steps given below with an example.

Example: Multiply 5 3/2 and 4

Step 1:  Converting the given mixed fraction to an improper fraction,
To convert, we first multiply the whole number with the denominator and then add the product to the numerator. Then the sum will be written on a numerator with the original denominator. 

5 3/2 = (5 x 2) + 3 = 10 + 3 = 13 = 13/2

Step 2: Write the whole number as a fraction,
4 = 4/1

Step 3: Next, multiplying the fractions, we get
13/2 x 4/1 = 4/1 = 52/2

Step 4: Converting the result back to a mixed number,
52/2 = 26.
 

Students think that multiplying mixed fractions is tricky and difficult. By following these tips and tricks, students can master multiplying mixed fractions.

• Always convert the mixed numbers to improper fractions before performing mathematical operations. 

• Verify the sign rules twice, always check if there is any negative number or not. 

• Simplify the fraction before multiplying to make the calculations easier. For example, when multiplying 8/9 and 3/4, 8 and 4 have a common factor of 4, and 3 and 9 have a common factor of 3. So, it can be simplified as 2/3 × 1/1. 

• Verify the final answer is in the correct required format, whether improper, mixed, or simplified.