104 LearnersLast updated on July 4th, 2025
Multiplying Mixed Fractions
A mixed fraction is a combination of a whole number and a proper fraction. Multiplication of mixed fractions is the multiplication of two mixed fractions. In this article, we will learn about the multiplication of mixed fractions.
What are Mixed Numbers?
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.
How to 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.
What is Multiplying Mixed Numbers?
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 .
|
Proper Fractions |
Improper Fractions |
Mixed Fractions |
|
Numerator less than Denominator |
The numerator is greater than or equal to the denominator |
A combination of a whole number and a proper fraction |
|
The value is 0 < 1. |
The value is 1 <= a |
The value is greater than 1 |
|
Example: 34, 23 |
Example: 3/2 , 13/6 |
Example: 5 2/3 , 7 3/4 |
Multiplying Mixed Fractions with Like Denominators
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 .
Multiplying Mixed Fractions with Unlike Denominators
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 .
Multiplying Mixed Fractions and Proper Fractions
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 .
Multiplying Mixed Fractions with Whole Numbers
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.
Tips and Tricks to Multiplying Mixed Fractions
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.
Common Mistakes and How to Avoid Them in Multiplying Mixed Fractions
When multiplying mixed fractions, students tend to make mistakes. Here are some common mistakes and ways to avoid them.
Mistake 1
Skipping the final simplification step
The result was left without simplifying it from improper to mixed fractions. Always check if the fraction can be simplified or turned into a mixed fraction after multiplying.
Mistake 2
Not simplifying large numbers before the final step
Not expressing the final answer as a mixed number or reducing it to the maximum. Check if the final answer can be reduced further, and simplify it.. If necessary, convert it to a mixed number.
Mistake 3
Multiplying fractions without simplifying the expressions
Direct multiplication of large numbers without simplification, which causes more difficulty in calculations.To check if we can cross-cancel the expressions before multiplying.
Mistake 4
Applying addition or division where multiplication is required.
Causing errors in calculation, especially when dealing with mixed numbers.Keeping yourself updated with the methods and rules, making sure the right operation is used.
Mistake 5
While converting the mixed number, misplacing the whole number
Converting a mixed number into an incorrect, improper fraction without using the right steps or formula.Using the correct formula for solving,
(Whole number Denominator) + Numerator = New Numerator.
Solved Examples for Multiplication of Mixed Fractions
Problem 1
Multiply 4 5/6 and 3 1/2
Given, 4 5/6 x 3 1/2
4 5/6 = 4 6 + 5 = 24 + 5 = 29 = 29/6
3 1/2 = 3 2 + 1 = 6 + 1 = 7 = 7/2
29/6 7/2 = 29 x 7/6 x 2 = 203/12
203/12 = 16 11/12
Explanation
16 11/12.
Problem 2
Multiply 6 3/2 and 3
Given, 6 3/2 x 3
6 3/2 = 6 x 2 + 3 = 12 + 3 = 15 = 15/2
3 = 3/1
15/2 x 3/1 = 15 x 3/2 x 1 = 45/2
45/2 = 22 1/2
Explanation
22 1/2.
Problem 3
Multiply 5 1/3 and 3/2
Given 5 1/3 x 3/2
5 1/3 = 5 x 3 + 1 = 15 + 1 = 16 = 16/3
16/3 x 3/2 = 16 x 3/3 x 2 = 48/6 = 8.
Explanation
8.
FAQs on Multiplying Mixed Fractions
1.How to multiply mixed fractions?
2.When multiplying mixed fractions, should we find a common denominator?
3.If my final answer is an improper fraction, what should I do?
4.Can I cross-cancel or simplify the expression before multiplication?
5.What are the real-life applications of multiplying mixed fractions?
6.How can children in Thailand use numbers in everyday life to understand Multiplying Mixed Fractions?
7.What are some fun ways kids in Thailand can practice Multiplying Mixed Fractions with numbers?
8.What role do numbers and Multiplying Mixed Fractions play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Multiplying Mixed Fractions skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
