120 LearnersLast updated on July 24th, 2025
Multiplying Fractions With Mixed Numbers
Multiplying a fraction by a mixed number involves calculating the product of a simple fraction and a mixed fraction. The fraction is a way of representing a part of the whole; it is written in the form p/q. A mixed fraction is a type of fraction, combining a whole number and a fraction; it can be written in the form N(p/q). Here, N can be any whole number, and p/q is the fraction. In this article, we will discuss more about multiplying fractions with mixed numbers.
What are fractions?
A fraction shows a part of something. It has two numbers: the numerator and the denominator. The numerator is the number above the fraction bar and represents the selected parts. The part written below the fraction bar is the denominator, and it is the total number of parts.
For example, if the cake is cut into 4 equal slices and you have eaten ¼ of the cake. Here, the numerator 1 is the slice you ate, and the denominator 4 is the total number of slices.
How to Multiply Fractions with Mixed Numbers?
Multiplying fractions with mixed numbers follows the steps given below.
Step 1: To multiply fractions with mixed numbers, first convert the mixed number to an improper fraction
The mixed fraction is a type of number that includes a whole number and a fraction. To convert a mixed fraction to a fraction,
1. Multiply the whole number and the denominator of the fraction.
2. Add the product to the numerator of the fraction.
3. The sum is the new numerator, and keeps the denominator the same.
Step 2: Multiply the fractions
As we converted the mixed fraction to an improper fraction, we now have two fractions. So, we multiply both the fractions now. To multiply the fractions, multiply the numerators and the denominators.
Step 3: Simplify the answer
Divide both the numerator and denominator by its GCF for simplification.
Step 4: Convert the improper fraction to a mixed fraction
If the answer is in an improper fraction, we need to convert it to a mixed number.
To convert, follow the steps given below.
1. First, divide the numerator by the denominator.
2. The quotient is the whole number, the remainder is the new numerator, and the denominator will be the same.
What are the Steps of Multiplying Fractions With Mixed Numbers
Let's look at the steps of multiplying fractions with mixed numbers by using the following example.
Example: Multiply ½ × 2 ¼
Step 1: Convert the mixed number to an improper fraction
1. Multiply the whole number by the denominator. Here, the whole number is 2, and the denominator is 4; 2 × 4 = 8.
2. Add the numerator in the fraction to the result. The numerator is 1, adding 1 to 8 gives 9.
3. Keep the denominator the same. Therefore, the final improper fraction is 9/4.
Step 2: Multiply the fractions
Multiply ½ × 9/4
To multiply fractions, we multiply the numerators and denominators of both fractions
1. Multiplying the numerator, we get 1 × 9 =9.
2. Multiplying the denominator, we get 2 × 4 = 8.
3. So the answer becomes 9/8.
4. If there is a common factor for both the numerator and the denominator, we can simplify the fraction. As 9 and 8 have no common factor, we cannot simplify 9/8.
Step 3: Convert it to a mixed number.
1. Divide the numerator by the denominator. Dividing 9/8, we will get 1 ⅛.
2. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.
The final answer is 1 ⅛.
Real Life Applications of Multiplying Fractions With Mixed Numbers
Multiplying fractions with mixed numbers is useful in many real-life situations, such as finance, healthcare, construction, etc.
Healthcare
Doctors and medical professionals often use fractions and mixed numbers to calculate medication dosages, IV drip rates, and for treatment plans.
Construction
In construction, workers use fraction measurements to calculate the amount of wood, tiles, or paint required for the work.
Finance
In finance, to calculate discounts, interest rates, and tax deductions, we multiply fractions with mixed numbers.
Common Mistakes and How to Avoid Them in Multiplying Fractions With Mixed Numbers
While multiplying fractions with mixed numbers, kids make mistakes. But by using the following mistakes and the ways to avoid them, they can avoid making these mistakes.
Mistake 1
Not converting the mixed number to an improper fraction.
Children forget to convert the mixed number to an improper fraction, which leads to a mistake. Always convert the mixed number to an improper fraction.
Mistake 2
Forgetting to simplify the final answer.
Forgetting to simplify the final answer when there is no common factor is an error. Always check whether the final answer can be simplified. If it can be simplified, simplify it. If not, leave it as it is.
Mistake 3
Confusing multiplication with division
Students mix up the operations within fractions; for example, when multiplying two fractions, they might mistakenly take the reciprocal of the second fraction, which is the method for dividing fractions. So always check and understand the operations first before solving.
Mistake 4
Not writing down all steps
Missing steps in calculations lead to a big mistake. Always show each step clearly to avoid miscalculations.
Mistake 5
Ignoring negative signs in fractions
Ignoring the negative sign will result in the wrong final answer. Keep track of negative signs; if both numbers are negative, then the answer is positive. Multiplying two negative numbers results in a positive product.
Solved Examples of Multiplying Fractions With Mixed Numbers
Problem 1
Multiply ¾ × 2 ⅖
1 ⅘
Explanation
Step 1: Convert 2 ⅖ to an improper fraction (2 × 5) + 2 = 10 + 2 = 12
Step 2: Multiply ¾ × 12/5
(3 × 12)/(4 × 5) = 36/20
Step 3: Simplify 36/20 = 18/10 = 9/5.
Step 4: Convert 9/5 to a mixed number; we will get 1 ⅘.
Problem 2
Multiply 2/7 × 3 ⅜.
27/28
Explanation
Step 1: Convert 3 ⅜ to an improper fraction. (3 × 8) + 3 = 24 + 3 = 27/8
Step 2: Multiply 2/7 × 27/8 = (2 × 27)/(7 × 8) = 54/56.
Step 3: Simplify 54/56 = 27/28.
Problem 3
Multiply 7/9 × 4 ½.
3 ½.
Explanation
Step 1: Convert 4 ½ to an improper fraction. (4 × 2) + 1 = 8 + 1 = 9/2.
Step 2: Multiply 7/9 × 9/2 = (7 × 9)/(9 × 2) = 63/18
Step 3: Simplify 63/18 = 7/2
Step 4: Convert 7/2 to a mixed number; we get 3 ½.
Problem 4
Multiply ⅓ × 5 ⅔.
1 8/9.
Explanation
Step 1: Convert 5 ⅔ to an improper fraction, (5 × 3) + 2 = 15 + 2 = 17/3.
Step 2: Multiply ⅓ × 17/3 = (1 × 17)/(3 × 3) = 17/9.
Step 3: Convert 17/9 to a mixed number, 1 8/9.
Problem 5
Multiply ⅜ × 2 5/9
23/24
Explanation
Step 1: Convert 2 5/9 to an improper fraction, (2 × 9) + 5 = 18 + 5 = 23/9
Step 2: Multiply ⅜ × 23/9 = (3 × 23)/(8 × 9) = 69/72.
Step 3: Simplify 69/72 = 23/24
FAQs on Multiplying Fractions With Mixed Numbers
1.Can multiplying fractions result in larger numbers?
2.Can the whole number be an answer to multiplying fractions with mixed numbers?
3.How do you multiply three fractions together?
4.What if one of the numbers is a whole number?
5.How to convert a mixed number to an improper fraction?
6.How can children in United States use numbers in everyday life to understand Multiplying Fractions With Mixed Numbers ?
7.What are some fun ways kids in United States can practice Multiplying Fractions With Mixed Numbers with numbers?
8.What role do numbers and Multiplying Fractions With Mixed Numbers play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Multiplying Fractions With Mixed Numbers 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.
