103 LearnersLast updated on July 4th, 2025
Multiplying Fractions with Whole Numbers
When we are multiplying a fraction with a whole number, we first convert the whole number into a fraction. We convert a whole number into a fraction by placing 1 as the denominator. Now, we apply the regular rules for multiplying fractions and whole numbers. Let us understand more about it along with some examples.
What are fractions?
Fraction is a way of representing a part of a whole or a portion of something. For example, there is pizza divided into 4 equal parts. If you eat 1 slice, you have eaten 1/4 of the pizza. Here 1 is the numerator which tells us how many parts you have. 4 is the denominator and tells us how many equal parts the whole is divided into.
What are Whole Numbers?
Whole numbers are the natural numbers, along with zero. The set of whole numbers is 0, 1, 2, … The difference between natural and whole numbers is that whole numbers include 0, while natural numbers begin from 1.
What is Multiplying Fractions with Whole Numbers?
Multiplying fractions by whole numbers is similar to adding the same fraction repeatedly. Where the fraction is added as many times as the whole number indicates. To multiply the fractions, we multiply the numerators together and the denominators together, and then simplify the result if needed. If we are multiplying the fraction by a whole number, we first write that whole number as a fraction by putting 1 over it. Then we use the multiplication rule that is a/b × c/d gives (a × c )/(b × d). The same rule works when multiplying fractions with whole numbers.
How to Multiply Mixed Fractions with Whole Numbers?
To multiply mixed fractions, we first need to convert those mixed fractions to an improper fraction. After converting it to improper fraction, follow these steps to multiply:
Step 1: Convert the mixed fraction into an improper fraction.
Step 2: Convert a whole number into a fraction by placing 1 over it.
Step 3: Multiply the numerators.
Step 4: Multiply the denominators.
Step 5: Simplify the result if needed.
For example, multiply 1 1/6 x 5
- Convert 1 1/6 into an improper fraction that is 7/6.
- Now convert 5 into a fraction by putting 1 over it
- Now multiply 7/6 x 5/1
7 ✕ 5 = 35
6 ✕ 1 = 6
- The result is 35/6, which is 556 as a mixed fraction.
Real Life Applications of Multiplying Fractions with Whole Numbers
- Construction and Measurement
It is used when we are working on home improvement tasks like cutting wood, measuring fabric. For example, if one piece of wood is 3/4 meter long, and you need 5 pieces, so you should multiply them 3/4 ✕ 5 is 15/4.
- Education and Grading
Teachers use fractions to calculate the grading and percentage. Suppose a quiz has 10 questions, and each is 1/10 of the total score. If a student answers 7 questions right, they will earn 1/10 ✕ 7 = 7/10 or 70%. This helps to assess performance clearly.
- Crafts and Arts
Artists and crafters often divide their materials into fractions for symmetry and balance. Let us take an example, if each decor uses 1/8 yard of ribbon and 12 decors are needed so we multiply 1/8 x 12 which gives 12/8 ribbon is needed. So by learning this concept, we can ensure the precision in supply use.
Common Mistakes and How to Avoid them in Multiplying Fractions With Whole Numbers
Children often make some mistakes when they are multiplying fractions with whole numbers. Here are some common mistakes children often make and some strategies on how to avoid them.
Mistake 1
Not converting Whole numbers to fractions
Sometimes students forget to express the whole number as a fraction, For example, writing 5 instead of 5/1. Students should always remember that any whole number can be converted to fractions just by placing 1 over it, which makes it easier to follow the rules of multiplication.
Mistake 2
Multiplying denominator incorrectly
Some students make the mistake of multiplying the whole number by both numerator and denominator. Instead of multiplying only for the numerator Students should practice the rules of multiplication and should multiply the both numerators together and both denominators together. If there is a/b ✕ c/d then compute a ✕c and b ✕ d.
Mistake 3
Skipping simplification
After multiplying, sometimes children leave the fraction unsimplified, leading to answers that are not in the simplest form. Students must always review the final answer and simplify the fraction by dividing the numerator and denominator by their greatest common factor.
Mistake 4
Confusing improper fractions with mixed fractions
Sometimes children confuse how to convert the improper fraction to the mixed fraction after multiplying and attempt it incorrectly. Students should learn the clear process of converting the improper fraction to mixed fractions, that is, dividing the numerator by the denominator to get the whole number as a remainder. The whole number becomes the numerator.
Mistake 5
Adding instead of multiplying
Students sometimes confuse between multiplication and addition and do 2/3 + 5 instead of 2/3 x 5 Students should practice some real-time applications and use real-world examples to understand the difference between multiplication and addition.
Solved examples on Multiplying Fractions With Whole numbers
Problem 1
Multiply 1/2 x 4
4/1
1 × 4 = 4
2 × 1 = 2
4/2 = 2
Explanation
First write the whole number into a fraction which is 4/1. Now multiply both the numerators and denominators, and then we get 4/2. If we simplify, we get 2 as the result.
Problem 2
Each plant in the garden requires 2/3 gallon of water. If there are 9 plants, how much water is needed?
2/3 x 9
Convert whole number into fraction: 9/1
Multiply the numerators: 2 × 9 = 18
Multiply the denominators: 3 × 1 = 3
18/3 = 6.
Explanation
Each plant needs ⅔ gallon of water, so multiply ⅔ by 9 to get the final result. This gives 18/3. If we simplify the answer we get the final result as 6. So 6 gallons of water is needed.
Problem 3
A piece of wood is 2/5 meter long. If you need 15 pieces of wood to build a fence, what is the total length of wood required ?
2/5 x 15
Convert whole number into fraction:15/1
Multiply the numerators: 2 × 15 = 30
Multiply the denominators: 5 × 1 = 5
30/5 = 6.
Explanation
To find the length of wood we needed, multiply the length of one piece which is 2/5 meter by the total number of pieces which is 15. It gives us a total of 30/5. The final result is 6 meters.
Problem 4
7/10 x 5
7/10 x 5
Convert whole number into fraction: 5/1
Multiply the numerators: 7 × 5 = 35
Multiply the denominators: 1 × 10 = 10
35/10 = 7/2
Explanation
To multiply 7/10 by 5, first write the whole number 5 into a fraction: 5/1. Then multiply the numerators and denominators of both the fractions. We get the result as 35/10, which simplifies to 7/2.
Problem 5
Multiply 3/5 x 10
3/5 x 10
Convert whole number into fraction: 10/1
Multiply the numerators: 3 × 10 = 30
Multiply the denominators: 5 × 1 = 5
30/5 = 6
Explanation
First, convert the whole number to a fraction, and then multiply the numerators and denominators of the two fractions. Divide the final result with the Greatest Common Factor of both the numerator and the denominator. The final answer is 6.
FAQs on Multiplying Fractions with Whole Numbers
1.What is a proper fraction?
2.What should I do if the final answer is an improper fraction?
3.Is the multiplication of fractions commutative?
4.Write real-life examples for multiplying fractions with the whole number?
5.What happens when you multiply a fraction by zero?
6.How can children in Philippines use numbers in everyday life to understand Multiplying Fractions with Whole Numbers?
7.What are some fun ways kids in Philippines can practice Multiplying Fractions with Whole Numbers with numbers?
8.What role do numbers and Multiplying Fractions with Whole Numbers play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Multiplying Fractions with Whole 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.
