101 LearnersLast updated on July 28th, 2025
Subtraction of Whole Number and Fraction
The mathematical operation of finding the difference between a whole number and a fraction is known as the subtraction of a whole number and a fraction. This operation is essential for simplifying expressions and solving problems that involve numbers in various forms.
What is Subtraction of Whole Number and Fraction?
Subtracting a fraction from a whole number involves converting the whole number into a fraction with the same denominator as the fraction being subtracted. Then, subtract the numerators while keeping the denominator constant.
A fraction consists of two parts:
Numerator: The top number of a fraction, representing how many parts we have.
Denominator: The bottom number of a fraction, indicating the total number of equal parts.
How to do Subtraction of Whole Number and Fraction?
When subtracting a fraction from a whole number, students should follow these steps:
Convert whole number: Change the whole number into a fraction with the same denominator as the given fraction.
Subtract numerators: Subtract the numerator of the fraction from the numerator of the converted whole number.
Simplify the result: Reduce the resulting fraction to its simplest form if necessary.
Methods to Subtract Whole Number and Fraction
The following are methods to subtract a whole number from a fraction:
Method 1: Common Denominator Method
To apply the common denominator method, follow these steps:
Step 1: Convert the whole number into a fraction with the same denominator as the fraction.
Step 2: Subtract the numerators while keeping the denominator constant.
Step 3: Simplify the fraction if possible.
Example: Subtract 1/2 from 3
Step 1: Convert 3 into a fraction: 3 = 6/2
Step 2: Subtract: 6/2 - 1/2 = 5/2
Step 3: Simplified result: 5/2
Method 2: Borrowing Method (for improper fractions)
When subtracting a fraction from a whole number where borrowing may be necessary:
Step 1: Convert the whole number into an improper fraction.
Step 2: Subtract the fraction.
Step 3: Simplify the result if possible.
Properties of Subtraction of Whole Number and Fraction
Subtraction of a whole number and a fraction has some characteristic properties:
- Subtraction is not commutative In subtraction, changing the order of the terms changes the result, i.e., A - B ≠ B - A
- Subtraction is not associative Unlike addition, we cannot regroup in subtraction. Changing the grouping of numbers changes the result. (A - B) - C ≠ A - (B - C)
- Subtracting zero from a number leaves it unchanged Subtracting zero from a number results in the same number: A - 0 = A
- Subtracting a fraction from itself results in zero A fraction minus itself equals zero: A/B - A/B = 0
Tips and Tricks for Subtraction of Whole Number and Fraction
Here are some helpful tips for effectively subtracting fractions from whole numbers:
Tip 1: Ensure the whole number is converted to a fraction with the same denominator as the fraction before subtracting.
Tip 2: Use visual models, such as number lines or fraction strips, to better understand the subtraction process.
Tip 3: When dealing with larger numbers, break them into smaller, more manageable parts if needed.
Forgetting to convert the whole number
Students often forget to convert the whole number into a fraction with a common denominator before subtracting. Ensure the whole number is expressed as a fraction with the same denominator.
Mistake 1
Subtracting denominators
Denominators should remain constant while only the numerators are subtracted. Changing denominators leads to incorrect results.
Mistake 2
Improper simplification
Ensure that the resulting fraction is simplified correctly to its lowest terms.
Mistake 3
Ignoring negative results
Be mindful of situations where the fraction is larger than the whole number, resulting in a negative answer.
Mistake 4
Misplacing numerators and denominators
Double-check that numerators and denominators are placed correctly, as mixing them up can lead to errors.
Mistake 5
Examples of Subtraction of Whole Number and Fraction
Subtract 1/4 from 5
19/4
Problem 1
Convert 5 to a fraction: 5 = 20/4 Subtract: 20/4 - 1/4 = 19/4
Subtract 2/3 from 4
Explanation
10/3
Problem 2
Convert 4 to a fraction: 4 = 12/3 Subtract: 12/3 - 2/3 = 10/3
Subtract 3/5 from 2
Explanation
7/5
Problem 3
Convert 2 to a fraction: 2 = 10/5 Subtract: 10/5 - 3/5 = 7/5
Subtract 5/8 from 6
Explanation
43/8
Problem 4
Convert 6 to a fraction: 6 = 48/8 Subtract: 48/8 - 5/8 = 43/8
Subtract 7/10 from 3
Explanation
23/10
Yes, but you first need to convert them to have a common denominator before subtraction.
1.What happens if the fraction is larger than the whole number?
2.What is a common denominator?
3.How do you simplify a fraction?
4.What is the first step in subtracting a fraction from a whole number?
5.How can children in Canada use numbers in everyday life to understand Subtraction of Whole Number and Fraction?
6.What are some fun ways kids in Canada can practice Subtraction of Whole Number and Fraction with numbers?
7.What role do numbers and Subtraction of Whole Number and Fraction play in helping children in Canada develop problem-solving skills?
8.How can families in Canada create number-rich environments to improve Subtraction of Whole Number and Fraction skills?
Common Mistakes and How to Avoid Them in Subtraction of Whole Number and Fraction
Subtraction involving whole numbers and fractions can be challenging, leading to common mistakes. Awareness of these errors can help students avoid them.
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.
