123 LearnersLast updated on July 22nd, 2025
Positive Integers
Positive integers are otherwise called natural numbers. These integers are always greater than zero. The numbers 1, 2, 3, 4, 5, and so on are the first few positive integers. In this article, we will learn more about positive integers.
What are Positive Integers?
In a number line, positive integers appear on the right side of zero. Therefore, positive integers are always greater than zero and never include zero or negative values. Integers are classified into three types: negative integers, zero, and positive integers.
How to represent positive integers on a number line
A number line is a visual tool that represents the numbers placed at proper intervals. By using the number line, we can understand how the positive and negative integers are placed. For that, we need to:
Step 1: Draw a straight horizontal line and mark an arrow on the right end to indicate that the value is increasing.
Step 2: Place 0 in the middle or at the leftmost starting point. The positive integers are always placed to the right of zero, and the negative integers to the left of zero.
Step 3: Mark equally spaced points on the line to the right of zero, and start marking them 1,2,3,4, etc. These are positive integers. Make sure equal spacing on the number line.
Look at the number line below to find out the positions and values of positive integers.
What are the operations on Positive Integers?
Positive integers are used to carry out basic mathematical operations such as:
- Addition (+)
- Subtraction (-)
- Multiplication (×)
- Division (÷)
Addition: The sum of two positive numbers always gives a positive integer.
For example, 4 + 5 = 9.
Subtraction: Subtracting a smaller positive integer from a larger one gives a positive integer.
For example, 8 – 3 = 5. However, subtracting a larger number from a smaller one results in a negative number.
Multiplication: The product of two positive numbers always results in a positive integer.
For example, 8 × 3 = 24.
Division: When a positive integer is divided by another positive integer, the resulting quotient is also positive.
For example, 12 ÷ 4 = 3. If the division is incomplete, the result will be a fraction or a decimal.
Common Mistakes and How to Avoid Them in Positive Integers
Understanding the concept of positive integers builds a strong foundation in kids to improve their basic arithmetic skills. However, they might make errors while working with integers. Given below are some common mistakes and the ways to solve them:
Mistake 1
Considering 0 as a positive integer.
Students should remember that o is neither positive nor negative, and positive integers begin from 1. Use a number line to confirm that 0 is neither positive nor negative. Numbers to the right of 0 in the number line are positive integers, and those on the left side of 0 are negative integers.
Mistake 2
Ordering numbers incorrectly on the number line.
Practice placing numbers on a number line. Note that the numbers increase as you move to the right, and use this visual tool to identify the integers.
Mistake 3
Assuming that positive integers are limited.
Positive integers are infinite. It goes like 1, 2, 3, 4, 5, and so on. To understand the limitlessness of the positive integers, students can use mathematical proof or exercises.
Mistake 4
Failing to use properties like closure, commutativity, and associativity when carrying out operations.
Exercises and examples help to review and practice these properties. Following these properties through examples will help students solve problems more easily.
Mistake 5
Making errors in arithmetic calculations
Double-check your calculations and use strategies like estimation or mental math checks. Practice problems regularly to build accuracy and confidence.
Real life applications of Positive Integers
Understanding the significance of positive integers allows us to deal with daily tasks such as counting, ordering, and distributing resources. Here are some real-life applications of positive integers:
- Positive integers are used to count objects such as books, students in a class, or the seats in a theater.
- Positive integers represent amounts like bank balances and salaries.
- Time units like hours, minutes, days, and years are measured using positive integers.
Solved examples of Positive Integers
Problem 1
If one box has 7 bananas and another box includes 5 bananas, how many bananas are there in total?
7 + 5 = 12
Explanation
Here, 7 and 5 are added together to get 12 bananas in total. When two positive integers are added, it gives another positive integer.
Problem 2
A boy had 16 cookies. He sold six cookies from the total. How many cookies are left?
16 – 6 = 10
Explanation
Here, 6 cookies are subtracted from 16, resulting in 10 cookies. Subtracting a smaller positive integer from a larger one gives a positive integer.
Problem 3
A school has 8 classrooms, and each classroom has 7 desks. How many desks are there in total?
8 × 7 = 56
Explanation
Here, there are 8 classrooms, each having 7 desks, resulting in 56 desks in total. Multiplying two positive integers results in another positive integer.
Problem 4
A tutor has 24 pens and wants to distribute them equally among 6 students. How many pens will each student get?
24 ÷ 6 = 4.
Explanation
Dividing a positive integer by another positive integer results in a positive integer. Here, each student gets 4 pens.
Problem 5
What is the smallest positive integer?
The smallest positive integer is 1.
Explanation
The positive integers are always greater than 0. Hence, 1 is the smallest positive integer.
FAQs on Positive Integers
1.What defines positive integers?
2.How are negative and positive integers distinct?
3.Is zero considered a positive integer?
4.What is the total sum of all positive integers?
5.What is the distinction between positive integers and whole numbers?
6.How can children in United Kingdom use numbers in everyday life to understand Positive Integers?
7.What are some fun ways kids in United Kingdom can practice Positive Integers with numbers?
8.What role do numbers and Positive Integers play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Positive Integers skills?
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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.
