Addition and Subtraction of Integers on Number Line

The topic “Addition and Subtraction of Integers on Number Line” is covered in this article. The article is on the topic of Addition and subtraction of integers on number lines is useful for students who are studying in grades 5-6. So, let’s begin!

What are Integers?

Integers are whole numbers, both positive and negative, including 0. They are numbers that do not have a fractional or decimal part and can be expressed as -n, 0, or n, where n is a positive whole number.

Examples of integers include -5, -3, 0, 2, 4, etc.

Representation of Integers on Number Line

Addition of Integers on Number Line

When adding integers on a number line, always start from ‘0’ and:

• Move to the right, if the integers being added are positive.
• Move to the left, if the integers being added are negative.

Example: Add 2 + 4.

Solution: As both the integers are positive, on the number line, we will start at 2 and move 4 steps to the right. We will reach number 6. Therefore, 2 + 4 = 6.

Example: Add -4 and -3

Solution: As both the integers are negative, we will start at -4. Then on moving 3 steps to the left, we will reach number -7. Therefore, -4 + (-3) = -7.

Subtraction of Integers on Number Line

When subtracting two integers on a number line, we;

• Move to the left, if two integers are positive.
• Move to the right, if two integers are negative

Example: Subtract -3 from -2.

Here, both integers 2 and 3 are negative. On the number line, we will start at -2 and move to -3 steps to the right. We will reach number 1. Therefore, -2 – (-3) = 1.

Example: Subtract -5 from -3.

Here, both the integers -5 and -3 are negative. On the number line, we will start at -3 and move to - steps to the right. We will reach the number -2. Therefore, -3 – (-5) = 2.

Absolute Value and Magnitude

Definition of Absolute Value
The absolute value of an integer is the distance of the number from zero on the number line, regardless of its sign. It is represented by two vertical bars (||) around the integer. For positive integers, the absolute value is the number itself, and for negative integers, the absolute value is the positive counterpart of that number.

For example:

• The absolute value of 5 is written as |5| and is equal to 5.
• The absolute value of -5 is written as |-5| and is also equal to 5.

Understanding the Magnitude of Integers on the Number Line
The magnitude of an integer represents its size or numerical value, ignoring its direction or sign. On the number line, the magnitude is the distance of the integer from zero, always considered as a positive value.

For example:

• The magnitude of 7 is 7, as it is 7 units away from zero on the positive side of the number line.
• The magnitude of -7 is also 7, as it is 7 units away from zero on the negative side of the number line.

Applications of Absolute Value in Real-Life Scenarios
Absolute value has various applications in real-life situations, such as measuring distance, temperature changes, and calculating differences. For instance, when determining the distance between two cities, you consider the absolute value of the difference in their coordinates to obtain a positive value regardless of their positions.

Properties of Integers

a. Commutative Property of Addition and Subtraction:
The commutative property states that the order of adding or subtracting numbers does not affect the result. In other words, for any two integers "a" and "b," "a + b" is equal to "b + a," and "a - b" is equal to "b - a."

For example:

4 + 7 = 7 + 4 = 11
7 - 4 = 3, but 4 - 7 = -3

b. Associative Property of Addition and Subtraction:
The associative property states that the grouping of numbers being added or subtracted does not change the result. In other words, for any three integers "a," "b," and "c," "(a + b) + c" is equal to "a + (b + c)," and "(a - b) - c" is equal to "a - (b - c)."

For example:

(3 + 5) + 2 = 8 + 2 = 10
3 + (5 + 2) = 3 + 7 = 10
(9 - 4) - 2 = 5 - 2 = 3
9 - (4 - 2) = 9 - 2 = 7

c. Identity Property of Addition and Subtraction:
The identity property states that adding zero to any number does not change the value of the number. Similarly, subtracting zero from any number also does not change its value.

For example:

8 + 0 = 8
15 - 0 = 15