A set of integers include zero, positive numbers and negative numbers excluding fractions. Even though arithmetic operations are applicable to integers, the rules for the addition and subtraction of integers are different.
A number line is a reference for comparing and ordering numbers. Every number on the number line is plotted with respect to the origin (zero) and the position of a number on a number line determines the value of that number. This implies that any number right to zero is known as Positive numbers and the numbers left to zero are known as Negative numbers.
ADDITION AND SUBTRACTION ON NUMBER LINE
Arithmetic operations on integers can be better explained on a number line. To begin with, one must know to locate integers on a number line. Zero is the middle point of a number line. All positive numbers occupy the right side of the zero whereas negative numbers occupy the left side of zero.
Whether it is addition or subtraction of two integers, begin with first number. Locate the first number on the number line. The first number lets us know where to begin. The second number lets know the direction of movement. If it is a positive number move to right side by that many units and if it is a negative number move to left side of the first number by that many units.
Positive numbers: When we add two positive numbers, the result will always be a positive number. Hence, on adding positive numbers direction of move will always be to right side.
For example, addition of 1 and 5 (1 + 5 = 6)
Here the first number is 1 and second number is 5; both are positive. First, locate 1 on number line. Then move 5 places to right will give 6.
Negative numbers: When we add two negative numbers, the result will always be a negative number. Hence, on adding negative numbers direction of the move will always be to the left side.
For example, addition of -2 and -3
Here the first number is -2 and the second number is -3; both are negative. Locate -2 on a number line. Then move 3 places to the left will give -5.
Positive numbers: When we subtract two positive numbers, move to the left as far as the value of the second number.
For example, subtract 5 from 2
Here the first number is 2 and the second number is 5; both are positive. First, locate 2 on a number line. Then move 5 places to the left will give -3.
Negative numbers: When we subtract two negative numbers, move to the right as far as the value of the second number.
For example, subtract -4 from -2
First, locate -2 on a number line. Then move 4 places to the right will give 2.