Addition of Integers

Addition of Integers:

a) Positive integer + Positive integer:

When two positive integers are added, we get a positive integer.
(+3) + (+2) = +5 [= 3 + 2]

b) Negative integer + Negative integer:

When two negative integers are added, we get a negative integer.
(-5) + (-3) = - 8

c) Positive integer + Negative integer:

When one positive and one negative integer are added we subtract them as whole numbers by considering the numbers without their sign and then put the sign of the bigger number with the subtraction obtained. The bigger integer is decided by ignoring the signs of the integers.
(+ 5) + (– 8) = (+ 5) + (– 5) + (– 3) = 0 + (– 3) = (– 3).

i) Let us add 3 and 5 on the number line.

On the number line, we first move 3 steps to the right from 0 to reach 3, then we move 5 steps to the right of 3 to reach 8. Thus, we get 3 + 5 = 8.

Remember:

• When we add a positive integer, we move to the right on a number line.

• When two positive integers are added, we get a positive integer.

ii) Let us add -3 and -5 on the number line.

On the number line, we first move 3 steps to the left of 0, reaching -3, then we move 5 steps to the left of -3 and reach -8. Thus, (-3) + (-5) = -8.

• When we add a negative integer on a number line, we move to the left.

• When two negative integers are added, we get a negative integer.

iii) Find the sum of (+5) and (-3) on the number line.

First, we move to the right of 0 by 5 steps, reaching 5. Then we move 3 steps to the left of 5, reaching 2. Thus, (+5) + (-3) = 2.

• When one positive and one negative integer are added, we take their difference and place the sign of the bigger integer. The bigger integer is decided by ignoring the signs of both integers.