Addition & Subtraction of Positive and Negative Integers- mathematics -jss1

ADDITION AND SUBTRACTION OF POSITIVE AND NEGATIVE INTEGERS

Meaning of Integers

Integers are all whole numbers and their negatives, including zero.
Examples: …, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

Positive integers: Numbers greater than zero (e.g. 1, 2, 3, …).

Negative integers: Numbers less than zero (e.g. -1, -2, -3, …).

Zero (0): Neither positive nor negative.

Number line (integers):
… -3, -2, -1, 0, 1, 2, 3 …

Addition of Integers

Rules for Addition

Same signs: add absolute values and keep the sign.
- (+4) + (+3) = +7
- (-5) + (-2) = -7

Different signs: subtract absolute values and keep the sign of the number with the larger absolute value.
- (+7) + (-4): 7 − 4 = 3 → result = +3
- (-8) + (+3): 8 − 3 = 5 → result = -5

Number-line method

To add a positive number: move right. To add a negative number: move left.

Example: Start at 2, add −5 → move 5 steps left → answer = −3.

Subtraction of Integers

Rule for subtraction

Subtracting an integer is the same as adding its opposite:

a − b = a + (−b)

Change the subtraction to addition, change the sign of the second number, then use the addition rules above.

Examples

7 − 5 = 7 + (−5) = +2

4 − (−3) = 4 + (+3) = +7

(−6) − 2 = (−6) + (−2) = −8

(−4) − (−5) = (−4) + (+5) = +1

Number-line hints: subtracting a positive → move left; subtracting a negative → move right.

examples

Example 1

(+8) + (−3): different signs → 8 − 3 = 5 → sign of larger absolute value (8 is positive) → +5.

Example 2

(−7) + (−6): same signs (negative) → 7 + 6 = 13 → −13.

Example 3

4 − (−9): rewrite as 4 + (+9) → 4 + 9 = 13.

Example 4

(−10) − (+5): rewrite as (−10) + (−5) → same sign (negative) → 10 + 5 = 15 → −15.

Example 5

(−2) − (−8): rewrite as (−2) + (+8) → different signs → 8 − 2 = 6 → sign of larger (8 positive) → +6.

Example 6

(+12) − (+15): rewrite as 12 + (−15) → different signs → 15 − 12 = 3 → bigger is negative → −3.

Example 7

(−20) + (+7): different signs → 20 − 7 = 13 → bigger is negative → −13.

Example 8

0 − (−4) → 0 + (+4) = +4.

Example 9

(−3) − 0 → (−3) + 0 = −3.

Example 10

(+5) + 0 = +5.

Real-life applications of Addition & Subtraction of Positive and Negative Integers

Temperature: below 0°C are negative, above 0°C positive. Example: −3°C to +2°C → increase of 5°C.

Banking: positive = balance, negative = overdraft/debt. Example: −₦500 + ₦200 = −₦300.

Elevation: above sea-level positive, below sea-level negative.

Games & scores: wins/losses shown with +/- values.

Tips & common mistakes

Always rewrite subtraction as addition of the opposite: a − b = a + (−b).

When adding different signs, subtract absolute values and keep the sign of the larger absolute value.

Use a number line to visualise moves left (negative) and right (positive).

Summary table

Operation	Same Signs	Different Signs
Addition	Add absolute values and keep the sign.	Subtract absolute values; sign = sign of number with larger absolute value.
Subtraction	Change subtraction to addition of opposite, then follow addition rules.