Integral Numbers and Number Lines
Integral numbers extend natural numbers in both directions and are useful for temperatures, debts, levels and changes above or below zero.
Definitions and signs
Integral numbers are positive and negative whole numbers, including zero: Z = {…, −3, −2, −1, 0, 1, 2, 3, …}. Decimal values such as 2.5 are not integral numbers. The opposite of +a is −a, and zero has no positive or negative sign.
Adding and subtracting
- On a signed number line, begin at the first number. Move right for a positive change and left for a negative change.
- Adding a negative is equivalent to subtracting its positive value. Subtracting a negative is equivalent to adding its positive value.
- The rules for signs in multiplication and division are: same signs give positive; different signs give negative.
Worked examples
- −2 + 7: start at −2 and move seven units right, giving 5.
- 3 − 8: start at 3 and move eight units left, giving −5.
- (−6) × (−4) = +24, while 35 ÷ (−7) = −5.
Practice
- Calculate −5 + 9, 4 − 11 and −7 − 3.
- Evaluate (−8) × 6 and (−48) ÷ (−12).
- State whether −12.4, 0, 17 and 3/2 belong to Z.
