Integers

What are integers?

Integers are the whole numbers ..., -3, -2, -1, 0, 1, 2, 3, ... In the Junior School CBC (KICD), Grade 8 Mathematics extends whole numbers to include negatives, used for temperatures, debts, and levels above or below sea level.

The number line

Numbers increase to the right. -9 < -2 < 0 < 3. A number further right is greater.

Addition

• Same signs: add and keep the sign. (-3) + (-4) = -7.
• Different signs: subtract the smaller size from the larger and use the sign of the larger. -5 + 8 = 3; 5 + (-8) = -3.

Subtraction

Subtracting an integer is adding its opposite.

• 7 - (-3) = 7 + 3 = 10.
• -4 - 6 = -4 + (-6) = -10.

Multiplication and division

Same rules for division.

• (-4) x (-6) = 24.
• (-20) / 5 = -4.
• (-18) / (-3) = 6.

Order of operations

Brackets first, then multiplication/division, then addition/subtraction. Example: -2 + 3 x (-4) = -2 + (-12) = -14.

Worked example

A diver at -15 m rises 9 m, then descends 4 m. Position: -15 + 9 - 4 = -6 + (-4) = -10 m, which is 10 m below sea level.

Try it

• Order from smallest: 5, -7, 0, -1, 3.
• Work out: -9 + 12, 6 - (-8), (-5) x 7, (-36) / (-9).
• A trader owes KES 300 and pays KES 450 to a friend who earlier owed him. Write the final amount as an integer expression.