Working with Integers: Worksheets

Working with integers. Comparing and ordering integers. Operations (Adding, Subtracting, Multiplying, Dividing) with integers including positive and negative integers.

What are integers?

All counting numbers, their negatives, and zero form the set of integers. An integer is a non-fractional number that can be positive, negative, or zero.

Absolute value of an integer

The numerical value of an integer, regardless its sign, is the absolute value of an integer.

Integers on Number Line

The easiest way to explain the concept of integers (and their operations) is by using a number line.

Comparing integers on a a number line

Referring to the number line on which integers are represented by points, here are the observations:

• Every negative integer is less than 0 and every positive integer is greater than 0.
• Every negative integer is less than every positive integer.
• If (a > b) then (-a < -b) and if (a < b) then (-a > -b).
• An integer is greater than all the integers to its left on the number line
• An integer is smaller than all the integers to its right on the number line

Fundamental Operations on Integers

Addition of Integers

• The sum of two positive integers is always a positive integer.
• The sum of two negative integers is always a negative integer.
• When adding a positive and a negative integer, we first find the difference between the numerical values and assign to it the sign of the integer with the greater numerical value.

Addition of Integers

a – (-b) = a + b

Multiplication of Integers

(+) x (+) = +

(-) x (-) = + (Example: -4 x -8 = 32)

(+) x (-) = – (Example: 4 x -8 = -32)

(-) x (+) = – (Example: -4 x 8 = -32)

Division of Integers

(+) ÷ (+) = +

(-) ÷ (-) = + (Example: -32 ÷ -4 = 8)

(+) ÷ (-) = – (Example: 32 ÷ -4 = -8)

(-) ÷ (+) = – (Example: -32 ÷ 4 = -8)