Integers

-4 -3 -2 -1 0 1 2 3 4

The integers are made up of three groups of numbers: •  the positive integers •  the negative integers •  zero

Here is a list representing all the integers: . . . , -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . Here is a graph representing all the integers:

Adding Integers Example 1: (+4) + (+5) = 9

Example 2: (-3) + (-7) = - 10

Example 3: (-7) + (+2) = - 5

Example 4: (-1) + (+9) = 8

*Adding two positive integers results in a larger positive integer.

*Adding two negative integers results in a larger negative integer.

*Adding two integers with different signs results in an integer with the same sign of the larger number.

Subtracting Integers Example 1: (+4) – (+1)

= 4 + (– 1) = 3

Example 2: (+9) – (-5) = 9 + 5 = 14

Example 3: (-2) – (-3) = (-2) + 3 = 1

*To subtract an integer, add its opposite.

Multiplying and Dividing Integers

If the integers have the same sign (both positive or both negative), the result of the multiplication or division will be a positive integer. Example 1: (2)(14) =28 Example 2: (-20) (-2) =10

Multiplying and Dividing Integers (continued)

If the integers have different signs (a positive and a negative), the result of the multiplication or division will be a negative integer. Example 1: (-9)(4) = -36 Example 2: 45 (-15) = -3

Problems with Integers Example 1:

An elevator went up three floors and down two floors. How much higher or lower was the elevator than when it started?

Solution: (+3) + (-2)

= 1 Therefore, the elevator was one

floor higher than when it started.

Problems with Integers (continued)

Example 2: Today’s high temperature was six degrees. Today’s low temperature was four degrees below zero. What was the change in temperature?

Solution: (+6) - (-4)

= 6 + 4 = 10 Therefore, there was a ten-degree

change in temperature.

Practice 1. 5 – (-2) + 6 2. 23 + (-6) 3. (-3) – (-4) – (-1) 4. (-3)(-5) 5. (18)(-2) 6. (-40)

10 7. A plane is flying at 30 000 m. The

temperature outside the plane is -27oC. As the plane lands, the temperature increases by 1oC for every 1000 m drop in altitude. What is the temperature on the ground?