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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:
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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.
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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.
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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
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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
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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.
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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.
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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?