Download 15 Adding and Subtracting Real Numbers The absolute value of a

1­5 Adding and Subtracting Real Numbers
The absolute value of a number is the distance from 0 on a number line. Absolute value is always positive. Addition Rule (Two numbers with the same sign)
To add two numbers that have the same sign, either both positive or negative:
1) add them together
2) keep the same sign
Example: ­13 + ­12 = ­25
13+ 12 = 25
Addition Rule (Two numbers with different signs)
To add two numbers that have different signs:
1) Subtract the smaller number from the larger number 2) Keep the sign of the bigger number
Examples: ­15 + 12 = ­3
15 + ­12 = 3
What is the sum?
a) ­16 + (­8)
b) ­11 + 9
c) 9 + (­11)
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Two numbers that are the same distance from 0 on a number line but lie in the opposite directions are opposites.
Property : Inverse Property of Addition
For every real number a, there is an additive inverse ­a such that a + (­a) or (­a) +a = 0. Definition of Subtraction:
Adding the opposite; m ­ n = m + (­n) Examples: 1) [11.2 ­ (­14.9)] ­ (3.1 ­ 8.8)]
2) 3
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­ 14 ­ 58
3) |28 ­ (­16)| + |­51 ­ (­31)|
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Evaluate each expression if x = ­3.2, y = 7.8, and z = ­4.7
1) ­14.2 ­ [z ­ (­y) + (3.8 ­ x)]
2) z ­ |[x ­ (­11)] ­ (13.1 ­ y)|
A reef explorer dives 25 ft to photograph brain coral and then rises 16 ft to travel over a ridge before diving 47 ft to survey the base of the reef. Then the diver rises 29 ft to see and underwater cavern. What is the location of the cavern in relation to the sea level?
27 below sea level
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