Download Notes for Lesson 1-2: Adding and Subtracting Real Numbers

Notes for Lesson 1-5: Adding and Subtracting Real Numbers
1 - Adding and subtracting numbers on a number line
To add or subtract on a number line:
a) start at zero
b) move to the first number
c) if adding - move right to add a positive number and left to add a negative number
if subtracting - move left to subtract a positive number and right to subtract a negative number
Examples: Adding using a number line
3  6
−3 + (−7)
5  (6)
−9 + 2
x
x
x
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10 -8 -6 -4 -2 0 2 4 6 8 10
x
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10 -8 -6 -4 -2 0 2 4 6 8 10
2 - Adding Real Numbers
Vocabulary:
Absolute Value - The distance from zero on a number line
Opposites - Two numbers the same distance from zero but in opposite directions
Additive Inverses - A number and its opposite
When adding real numbers without a number line:
If the 2 numbers have the same sign, add their absolute values and use the sign of the numbers
If the 2 numbers have different signs, find the difference of their absolute values and use the sign of the
number with the greater absolute value.
Examples: Add
3
5
−12 + 7
−18 + (−2)
−4.8 + 9.5
− 4 + (− 6)
−16 + (−8)
−11 + 9
9 + (−11)
−6 + (−2)
3 - Subtracting Real Numbers
When subtracting real numbers without a number line:
Add the opposite, then follow the rules for adding signed numbers.
Examples: Subtract
−8 − (−13)
3.5 − 12.4
48 − (−87)
−3 − 5
4 - Application
A reef explorer dives 25 ft to photograph coral and then rises 16 ft to travel over a ridge before diving 47 ft to
survey the base of the coral. Then the diver rises 29 feet to see an underwater cavern. What is the location of
the cavern in relation to sea level?
0 − 25 + 16 − 47 + 29
0 + (−25) + 16 + (−47) + 29
0 + (16 + 29) + (−47 + −25)
0 + 45 + (−72)
−27 𝑓𝑡