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Objective
• The learner will add and
subtract real numbers
Lessons 2-2
Adding Real Numbers
Pages 24 - 31
Subtracting Real Numbers
Pages 32 - 36
Addition Rules
• Like or Same Signs
Add the numbers and keep the sign
Ex) 3 + 5= 8
-4 + -1= -5
• Unlike or Different Signs
Find the difference (subtract) their absolute
values. The result has the sign of the
number with largest absolute value
Ex) -10 + 3 = -7
8 + (-4) = 4
Note: Keep the sign of the number that is furthest from
zero
Example #1
You can use number lines as models to add real numbers.
Let’s try these together:
• -6 + 4
c. 3 + 2
b. 4 + (-5)
d. -5 + (-9)
Now you try:
• -3 + (-8)
c. -2 + 1
b. 9 + (-3)
d. 7 + 4
Subtraction Rule
•
Add its opposite!!
Change the subtraction sign to an
addition sign and switch the sign of
the number that follows it.
Ex) - 5 - 4 =
-5 + -4 = 9
(-2) - (-3) =
(-2) + 3 = 1
Note: You are not subtracting the FIRST number;
therefore you DO NOT change the sign of the
first number, only the one being subtracted
(the second number)
Example #1
You can use a number line to subtract numbers just
like you used it to add numbers.
Let’s try these together
a. 2 – 6
b. -1 – 4
Now its your turn
a. -3 – 8
b. 7 – 2
Videos
• Subtracting Positive & Negative Numbers
• Subtracting Double Negative Numbers
Example #3
A football team gains 2 yds and then
loses 7 yds in two plays. You express
a loss of 7 yd as -7. Use addition to
find the result of the two plays.
2 + (-7) = -5
The result of both plays is a loss of 5
yards.
Now you try:
The temperature falls 15
degrees and then rises 18
degrees. Use addition to find
the change in temperature.
Applying Addition
You can evaluate expressions
that involve addition.
Substitute a value for the
variable(s).
Then simplify the expression.
Example #4
Evaluate –n + 8.9 for n = -2.3
-n + 8.9 = - (-2.3) + 8.9 (Substitute -2.3 for n)
= 2.3 + 8.9 (two negatives make
positive)
= 11.2 (Simplify)
Now you try:
Evaluate each expression for
t = -7.1
a.
b.
c.
d.
t + (-4.3)
-2 + t
8.5 + (-t)
-t + 7.49
Example #5
A rock climber climbs a mountain. The base of
the mountain is 132 ft below sea level.
a. Write an expression to represent the
climber’s height below or above sea level.
Relate: 132 ft below sea level plus feet
the route rises
Define: let h = feet the route rises
Write: -132 + h
Your expression would be -132 + h
Example #5 cont.
Find the climber’s height above sea level when
he is 485 ft above the base of the mountain.
-132 + h = -132 + 485 (Substitute 485 for h)
= 353 (Simplify)
The climber’s height is 353 above sea level.
Now you try:
The temperature one winter morning is
-14 degrees. Define a variable and
write an expression to find the
temperature after it changes. Then
evaluate your expression for a
decrease of 11 degrees.
When you simplify an expression,
you work within grouping symbols
first. Absolute value symbols are
grouping symbols. Therefore, find
the value of an expression within
the absolute value signs before
finding the absolute value.
Example #4
Simplify | 5 – 11 |
| 5 – 11 | = | -6 | (Subtract within
abs. value)
= 6 (absolute value of -6
is 6)
Now you try:
Simplify each expression:
a.
b.
c.
d.
|8–7|
|7–8|
| -10 – (-4) |
| -4 – (-10) |
Now you try:
Evaluate each expression for
t = -2 and r = -7.
a. r – t
b. t – r
c. - t – r
d. - r – (- t)
Now you try:
Find the closing
stocks of ABC
and PQR on
Wednesday.