Download Finding Absolute Value and Adding/Subtracting Real Numbers

FINDING ABSOLUTE VALUE AND
ADDING/SUBTRACTING REAL NUMBERS
THE NUMBER SYSTEM, EXPRESSIONS AND EQUATIONS
WARM-UP
1. The set of _________________ includes all rational and irrational numbers.
2. 54.2 − 27.38
3.
1
2
+
3
8
4. 1.09 + 76.9
5.
3
4
−
3
8
CORRECTING HOMEWORK
 Remember cheating is not okay and not worth it.
 Be fair and honest.
 Be kind.
 Don’t forget to put “C.B. ___________” with your name.
 Trade with a neighbor.
“NEW” STUFF
 The absolute value of a number is its distance from 0 on a number line.
 Absolute value is denoted using vertical bars, e.g. 4 means “the absolute value of 4”
 Because it is a distance, absolute value is always positive.
EXAMPLE
a. |0|
b. | − 7.12|
c.
3
1−4
d. −|11 − 2|
ADDING AND SUBTRACTING REAL NUMBERS
Rules for Adding Real Numbers
To add numbers with the same sign, add
their absolute values. The sum will have the
original sign.
To add numbers with different signs, find
the difference of their absolute values. The
sum will have the sign of the larger
number.
A little song to help you remember:
(to the tune of Row, Row, Row Your Boat)
Same signs, add and keep
Different signs, subtract
Keep the sign of the larger number
Then you’ll be exact.
SUBTRACTING REAL NUMBERS
 Two numbers with the same absolute value but different signs are opposites or additive inverses of each
other.
 The sum of a number and its inverse is 0.
 Inverse Property of Addition: For every real number 𝑎, 𝑎 + −𝑎 = −𝑎 + 𝑎 = 0
Rules for Subtracting Real Numbers
To subtract a real number, add its inverse.
Then follow the rules for adding real
numbers.
EXAMPLES
 Simplify.
a. (−12) + 21
b. −19 + (−8)
c. 3.2 − −5.1
d. −13 − 12
EXAMPLES FROM THE REAL WORLD
 On the first down, the Aggies lost 4 yards. They gained 7 yards on the second down. What was their total yard
gain (or loss)?
 Dr. Hodgens collected a water sample at a depth of 23 meters from the surface. He descended another 12
meters to collect a plant sample. Where was Dr. Hodgens in relation to the surface when he retrieved the plant
sample?
LESSON PRACTICE
a.
−3.4
b.
−23.4 + 18.72
c.
−
2
3
+ −
1
6
d. 14 − (−22)
e.
f.
−
2
3
− −
1
6
The set of real numbers is closed under addition.
g. The set of real numbers is closed under subtraction.
h. The set of integers is closed under subtraction.
HOMEWORK
 1st and 2nd periods: Pg. 29-30 #1-30
 3rd period: Pg. 25-26 #1-15