8.1 Add Integers Using the Inverse
Property Of Addition
Common Core Standards
7.NS.1. Apply and extend previous understandings of addition and subtraction
to add and subtract rational numbers; represent addition and subtraction on a
horizontal or vertical number line diagram. a. Describe situations in which
opposite quantities combine to make 0. For example, a hydrogen atom has 0
charge because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive
or negative direction depending on whether q is positive or negative. Show that
a number and its opposite have a sum of 0 (are additive inverses). Interpret
sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p
– q = p + (–q). Show that the distance between two rational numbers on the
number line is the absolute value of their difference, and apply this principle in
real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational
numbers.
WARM-UP
1) Place the integers on the number line.
−9, − 5, − 2, 1, 5,7
0
2) Which is the largest?
3) Which is the smallest?
4) Which is opposite of 9?
Add Integers using the Inverse
Property of Addition
You have $50 in your pocket, but you owe a friend
$57. Do you really have any money?
NOTES
Two numbers that are the same distance from zero are
called opposites (additive inverses).
-10 -8 -6 -4 -2 0 2 4 6 8 10
Concept Check
Find the opposites.
6
−4
Find the number that is the same distance from zero.
−7
3
NOTES
The Inverse Property of Addition: opposites added
together always equals zero.
Concept Check
Evaluate the expressions.
−1 + 1
x + (− x)
148 + (−148)
EXAMPLES
Evaluate the expressions.
−4 + 4 + 13
7 + 26 + (−7)
843 + (−843) + (−11)
NOTES
To add positives to negatives cancel equal amounts out
then count the extra positives or negatives.
Concept Check
−5 + 7
+
=
+
=
3 + (−7)
EXAMPLES
Evaluate the expressions.
+
=
+
=
EXAMPLES
Evaluate the expressions.
−9 + 2
7 + (−4)
−14 + 19
38 + (−21)
EXAMPLES
Fred had $68 in his pocket, but owed his friend $14.
How much money did Fred have?
A football team lost 3 yards on the first play then
gained 8 yards on the next. How many total yards did
they gain?
PRACTICE
What is the opposite of 7?
What is the additive inverse
of -12?
Evaluate the expressions.
−16 + 8 + 16
19 + (−12)
10 + (−23)
15 + (−4)
PRACTICE
An atom has 4 positively charged protons and 4
negatively charged electrons, what is the total
charge of the atom?
Sam had $58 in the bank, but owed his friend $80.
How much money did Sam really have?
MORE PRACTICE
Evaluate the expressions.
−91 + 14
68 + (−17)
FINAL QUESTION
A football team lost 12 yards on their first play then
gained 12 yards back on the next.
This is an example of what property?