Ch 2 – Integers
2.1 – Graphing Integers on a Number Line
Number Line:
Positive Number:
Negative Number:
Zero:
Integers:
Venn Diagram:
Natural Numbers:
Whole Numbers:
Integers:
Graphing on a Number Line:
Coordinate:
Example: Name the coordinates of G, H, and J.
Example: Graph points K, L, and M on a number line if K has coordinate -4, L has coordinate 2, and M has
coordinate -1.
Example: Name the coordinates of A, B, and C.
Example: Graph points X, Y, and Z on a number line if X has coordinate 4, Y has coordinate 0, and Z has
coordinate -3.
Numbers on a Number Line:
Example:
Replace each ♥ with < or > to make a true
sentence.
3 ♥ -4
-1 ♥ -3
Absolute Value:
Example:
|-1|
|9|
|4| + |-5|
|-5| - |2|
2.2 – The Coordinate Plane
Coordinate System:
Coordinate Plane:
x-axis:
y-axis:
Origin:
Ordered Pair:
x-coordinate:
y-coordinate:
Example: Write the ordered pair that names each point.
Example: Graph each ordered pair on the coordinate plane.
V(2, 4)
W(-4, -1)
R(2, -4)
S(-1, 4)
T(0, -3)
Quadrants:
Example: Name the quadrants in which each point is located.
C(-2, -7)
D(-4, 9)
E(0, -3)
F(1, 0)
G(3, -1)
Example: The first zeppelin flown in 1900 flew at a speed of 18 mph. Let x represent the number of hours.
Then 18x represents the total distance traveled in x hours. Evaluate the expression to find the distances
traveled in 1, 2, and 3 hours. Then graph the ordered pairs (time, distance).
2.3 – Adding Integers
Adding Integers with the Same Sign:
Examples:
6+7
8+9
-5 + (-8)
-2 + (-4)
Zero Pair:
Opposites or Additive Inverses:
Adding Inverse Property:
Adding Integers with Different Signs:
Examples:
-9 + 5
6 + (-8)
-7 + 5
-4 + 9
Example: Traci opened a checking account with a deposit of $100. During the next week, she wrote checks
for $45 and $65 and made a deposit of $28. Find the balance in her account.
Example: Simplify:
-7y + 6y
6m + 4m + (-2m)
-8y + 3y
2.4 – Subtracting Integers
Subtracting Integers:
Examples:
10 – 3
5 – (-1)
-7 – (-6)
-4 – 6
-1 – 8
-7 – (-2)
3 – (-5)
-8 – 3
4–6
-7 – (-11)
-7 – (-10)
9–3
Example:
Evaluate a – b if a = -8 and b = -2.
Evaluate m – n if m = 5 and n = -3.
Evaluate w – x + y – z if w = -5, x = -7, y = 10 and z = -5
Example:
During one school year, 23 new students moved into a school district and 52 students moved out of
the school district. Find the change in the number of students resulting from these moves.
2.5 – Multiplying Integers
Multiplying Two Integers with Different Signs:
Multiplying Two Integers with the Same Sign:
Example: Find each product
4(-3)
15(-3)
-2(7)
10(4)
-7(7)
-8(-6)
10(-3)
Example: Find each product
7(-3)(-6)
-2(-3)(4)
4(-5)(-12)(-5)
(-1)(-5)(-2)(-3)
Example:
Evaluate 4ab if a = -3 and b = -5.
Simplify (4m)(-7n).
Evaluate -5n if n = -7.
Simplify (2a)(-5).
Evaluate 2xy if x = -4 and y = -2.
Simplify 12(-3z).
Example:
The graph of A(3, 5), B(-2, 4), and C(0, 1) are connected with
line segments to form a triangle. Multiply each y-coordinate by -1 and
redraw the triangle. Describe how the position of the triangle changed.
2.6 – Dividing Integers
Dividing Integers:
-
-
Summary of Multiplying/Dividing
X
=
X
=
÷
=
÷
=
Example:
-12 ÷ 3
-20 ÷ (-4)
-50 ÷ (-10)
16 ÷ (-2)
-9 ÷ 3
Example:
Evaluate (6x) ÷ y if x = -4 and y = 8.
Evaluate -12 ÷ x if x = -3.
Example: In the last 5 years at a high school, the number of students with no tardies during the entire school
year dropped from 315 to 95. What was the average change in the number of students without a tardy for
those 5 years?