Chapter 11
Lessons 11-4, 11-6, 11-7, NS.8
STUDY GUIDE
This study guide provides you with an overview of the types of problems and skills that we will learn or have learned in the lessons listed above. In addition to this guide, review your 11-1 to 11-3 study guide, and we will complete additional review problems in class, as we get closer to the test.
Review your class notes too!
Lesson 11-4: Multiplying Integers
When the signs are the SAME, the product is POSITIVE.
When the signs are DIFFERENT, the product is NEGATIVE.
Example 1 Multiply Integers with Different Signs
Multiply 5 (−3).
5 (−3) = −15The integers have different signs. The product is negative.
Example 2 Multiply Integers with Different Signs
Multiply –7 5.
−7 5 = −35The integers have different signs. The product is negative.
Example 3 Multiply Integers with Same Signs
Multiply 3 8.
3 8 = 24The integers have the same sign. The product is positive.
Example 4 Multiply Integers with Same Signs
Multiply −9 (−5).
−9 (−5) = 45The integers have the same sign. The product is positive.
Lesson 11-6: Dividing Integers
When the signs are the SAME, the quotient is POSITIVE.
When the signs are DIFFERENT, the quotient is NEGATIVE.
Example 1 Divide Integers
Divide −6 3.
−6 ÷ 3 = −2.The integers have different signs. The quotient is negative.
Example 2 Divide Integers
Divide 27 3.
27 ÷ 3 = 9.The integers have the same sign. The quotient is positive.
Example 3 Divide Integers
Find −21 3.
−21 3 = −7.The integers have different signs. The quotient is negative.
Example 4 Divide Integers
Find 42 (−7).
42 ÷ (−7) = −6.The integers have different signs. The quotient is negative.
Example 5 Divide Integers
Find −35 (−7).
−35 (−7) = 5.The integers have the same sign. The quotient is positive.
Example 6Evaluate with Integers
Find m n if m= 81 and n= -9
m nSubstitute first.
81 (−9) = -9The integers have different signs. The quotient is negative.
Lesson 4-9 and Lesson 11-7: The Coordinate Plane
When graphing ordered pairs, the x coordinate (the first number) tells you whether to go right (+) or left (-), and the y coordinate (the second number) tells you whether to go up (+) or down (-).
( - , +) (+ , +)
( - , - ) ( + , -)
Example 1 Naming Points Using Ordered Pairs
Write the ordered pair that names point B.
Identify the quadrant.
Step 1 Start at the origin. Move right along the x-axis until you are under point B. The x-coordinate of the ordered pair is 5.
Step 2 Now move up until you reach point B. They-coordinate is 6.
So, point B is named by the ordered pair (5, 6). This point is in Quadrant I.
Example 2 Graphing Ordered Pairs
Graph the point D(4, 3).
Identify the quadrant.
- Start at the origin.
- Move 4 units to the right on the x-axis.
- The value 3 is halfway between 3 and 4. So, on the y-axis move up halfway between 3 and 4.
- Draw a dot and label the dot D.
So, point D is named by the ordered pair (4, 3).
This point is in Quadrant I.
Example 3Graph Ordered Pairs
Graph point H at (−3, 2). Identify the quadrant.
This point is in Quadrant II.
Example 3 Identify Ordered Pairs
Identify the ordered pair that names point F. Then identify the quadrant in which point F is located.
Step 1Start at the origin. Move left on the x-axis to find the x-coordinate of point F, which is –3.
Step 2Move down the y-axis to find the y-coordinate, which is –4.
Point F is named by (−3, −4). Point F is in Quadrant III.
Example 4 Identify Ordered Pairs
Identify the ordered pair that names point G. Then identify the quadrant in which point G is located.
Step 1Start at the origin. Move right on the x-axis to find the x-coordinate of point G, which is 4.
Step 2Move down the y-axis to find the y-coordinate, which is –2.
Point G is named by (4, −2). Point G is in Quadrant IV.
Lesson NS.8: Distance on the Coordinate Plane
Use the coordinate plane at the right to answer questions.
Plot and label a point at each of the following coordinates:
Q: (-5, 5)S: (3, 7)
R: (-4, -2)T: (3, -5)
What is the distance between points S and T?
12 units
Draw quadrilateral JKLM with the following vertices:
J: (2,3)L: (-2,-3)
K: (-2,3)M: (2,-3)
What is the distance between point J and point K? 4 units
What is the distance between point K and point L?6 units
What type of quadrilateral did you make? rectangle
What is the perimeter of the quadrilateral? Show your work.
4 + 4 + 6 + 6 = 20 units