1. Multiplying and Dividing Integers
2-3
Multiplying and Dividing Integers
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Warm Up
Multiply or divide.
1. 5(8) 40
2. 6(12) 72 36 9 49 7 3. 4 4. 7
192 16 12
5. 18(7)
126 6.

3. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Problem of the Day
Complete the pyramid by filling in the missing numbers. Each number is the sum of the numbers in the two boxes below it. –4 –8 4 –7 –1 5 –9 8 2 –3

4. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Learn to multiply and divide integers.

5. Insert Lesson Title Here
Course 3
2-3
Multiplying and Dividing Integers
Insert Lesson Title Here
A positive number multiplied by an integer can be written as repeated addition.
3(–200) = –200 + (–200) + (–200) = –600
From what you know about adding and subtracting integers, you can see that a positive integer times a negative integer is negative.

6. Insert Lesson Title Here
Course 3
2-3
Multiplying and Dividing Integers
Insert Lesson Title Here
You know that multiplying two positive integers together gives you a positive answer. Look for a pattern in the integer multiplication at right to understand the rules for multiplying two negative integers.
3(–200) =
2(–200) =
1(–200) =
0(–200) =
–1(–200) =
–2(–200) =
–3(–200) =
–600
+ 200
–400
+ 200
–200
+ 200
The product of two negative integers is a positive integer.
200
400
600

7. MULTIPLYING AND DIVIDING TWO INTEGERS
Course 3
2-3
Multiplying and Dividing Integers
Insert Lesson Title Here
MULTIPLYING AND DIVIDING TWO INTEGERS
If the signs are the same, the sign of the answer is positive.
If the signs are different, the sign of the answer is negative.

8. Additional Example 1A & 1B: Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Additional Example 1A & 1B: Multiplying and Dividing Integers
Multiply or divide.
A. –6(4)
Signs are different.
= –24
Answer is negative.
B. –8(–5)
Signs are the same.
= 40
Answer is positive.

9. Additional Example 1C & 1D: Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Additional Example 1C & 1D: Multiplying and Dividing Integers
Multiply or divide.
–18 2 C.
Signs are different.
= –9
Answer is negative.
–25 –5 D.
Signs are the same.
= 5
Answer is positive.

10. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Try This: Example 1A & 1B
Multiply or divide.
A. 5(–2)
Signs are different.
= –10
Answer is negative.
B. –3(–2)
Signs are the same.
= 6
Answer is positive.

11. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Try This: Example 1C & 1D
Multiply or divide.
–24 3 C.
Signs are different.
= –8
Answer is negative.
–12 –2 D.
Signs are the same.
= 6
Answer is positive.

12. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Order of Operations
1. Parentheses
2. Exponents
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
Remember!

13. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Additional Example 2A & 2B: Using the Order of Operations with Integers
Simplify.
A. 3(–6 – 12)
Subtract inside the parentheses.
= 3(–18)
Think: The signs are different.
= –54
The answer is negative.
B. –5(–5 + 2)
Subtract inside the parentheses.
= –5(–3)
Think: The signs are the same.
= 15
The answer is positive.

14. Additional Example 2C: Using the Order of Operations with Integers
Course 3
2-3
Multiplying and Dividing Integers
Additional Example 2C: Using the Order of Operations with Integers
Simplify.
C. –2(14 – 5)
Subtract inside the parentheses.
= –2(9)
Think: The signs are different.
= –18
The answer is negative.

15. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Try This: Example 2A & 2B
Simplify.
A. 2(1 – 8)
Subtract inside the parentheses.
= 2(–7)
Think: The signs are different.
= –14
The answer is negative.
B. 4(–3 – 8)
Subtract inside the parentheses.
= 4(–11)
Think: The signs are different.
= –44
The answer is negative.

16. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Try This: Example 2C
Simplify.
C. –3(6 – 9)
Subtract inside the parentheses.
= –3(–3)
Think: The signs are the same.
= 9
The answer is positive.

17. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
The order of operations can be used to find ordered pair solutions of integer equations. Substitute an integer value for one variable to find the value of the other variable in the ordered pair.

18. Additional Example 3: Plotting Integer Solutions of Equations
Course 3
2-3
Multiplying and Dividing Integers
Additional Example 3: Plotting Integer Solutions of Equations
Complete a table of solutions for y = 3x – 1 for x = –2, –1, 0, 1, and 2. Plot the points on a coordinate plane. y 10 8 6 4 2 2 4 6 8 x
3x – 1 y
(x, y) –2 –1 1 2
(2, 5)
3(–2) – 1 –7
(–2, –7)
(1, 2)
3(–1) – 1 –4
(–1, –4) x
(0, –1)
10 8 6 4 
3(0) – 1 –1
(0, –1)
(–1, –4)
3(1) – 1 2
(1, 2)
(–2, –7)
3(2) – 1 5
(2, 5)

19. Multiplying and Dividing Integers
Course 3
2-3
Multiplying and Dividing Integers
Try This: Example 3
Complete a table of solutions for y = 2x – 3 for x = –2, –1, 0, 1, and 2. Plot the points on a coordinate plane. y 10 8 6 4 2 2 4 6 8 x
2x – 3 y
(x, y) –2 –1 1 2
2(–2) – 3 –7
(–2, –7)
(2, 1)
2(–1) – 3 –5
(–1, –5) x
(1, –1)
10 8 6 4 
2(0) – 3 –3
(0, –3)
(0, –3)
(–1, –5)
2(1) – 3 –1
(1, –1)
(–2, –7)
2(2) – 3 1
(2, 1)

20. Multiplying and Dividing Integers Insert Lesson Title Here
Course 3
2-3
Multiplying and Dividing Integers
Insert Lesson Title Here
Lesson Quiz: Part 1
Perform the given operations.
1. –8(4)
–32 2.
–12(5)
–10 6
Evaluate the expressions for the given value of the variable.
3. –4t – 9 for t = –6 15
–36 t
for t = 9 –4

21. Multiplying and Dividing Integers Insert Lesson Title Here
Course 3
2-3
Multiplying and Dividing Integers
Insert Lesson Title Here
Lesson Quiz: Part 2
5. Complete a table of solutions for y = 4x + 1 for x = –3, –1, 1, and 3. x
4x + 1 y
(x, y) –3 –1 1 3
4(–3) + 1
–11
(–3, –11)
4(–1) + 1 –3
(–1, –3)
4(1) + 1 5
(1, 5)
4(3) + 1 13
(3, 13)