Download Course 3 Chapter 2 Lesson 3

2-3 Multiplying and Dividing Integers
Today’s Learning Goal Assignment
Learn to
multiply and
divide integers.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Lesson Quiz: Part 1
Perform the given operations.
1. –8(4)
–32
2. –12(5)
6
–10
Evaluate the expressions for the given
value of the variable.
3. –4t – 9 for t = –6
15
4. –36 for t = 9
–4
t
Pre-Algebra
2-3 Multiplying and Dividing Integers
Lesson Quiz: Part 2
5. Complete a table of solutions for y = 4x + 1
for x = –3, –1, 1, and 3.
x
y
(x, y)
–3 4(–3) + 1 –11 (–3, –11)
–1 4(–1) + 1 –3 (–1, –3)
(1, 5)
5
1 4(1) + 1
4(3) + 1
(3, 13)
13
3
Pre-Algebra
4x + 1
2-3 Multiplying and Dividing Integers
Are we ready for the
FAST TRACK?
Pre-Algebra
2-3 Multiplying and Dividing Integers
Pre-Algebra: 2-3 HW
Page 734
(Yes, page 734)
#1-41 ODD
Pre-Algebra
2-3
2-3 Multiplying
Multiplyingand
andDividing
DividingIntegers
Integers
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
2-3 Multiplying and Dividing Integers
Warm Up
Multiply or divide.
1. 5(8)
3.
36
9
5. 18(7)
Pre-Algebra
40
4
126
2. 6(12)
4.
6.
49
7
192
16
72
7
12
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
–7
2
Pre-Algebra
–9
4
–1
5
8
–3
2-3 Multiplying and Dividing Integers
Learn to multiply and divide integers.
Pre-Algebra
2-3 Multiplying and Dividing Integers
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.
Pre-Algebra
2-3 Multiplying and Dividing Integers
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.
Pre-Algebra
3(–200) = –600
2(–200) = –400
1(–200) = –200
0(–200) = 0
+ 200
+ 200
+ 200
–1(–200) = 200 The product of
two negative
–2(–200) = 400 integers is a
positive
–3(–200) = 600
integer.
2-3 Multiplying and Dividing Integers
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.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Additional Example 1A & 1B: Multiplying and Dividing
Integers
Multiply or divide.
A. –6(4)
= –24
B. –8(–5)
= 40
Pre-Algebra
Signs are different.
Answer is negative.
Signs are the same.
Answer is positive.
2-3 Multiplying and Dividing Integers
Additional Example 1C & 1D: Multiplying and Dividing
Integers
Multiply or divide.
–18
2
C.
= –9
Signs are different.
Answer is negative.
–25
–5
Signs are the same
=5
Answer is positive.
D.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Try This: Example 1A & 1B
Multiply or divide.
A. 5(–2)
= –10
B. –3(–2)
=6
Pre-Algebra
Signs are different.
Answer is negative.
Signs are the same.
Answer is positive.
2-3 Multiplying and Dividing Integers
Try This: Example 1C & 1D
Multiply or divide.
–24
3
C.
= –8
Signs are different.
Answer is negative.
–12
–2
Signs are the same
=6
Answer is positive.
D.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Remember!
Order of Operations
1. Parentheses
2. Exponents
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
Pre-Algebra
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
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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.
Pre-Algebra
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
x
3x – 1
–2 3(–2) – 1
y
–7
–1 3(–1) – 1
3(0) – 1
0
3(1) – 1
1
3(2) – 1
2
–4
–1
Pre-Algebra
2
5
(x, y)
(–2, –7)
(–1, –4)
(0, –1)
(1, 2)
(2, 5)
10
8
(2, 5)
6
4 (1, 2)
2
(0, –1)
10 8 6 4 2
2
(–1, –4)
4
(–2, –7)6
8
10
2
4
6
x
8 10
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
x
2x – 3
–2 2(–2) – 3
y
–7
–1 2(–1) – 3
2(0) – 3
0
2(1) – 3
1
2(2) – 3
2
–5
–3
Pre-Algebra
–1
1
(x, y)
(–2, –7)
(–1, –5)
(0, –3)
(1, –1)
(2, 1)
10
8
6
4
(2, 1)
2
10 8 6 4
(0,2
–3)
2
(–1, –5)
4
(–2, –7)6
8
10
2
4 6 8 10
(1, –1)
x