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Pre-Algebra
2-3 Multiplying and Dividing Integers
2-3 Multiplying and Dividing Integers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
2-3 Multiplying and Dividing Integers
Warm UpMultiply or divide.
Pre-Algebra
2-3 Multiplying and Dividing Integers
40 72
7
12
4
126
1. 5(8) 2. 6(12)
3.36
94.
49
7
192
165. 18(7) 6.
Pre-Algebra
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.
–9 8
–7 –1 5
–4
–8
–32
4
Pre-Algebra
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.
3(–200) =
2(–200) =
1(–200) =
0(–200) =
–1(–200) =
–2(–200) =
–3(–200) =
–600
–400+ 200
–200
0
200
400
600
+ 200
+ 200
The product of two negative integers is a positive integer.
Pre-Algebra
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
A. –6(4)
B. –8(–5)
= 40
= –24
Signs are different.
Signs are the same.
Answer is negative.
Answer is positive.
Multiply or divide.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Additional Example 1C & 1D: Multiplying and Dividing Integers
C.
= –9
Signs are different.
Answer is negative.
Multiply or divide.
–182
D.
= 5
Signs are the same.
Answer is positive.
–25–5
Pre-Algebra
2-3 Multiplying and Dividing Integers
Try This: Example 1A & 1B
A. 5(–2)
B. –3(–2)
= 6
= –10
Signs are different.
Signs are the same.
Answer is negative.
Answer is positive.
Multiply or divide.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Try This: Example 1C & 1D
C.
= –8
Signs are different.
Answer is negative.
Multiply or divide.
–243
D.
= 6
Signs are the same.
Answer is positive.
–12–2
Pre-Algebra
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!
Pre-Algebra
2-3 Multiplying and Dividing Integers
Additional Example 2A & 2B: Using the Order of Operations with Integers
A. 3(–6 – 12)
= –54
= 3(–18)Subtract inside the parentheses.
Think: The signs are different.
The answer is negative.
Simplify.
B. –5(–5 + 2)
= 15
= –5(–3)Subtract inside the parentheses.
Think: The signs are the same.
The answer is positive.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Additional Example 2C: Using the Order of Operations with Integers
C. –2(14 – 5)
= –18
= –2(9)Subtract inside the parentheses.
Think: The signs are different.
The answer is negative.
Simplify.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Try This: Example 2A & 2B
A. 2(1 – 8)
= –14
= 2(–7)Subtract inside the parentheses.
Think: The signs are different.
The answer is negative.
Simplify.
B. 4(–3 – 8)
= –44
= 4(–11)Subtract inside the parentheses.
Think: The signs are different.
The answer is negative.
Pre-Algebra
2-3 Multiplying and Dividing Integers
Try This: Example 2C
C. –3(6 – 9)
= 9
= –3(–3)Subtract inside the parentheses.
Think: The signs are the same.
The answer is positive.
Simplify.
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
x
y
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.
x 3x – 1 y (x, y)
–2
–1
0
1
2
3(–2) – 1
3(–1) – 13(0) – 1
3(1) – 13(2) – 1
–7
–4–1
25
(–2, –7)
(–1, –4)
(0, –1)
(1, 2)(2, 5)
10 8 6 4 2 2 4 6 8 10
10 8 6 4
2
246810
(–2, –7)
(–1, –4)
(0, –1)
(1, 2)
(2, 5)
Pre-Algebra
2-3 Multiplying and Dividing Integers
x
y
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.
x 2x – 3 y (x, y)
–2
–1
0
1
2
2(–2) – 3
2(–1) – 32(0) – 3
2(1) – 32(2) – 3
–7
–5–3
–1
1
(–2, –7)
(–1, –5)
(0, –3)
(1, –1)(2, 1)
10 8 6 4 2 2 4 6 8 10
10 8 6 4
2
246810
(–2, –7)
(–1, –5)
(0, –3)
(1, –1)
(2, 1)
Pre-Algebra
2-3 Multiplying and Dividing Integers
Lesson Quiz: Part 1
Perform the given operations.
1. –8(4)
2.
–32
6–12(5)–10
Evaluate the expressions for the given value of the variable.
3. –4t – 9 for t = –6
4. for t = 9
15
–4–36t
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 4x + 1 y (x, y)
–3
–1
1
3
4(–3) + 1
4(–1) + 14(1) + 1
4(3) + 1
–11
–3
5
13
(1, 5)
(3, 13)
(–3, –11)
(–1, –3)