Transcript Multiplying and Dividing Integers

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
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–9
4
–1
5
8
–3
2-3 Multiplying and Dividing Integers
Learn to multiply and divide integers.
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2-3 Multiplying
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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.
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2-3 Multiplying
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Dividing
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.
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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.
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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.
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Love/Hate
Love to Love
++=+
Love to Hate
+-=-
Hate to Love
-+=-
Hate to Hate
--=+
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
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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.
C.
–18
2
= –9
D.
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Signs are different.
Answer is negative.
–25
–5
Signs are the same
=5
Answer is positive.
2-3 Multiplying and Dividing Integers
Try This: Example 1A & 1B
Multiply or divide.
A. 5(–2)
= –10
B. –3(–2)
=6
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Signs are different.
Answer is negative.
Signs are the same.
Answer is positive.
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.
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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
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2-3 Multiplying and Dividing Integers
Additional Example 2C: Using the Order of
Operations with Integers
Simplify.
C. –2(14 – 5)
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Subtract inside the parentheses.
= –2(9)
Think: The signs are different.
= –18
The answer is negative.
2-3 Multiplying and Dividing Integers
Try This: Example 2A & 2B
Simplify.
A. 2(1 – 8)
= 2(–7)
Think: The signs are different.
= –14
The answer is negative.
B. 4(–3 – 8)
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Subtract inside the parentheses.
Subtract inside the parentheses.
= 4(–11)
Think: The signs are different.
= –44
The answer is negative.
2-3 Multiplying and Dividing Integers
Try This: Example 2C
Simplify.
C. –3(6 – 9)
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Subtract inside the parentheses.
= –3(–3)
Think: The signs are the same.
=9
The answer is positive.
2-3 Multiplying
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Dividing
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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
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Dividing
Insert Lesson
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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
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4x + 1