Transcript 1-6

1-6 Multiplying and Dividing Integers
Warm Up
Problem of the Day
Lesson Presentation
Course 3
1-6 Multiplying and Dividing Integers
Warm Up
Multiply or divide.
1. 5(8)
3.
36
9
5. 18(7)
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40
4
126
2. 6(12)
4.
6.
49
7
192
16
72
7
12
1-6 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
1-6 Multiplying and Dividing Integers
SC Standard 8-2.1
Apply an algorithm to add, subtract,
multiply, and divide integers
Learn to multiply and divide integers.
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1-6 Multiplying
Insert Lesson
HereIntegers
andTitle
Dividing
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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1-6 Multiplying
Insert Lesson
HereIntegers
andTitle
Dividing
multiplying two
positive integers
together gives you
a positive answer.
(+)
3(–200) = –600
2
x
(–200) = –400
1(–200) = –200
0(–200) = 0
multiplying two
negative integers
together gives you
a positive answer
(+).
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+ 200
+ 200
+ 200
–1(–200) = 200 The product of
two negative
–2(–200) = 400 integers is a
positive integer.
–3(–200) = 600
1-6 Multiplying
Insert Lesson
HereIntegers
andTitle
Dividing
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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1-6 Multiplying and Dividing Integers
Additional Example 1: 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.
1-6 Multiplying and Dividing Integers
Additional Example 1: Multiplying and Dividing
Integers
Multiply or divide.
C.
D.
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–18
2
Signs are different.
= –9
Answer is negative.
–25
–5
Signs are the same.
=5
Answer is positive.
1-6 Multiplying and Dividing Integers
Check It Out: Example 1
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.
1-6 Multiplying and Dividing Integers
Check It Out: Example 1
Multiply or divide.
C.
D.
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–24
3
Signs are different.
= –8
Answer is negative.
–12
–2
Signs are the same.
=6
Answer is positive.
1-6 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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1-6 Multiplying and Dividing Integers
Calculator
Example!
Exercise Example : 3(2-9) +6(2(5-3))
Calculator DEMO: 3x(2-9) + 6 x (2 x (5-3))
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1-6 Multiplying and Dividing Integers
Additional Example 2: 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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1-6 Multiplying and Dividing Integers
Additional Example 2: 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.
1-6 Multiplying and Dividing Integers
Check It Out: Example 2
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.
1-6 Multiplying and Dividing Integers
Check It Out: Example 2
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 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.
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1-6 Multiplying and Dividing Integers
Additional Example 3: Sports Application
A golfer plays 5 holes. On 3 holes, he has a
gain of 4 strokes each. On 2 holes, he has a
loss of 4 strokes each. Each gain in strokes
can be represented by a positive integer, and
each loss can be represented by a negative
integer. Find the total net change in strokes.
3(4) + 2(–4)
Add the losses to the gains.
= 12 + (–8)
Multiply.
=4
Add.
The golfer changed by a total gain of 4 strokes.
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1-6 Multiplying and Dividing Integers
Check It Out: Example 3
A golfer plays 9 holes. On 3 holes, he has a
gain of 3 strokes each. On 4 holes, he has a
loss of 3 strokes each. Each gain in strokes
can be represented by a positive integer, and
each loss can be represented by a negative
integer. Find the total net change in strokes.
3(3) + 4(–3)
Add the losses to the gains.
= 9 + (–12)
Multiply.
= -3
Add.
The golfer changed by a total loss of 3 strokes.
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1-6 Multiplying
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Dividing
Insert Lesson
HereIntegers
Lesson Quiz: Part I
Multiply or Divide.
1. –8(4)
–32
2. –12(5)
6
–10
Simplify.
3. –2(13 – 4)
– 18
4. 6(-5 – 3)
– 48
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1-6 Multiplying
andTitle
Dividing
Insert Lesson
HereIntegers
Lesson Quiz: Part II
5. Evin completes 11 transactions in his bank
account. In 6 transactions, he withdraws
$10. in 5 transaction, he deposits $20. Find
the total net change in dollars.
$40
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