Evaluating Algebraic Expressions 1-6Multiplying and Dividing Integers Warm Up Warm Up California...
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Transcript of Evaluating Algebraic Expressions 1-6Multiplying and Dividing Integers Warm Up Warm Up California...
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing Integers
Warm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing Integers
Warm UpMultiply or divide.
40 72
7
12
4
126
1. 5(8) 2. 6(12)
3.36
94. 49
7
192
165. 18(7) 6.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing Integers
NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
California Standards
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing Integers
If a football team loses 10 yards in each of 3 plays, the total change in yards can be represented by 3(–10). You can write this product as repeated addition.
3(–10) = –10 + (–10) + (–10) = –30
Notice that a positive integer multiplied by a negative integer gives a negative product.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing Integers
You already know that the product of two positive integers is a positive integer. The pattern shown at right can help you understand that the product of two negative integers is also a positive integer.
3(–10) =
2(–10) =
1(–10) =
0(–10) =
–1(–10) =
–2(–10) =
–3(–10) =
–30
–20+ 10
–10
0
10
20
30
+ 10
+ 10
+ 10
+ 10
+ 10
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing Integers
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersAdditional Example 1: Multiplying and Dividing Integers
A. –6(4)
B. –8(–5)(2)
40(2)
–24
Signs are different.
Multiply two integers.
Answer is negative.
Answer is positive.
Multiply or divide.
–8(–5)(2) Signs are the same.
40(2) Signs are the same.
Answer is positive.80
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersAdditional Example 1: 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
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersCheck It Out! Example 1
A. 5(–2)
B. –3(–2)(4)
6(4)
–10
Signs are different.
Signs are the same.
Answer is negative.
Answer is positive.
Multiply or divide.
–3(–2)(4)
Signs are the same.6(4)
24 Answer is positive.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersCheck It Out! Example 1
C.
–8
Signs are different.
Answer is negative.
Multiply or divide.
–243
D.
6
Signs are the same.
Answer is positive.
–12–2
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersAdditional Example 2: Using the Order of
Operations with Integers
A. 3(–6 – 12)
–54
3(–18)
Add the opposite of 12 inside the parentheses.
Think: The signs are different.
The answer is negative.
Simplify.
B. –5(–5 + 2)
15
–5(–3)Add inside the parentheses.
Think: The signs are the same.
The answer is positive.
3(–6 + –12)
Subtract inside the parentheses.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersAdditional Example 2: Using the Order of
Operations with Integers
C. –2(14) – 5
–33
–28 – 5
Multiply.
Same sign; use the sign of the integers.
The answer is negative.
Simplify.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersCheck It Out! Example 2
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.
2(1 + –8) Add the opposite of 8 inside the parentheses.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersCheck It Out! Example 2
C. –3(6) – 9
–27
–18 – 9
Multiply.
Same sign; use the sign of the integers.
The answer is negative.
Simplify.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersAdditional Example 3: Sports Application
A golfer plays 5 holes. On 3 holes, he is 4 strokes over par. On 2 holes, he is 4 strokes under par. Each score over par can be represented by a positive integer, and each score under par can be represented by a negative integer. Find the total score relative to par.
3(4) + 2(–4)
4
12 + (–8)
Add the strokes over par to under par.
Multiply.
Add.
The golfer's score was 4 over par.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersCheck It Out! Example 3
3(3) + 4(–3)
–3
9 + (–12)
Add the strokes over par to under par.
Multiply.
Add.
The golfer's score was 3 under par.
A golfer plays 7 holes. On 3 holes, he has a gain of 3 strokes. On 4 holes, he is 3 strokes under par. Each score over par can be represented by a positive integer, and each score under par can be represented by a negative integer. Find the total score relative to par.
Evaluating Algebraic Expressions
1-6 Multiplying and Dividing IntegersLesson Quiz
Multiply or divide.
1. –8(4) 2.–32 6–12(5)–10
Simplify.
3. –2(13 – 4) 4. 6(–5 – 3)–18 –48
5. Evin completes 11 transactions in his bank account. In 6 transactions, he withdraws $10. In 5 transactions, he deposits $20. Find the total net change in dollars. $40
