Review Multiplying integers Rule…    SAME (Like) SIGNS DIFFERENT (Unlike) SIGNS  

                         

Review Dividing Integers Rules…  

                                     

***Division has the same rules as multiplication!

Name ________________________________________ Date __________________ Class __________________

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

31

Multiplying Integers Success for English Learners

Problem 1 Multiply: −8 × 5.

Use the absolute values of the numbers.

|−8| = 8 |5| = 5

Think about multiplying integers.

Since 8 × 5 = 40, (−8)(5) = −40

Problem 2 Multiply: −6 × −4.

Use the absolute values of the numbers.

|−6| = 6 |−4| = 4

Think about multiplying integers.

Since, 6 × 4 = 24, (−6)(−4) = 24

You have money in a bank account. You take out $20 each week for three weeks. After the three weeks, what is the change in the amount of money in your account?

1. What integer shows the money you take out each week? __________

2. What integer shows the number of weeks you take money out?

_________________________________________________________________________________________

3. What expression can you use to solve the problem? _________________

4. What is the change in your account after three weeks? _______________

Answer each question. 5. You know 50 × 8 = 400. Explain how that helps you find (−50)(−8).

_________________________________________________________________________________________

_________________________________________________________________________________________

6. Are the products of 4 × −8 and −4 × 8 the same? Explain.

_________________________________________________________________________________________

_________________________________________________________________________________________

LESSON

2-1

(1)(−1) = −1 (−1)(1) = −1 Multiply numbers with different signs,

and get a negative product.

(1)(1) = 1 (−1)(−1) = 1 Multiply numbers with the same sign,

and get a positive product.

Name ________________________________________ Date __________________ Class __________________

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

31

Multiplying Integers Success for English Learners

Problem 1 Multiply: −8 × 5.

Use the absolute values of the numbers.

|−8| = 8 |5| = 5

Think about multiplying integers.

Since 8 × 5 = 40, (−8)(5) = −40

Problem 2 Multiply: −6 × −4.

Use the absolute values of the numbers.

|−6| = 6 |−4| = 4

Think about multiplying integers.

Since, 6 × 4 = 24, (−6)(−4) = 24

You have money in a bank account. You take out $20 each week for three weeks. After the three weeks, what is the change in the amount of money in your account?

1. What integer shows the money you take out each week? __________

2. What integer shows the number of weeks you take money out?

_________________________________________________________________________________________

3. What expression can you use to solve the problem? _________________

4. What is the change in your account after three weeks? _______________

Answer each question. 5. You know 50 × 8 = 400. Explain how that helps you find (−50)(−8).

_________________________________________________________________________________________

_________________________________________________________________________________________

6. Are the products of 4 × −8 and −4 × 8 the same? Explain.

_________________________________________________________________________________________

_________________________________________________________________________________________

LESSON

2-1

(1)(−1) = −1 (−1)(1) = −1 Multiply numbers with different signs,

and get a negative product.

(1)(1) = 1 (−1)(−1) = 1 Multiply numbers with the same sign,

and get a positive product.

Guided Practice

Find each quotient. (Example 1)

1. -14 ____ 2 2. 21 ÷ (-3)

3. 26 ____ -13 4. 0 ÷ (-4)

5. -45 ____ -5 6. -30 ÷ (10)

7. -11 ____ -1 8. -31 ÷ (-31)

9. 0 ___ -7 10. -121 _____ -11

11. 84 ÷ (-7) 12. 500 ____ -25

13. -6 ÷ (0) 14. -63 ____ -21

Write a division expression for each problem. Then find the value of the expression. (Example 2)

15. Clark made four of his truck payments late and was fined four late fees. The total change to his savings from late fees was -$40. How much was one late fee?

16. Jan received -22 points on her exam. She got 11 questions wrong out of 50 questions. How much was Jan penalized for each wrong answer?

17. Allen’s score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How many targets did he miss?

18. Louisa’s savings change by -$9 each time she goes bowling. In all, it changed by -$99 during the summer. How many times did she go bowling in the summer?

19. How is the process of dividing integers similar to the process of multiplying integers?

ESSENTIAL QUESTION CHECK-IN???

-7 -7

9

1

-12

-3

11

11

undefined

0

-20

3

0

-40 ÷ (4) = -10; $10

-75 ÷ (-15) = 5; 5 targets

-22 ÷ (11) = -2; 2 points

-99 ÷ (-9) = 11; 11 times

In both cases, if the signs of the initial numbers are

the same, the answer will be positive. If the signs are

different, the answer will be negative.

-2

Unit 146

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7_MFLESE056701_U1M02L2.indd 46 08/04/14 7:29 PM

Olympic Trivia Quiz

Winter Quiz

Summer Quiz

-3 points

-7 points

-33 points

-56 points

Points lost foreach wrong answer Total points lost

Math On the Spotmy.hrw.com

Math TrainerOnline Assessment

and Intervention

Personal

my.hrw.com

Using Integer Division to Solve ProblemsYou can use integer division to solve real-world problems. For some problems, you may need to perform more than one step. Be sure to check that the sign of the quotient makes sense for the situation.

Jake answers questions in two different online Olympic trivia quizzes. In each quiz, he loses points when he gives an incorrect answer. The table shows the points lost for each wrong answer in each quiz and Jake’s total points lost in each quiz. In which quiz did he have more wrong answers?

Find the number of incorrect answers in the winter quiz.

-33 ÷ (-3) = 11

Find the number of incorrect answers Jake gave in the summer quiz.

-56 ÷ (-7) = 8

Compare the numbers of wrong answers.

11 > 8, so Jake had more wrong answers in the winter quiz.

EXAMPLEXAMPLE 2

STEP 1

STEP 2

STEP 3

5. A penalty in Meteor-Mania is -5 seconds. A penalty in Cosmic Calamity is -7 seconds. Yolanda had penalties totaling -25 seconds in a game of Meteor-Mania and -35 seconds in a game of Cosmic Calamity. In which game did Yolanda receive more penalties? Justify your answer.

YOUR TURN

What is the sign of each quotient in Steps 1 and 2? Why does this make sense

for the situation?

Math TalkMathematical Practices

What is the sign of each

Math Talk

7.NS.1.3, 7.NS.1.2

Divide the total points lost by the number of points lost per wrong answer.

Divide the total points lost by the number of points lost per wrong answer.

Both signs are positive, which makes sense because the quotient gives the number of incorrect answers Jake gave.

Yolanda received the same number of penalties in each

game; 5. -25 ÷ (-5) = 5 and -35 ÷ (-7) = 5.

45Lesson 2.2

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Visual CuesPresent the following rules to the students:

Two like signs make a positive sign.

Two unlike signs make a negative sign.

Like Signs Unlike Signs

(+) ÷ (+) = (+) (-) ÷ (+) = (-)

(-) ÷ (-) = (+) (+) ÷ (-) = (-)

Zero divided by any number is zero, and division by zero is undefined.

Critical ThinkingHave students place the correct signs in front of the dividend and the divisor to make the sentence true. Have them list all possible answers.

1. __8 ÷ __8 = -1 +, - or -, +2. __36 ÷ __4 = 9 +, + or -, -3. __ 10 ÷ __2 = -5 +, - or -, +4. __ 63 ÷ __ 7 = 9 +, + or -, -5. __ 12 ÷ __ 4 = -3 +, - or -, +

Additional ResourcesDifferentiated Instruction includes: • Reading Strategies • Success for English Learners ELL

• Reteach • Challenge PRE-AP

DIFFERENTIATE INSTRUCTION

Dividing Integers 46

DO NOT EDIT--Changes must be made through "File info"CorrectionKey=B

Guided Practice

Find each quotient. (Example 1)

1. -14 ____ 2 2. 21 ÷ (-3)

3. 26 ____ -13 4. 0 ÷ (-4)

5. -45 ____ -5 6. -30 ÷ (10)

7. -11 ____ -1 8. -31 ÷ (-31)

9. 0 ___ -7 10. -121 _____ -11

11. 84 ÷ (-7) 12. 500 ____ -25

13. -6 ÷ (0) 14. -63 ____ -21

Write a division expression for each problem. Then find the value of the expression. (Example 2)

15. Clark made four of his truck payments late and was fined four late fees. The total change to his savings from late fees was -$40. How much was one late fee?

16. Jan received -22 points on her exam. She got 11 questions wrong out of 50 questions. How much was Jan penalized for each wrong answer?

17. Allen’s score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How many targets did he miss?

18. Louisa’s savings change by -$9 each time she goes bowling. In all, it changed by -$99 during the summer. How many times did she go bowling in the summer?

19. How is the process of dividing integers similar to the process of multiplying integers?

ESSENTIAL QUESTION CHECK-IN???

-7 -7

9

1

-12

-3

11

11

undefined

0

-20

3

0

-40 ÷ (4) = -10; $10

-75 ÷ (-15) = 5; 5 targets

-22 ÷ (11) = -2; 2 points

-99 ÷ (-9) = 11; 11 times

In both cases, if the signs of the initial numbers are

the same, the answer will be positive. If the signs are

different, the answer will be negative.

-2

Unit 146

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DO NOT EDIT--Changes must be made through “File info”CorrectionKey=B

7_MFLESE056701_U1M02L2.indd 46 08/04/14 7:29 PM

Olympic Trivia Quiz

Winter Quiz

Summer Quiz

-3 points

-7 points

-33 points

-56 points

Points lost foreach wrong answer Total points lost

Math On the Spotmy.hrw.com

Math TrainerOnline Assessment

and Intervention

Personal

my.hrw.com

Using Integer Division to Solve ProblemsYou can use integer division to solve real-world problems. For some problems, you may need to perform more than one step. Be sure to check that the sign of the quotient makes sense for the situation.

Jake answers questions in two different online Olympic trivia quizzes. In each quiz, he loses points when he gives an incorrect answer. The table shows the points lost for each wrong answer in each quiz and Jake’s total points lost in each quiz. In which quiz did he have more wrong answers?

Find the number of incorrect answers in the winter quiz.

-33 ÷ (-3) = 11

Find the number of incorrect answers Jake gave in the summer quiz.

-56 ÷ (-7) = 8

Compare the numbers of wrong answers.

11 > 8, so Jake had more wrong answers in the winter quiz.

EXAMPLEXAMPLE 2

STEP 1

STEP 2

STEP 3

5. A penalty in Meteor-Mania is -5 seconds. A penalty in Cosmic Calamity is -7 seconds. Yolanda had penalties totaling -25 seconds in a game of Meteor-Mania and -35 seconds in a game of Cosmic Calamity. In which game did Yolanda receive more penalties? Justify your answer.

YOUR TURN

What is the sign of each quotient in Steps 1 and 2? Why does this make sense

for the situation?

Math TalkMathematical Practices

What is the sign of each

Math Talk

7.NS.1.3, 7.NS.1.2

Divide the total points lost by the number of points lost per wrong answer.

Divide the total points lost by the number of points lost per wrong answer.

Both signs are positive, which makes sense because the quotient gives the number of incorrect answers Jake gave.

Yolanda received the same number of penalties in each

game; 5. -25 ÷ (-5) = 5 and -35 ÷ (-7) = 5.

45Lesson 2.2

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DO NOT EDIT--Changes must be made through “File info”CorrectionKey=B

7_MFLESE056701_U1M02L2.indd 45 08/04/14 7:29 PM

Visual CuesPresent the following rules to the students:

Two like signs make a positive sign.

Two unlike signs make a negative sign.

Like Signs Unlike Signs

(+) ÷ (+) = (+) (-) ÷ (+) = (-)

(-) ÷ (-) = (+) (+) ÷ (-) = (-)

Zero divided by any number is zero, and division by zero is undefined.

Critical ThinkingHave students place the correct signs in front of the dividend and the divisor to make the sentence true. Have them list all possible answers.

1. __8 ÷ __8 = -1 +, - or -, +2. __36 ÷ __4 = 9 +, + or -, -3. __ 10 ÷ __2 = -5 +, - or -, +4. __ 63 ÷ __ 7 = 9 +, + or -, -5. __ 12 ÷ __ 4 = -3 +, - or -, +

Additional ResourcesDifferentiated Instruction includes: • Reading Strategies • Success for English Learners ELL

• Reteach • Challenge PRE-AP

DIFFERENTIATE INSTRUCTION

Dividing Integers 46

DO NOT EDIT--Changes must be made through "File info"CorrectionKey=B