Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 2 Lesson 2.3 Multiplying and Dividing Integers to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 2 Lesson 2.3 Answer Key Multiplying and Dividing Integers

### Math in Focus Grade 7 Chapter 2 Lesson 2.3 Guided Practice Answer Key

Lesson Objective

- Multiply and divide integers.

**Hands-On Activity**

Explore Multiplication Rules Using Repeated Addition

Work individually.

You can think of multiplying integers as repeated addition.

Step 1

Use a number line to model and complete the multiplication of integers as repeated addition.

a) Evaluate 3 – 2.

3 • 2 means three groups of 2.

3 • 2 = 2 • 3

= 2 + 2 + 2

= 6

Commutative property of multiplication:

Two or more numbers can be multiplied in any order.

b) Evaluate 3 • (-2).

3 • (- 2) means three groups of -2.

3 • (-2) = (-2) • 3

= -2 + (-2) + (-2)

=

The expression 3 • (-2) can also be written as 3(-2).

The expression (-2) • 3 can also be written as -2(3).

Step 2.

Copy and complete the table using repeated addition.

Answer:

**Math Journal**

Study the pattern in the table from step 2.

a) What do you observe about the sign of the product of two positive integers?

Answer:

I observed the product of two positive integers with ‘ + ‘ sign.

b) What do you observe about the sign of the product of a positive and a negative integer?

Answer:

I observed the product of a positive and a negative integer with ‘ – ‘ sign.

Step 3.

Use a number line to model and complete the multiplication as addition of the opposite.

a) Evaluate -3 • 2.

You can say that -3 • 2 is the opposite of three groups of 2, 6.

-3 • 2 = -(3)(2)

=

Answer:

I can say that -3 • 2 is the opposite of three groups of 2, 6.

-3 • 2 = -(3)(2)

b) Evaluate -3 • (-2).

You can say that -3 • (-2) is the opposite of three groups of -2, -6.

-3 • (-2) = -(3)(-2)

= -()

=

Answer:

I can say that -3 • (-2) is the opposite of three groups of -2, -6.

-3 • (-2) = -(3)(-2)

-()

Step 4.

Copy and complete the table using addition of the opposite and your results from Step 2.

Answer:

Math Journal Based on your observations in Step 1 to Step 4,

a) What do you observe about the sign of the product of two integers with the same sign?

Answer:

I observed the product of two integers with the same sign results ‘ + ‘ sign.

b) What do you observe about the sign of the product of a positive integer and a negative integer? of integers with different signs?

Answer:

I observed the product of a positive integer and a negative integer with ‘ – ‘ sign.

**Evaluate each product.**

Question 1.

9(-8)

Answer:

9(-8) = **– 72**

Explanation:

Perform multiplication operation on above two numbers. Multiply 9 with -8 the product is -72. The product of a positive integer and a negative integer is represented with ‘ – ‘ sign.

Question 2.

-7 • (-5)

Answer:

-7 • (-5) = -(7)(-5) = -(-35) =** 35
**Explanation:

Explanation:

Perform multiplication operation on above two numbers. Multiply -7 with -5 the product is 35. The product of two integers with the same sign results ‘ + ‘ sign.

Question 3.

3(-4)(6)

Answer:

3(-4)(6) = (-12)(6) = **-72**

Explanation:

Perform multiplication operation on above three numbers. First multiply 3 with -4 the product is -12. Next multiply -12 with 6 the product is -72. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

**Think Math**

Will the product of three negative numbers be positive or negative? What about the product of four negative numbers? Explain your answers.

Answer:

The product of three negative numbers is **negative**.

The product of four negative numbers is **positive**.

Explanation:

Odd numbers of negative integers will have a negative product. Even numbers of negative integers will have a positive product.

**Solve.**

Question 4.

In a regional golf championship, Steven plays four rounds. The score for a round is recorded as positive (over par) or negative (under par). If Steven scores 6 points under par for all four rounds, what is his total score for his game?

• (-6) =

His score is points.

Answer:

**4** • (-6) = **-24**

His total score is -24 points.

Explanation:

In a regional golf championship, Steven plays four rounds. It is represented with the number 4. Steven scores 6 points under par for all four rounds. Here under par is represented with ‘-‘ sign. 6 points is represented with -6. Multiply 4 with -6 the product is -24. His total score is -24 points.

Question 5.

The price of a stock falls $2 each day for 9 days. Find the total change in the price of the stock during this time.

Answer:

**$2 • 9 = $18**

The price of a stock falls by **$18**.

Explanation:

The price of a stock falls $2 each day for 9 days. Multiply $2 with 9 the product is $18. The total change in the price of the stock during this time falls by $18.

**Evaluate each quotient.**

Question 6.

-36 ÷ (-4)

Answer:

-36 ÷ (-4) = 9

The quotient is **9**.

Explanation:

Perform division operation on above two numbers. Divide -36 by -4 the quotient is 9. Even numbers of negative integers will have a positive quotient.

Question 7.

-35 ÷ 5

Answer:

-35 ÷ 5 = -7

The quotient is **-7**.

Explanation:

Perform division operation on above two numbers. Divide -35 by 5 the quotient is -7. Odd numbers of negative integers will have a negative quotient.

Question 8.

45 ÷ (-3)

Answer:

45 ÷ (-3) = **-15**

The quotient is -15.

Explanation:

Perform division operation on above two numbers. Divide 45 by -3the quotient is -15 Odd numbers of negative integers will have a negative quotient.

**Solve.**

Question 9.

Find the change in elevation per minute of a hiker who descended 320 feet in 40 minutes.

Answer:

**-320 ÷ 40 = -8 feet/min
**Explanation:

**A hiker who descended 320 feet in 40 minutes is represented with -320 feet in 40 minutes. The change in elevation per minute of a hiker who descended 320 feet in 40 minutes is -8 feet/min.**

### Math in Focus Course 2A Practice 2.3 Answer Key

**Evaluate each product.**

Question 1.

5 • (-7)

Answer:

5 • (-7) = **-35**

Explanation:

Perform multiplication operation on above two numbers. Multiply 5 with -7 the product is -35. The product of a positive integer and a negative integer is represented with ‘ – ‘ sign.

Question 2.

12 • (-9)

Answer:

12 • (-9) = **-108**

Explanation:

Perform multiplication operation on above two numbers. Multiply 12 with -9 the product is -108. The product of a positive integer and a negative integer is represented with ‘ – ‘ sign.

Question 3.

-6 • 8

Answer:

-6 • 8 = **-48**

Explanation:

Perform multiplication operation on above two numbers. Multiply -6 with 8 the product is -48. The product of a negative integer and a positive integer is represented with ‘ – ‘ sign.

Question 4.

-3 • 15

Answer:

-3 • 15 = **-45**

Explanation:

Perform multiplication operation on above two numbers. Multiply -3 with 15 the product is -45. The product of a negative integer and a positive integer is represented with ‘ – ‘ sign.

Question 5.

-4 • (-12)

Answer:

-4 • (-12) = -(4) • (-12) = -(-48) = **48**

Explanation:

Perform multiplication operation on above two numbers. Multiply -4 with -12 the product is 48. The product of two integers with the same sign results ‘ + ‘ sign.

Question 6.

-8 • (-20)

Answer:

-8 • (-20) = -(8) • (-20) = -(-160) = **160**

Explanation:

Perform multiplication operation on above two numbers. Multiply -8 with -20 the product is 160. The product of two integers with the same sign results ‘ + ‘ sign.

Question 7.

-14 . 0

Answer:

-14 • 0 = **0**

Explanation:

Perform multiplication operation on above two numbers. Multiply -14 with 0 the product is 0.

Question 8.

0 • (-50)

Answer:

0 • (-50) = **0**

Explanation:

Perform multiplication operation on above two numbers. Multiply 0 with -50 the product is 0.

Question 9.

-3 • 12 • 7

Answer:

-3 • 12 • 7= (-36)• 7 = **-252**

Explanation:

Perform multiplication operation on above three numbers. First multiply -3 with 12 the product is -36. Next multiply -36 with 7 the product is -252. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

Question 10.

8 • (-4) • 2

Answer:

8 • (-4) • 2= (-32)• 2 = **-64**

Explanation:

Perform multiplication operation on above three numbers. First multiply 8 with -4 the product is -32. Next multiply -32 with 2 the product is -64. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

Question 11.

20 • 5 • (-5)

Answer:

20 • 5 • (-5) = 100 • (-5)= **-500**

Explanation:

Perform multiplication operation on above three numbers. First multiply 20 with 5 the product is 100. Next multiply 100 with -5 the product is -500. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

Question 12.

-4 • 10 • (-6)

Answer:

-4 • 10 • (-6) = -40 • (-6) = **240**

Explanation:

Perform multiplication operation on above three numbers. First multiply -4 with 10 the product is -40. Next multiply -40 with -6 the product is -240. The product of a two negative integers and a positive integer is represented with ‘ + ‘ sign.

Question 13.

-7 • (-2) • 10

Answer:

-7 • (-2) • 10 = 14 • 10 = **140**

Explanation:

Perform multiplication operation on above three numbers. First multiply -7 with -2 the product is 14. Next multiply 14 with 10 the product is 140. The product of a two negative integers and a positive integer is represented with ‘ + ‘ sign.

Question 14.

9 • (-6) • (-4)

Answer:

9 • (-6) • (-4) = (-54) • (-4) = **216**

Explanation:

Perform multiplication operation on above three numbers. First multiply 9 with -6 the product is -54. Next multiply -54 with -4 the product is 216. The product of a two negative integers and a positive integer is represented with ‘ + ‘ sign.

Question 15.

-2 • (-8) • (-7)

Answer:

-2 • (-8) • (-7) = 16 • (-7) = **-112**

Explanation:

Perform multiplication operation on above three numbers. First multiply -2 with -8 the product is -16. Next multiply 16 with -7 the product is -112. The product of a three negative integers is represented with ‘ – ‘ sign.

Question 16.

-5 • (-12) • (-3)

Answer:

-5 • (-12) • (-3) = 60 • (-3) = **-180**

Explanation:

Perform multiplication operation on above three numbers. First multiply -5 with -12 the product is 60. Next multiply 60 with -3 the product is -180. The product of a three negative integers is represented with ‘ – ‘ sign.

Question 17.

14 • 0 • (-15)

Answer:

14 • 0 • (-15) = 0 • (-15) = **0**

Explanation:

Perform multiplication operation on above three numbers. First multiply 14 with 0 the product is 0. Next multiply 0 with -15 the product is 0.

Question 18.

-30 • (-2) • 0

Answer:

-30 • (-2) • 0 = 60 • 0 = **0**

Explanation:

Perform multiplication operation on above three numbers. First multiply -30 with -2 the product is 60. Next multiply 60 with 0 the product is 0.

Question 19.

-6 • (-7) • 2 • 5

Answer:

-6 • (-7) • 2 • 5

= 42 • 2 • 5

= 84 • 5

= **420 **

Explanation:

Perform multiplication operation on above three numbers.

First multiply -6 with -7 the product is 42.

Next multiply 42 with 2 the product is 84.

Multiply the obtained product 84 with 5 the product is 420.

The product of a two negative integers and two positive integer is represented with ‘ + ‘ sign.

Question 20.

-8 • (-2) • (-4) • 12

Answer:

-8 • (-2) • (-4) • 12

= 16 • (-4) • 12

= -64 • 12

= **-768
**Explanation:

Perform multiplication operation on above three numbers.

First multiply -8 with -2 the product is 16.

Next multiply 16 with 4 the product is -64.

Multiply the above product -64 with 12 the product is -768.

The product of a three negative integers and a positive integer is represented with ‘ – ‘ sign.

Question 21.

-9 • (-5) • (-4) • (-3)

Answer:

-9 • (-5) • (-4) • (-3)

= 45 • (-4) • (-3)

= -180 • (-3)

= **540**

Explanation:

Perform multiplication operation on above three numbers.

First multiply -9 with -5 the product is 45.

Next multiply 45 with -4 the product is -180.

Multiply the above product -180 with -3 the product is 540.

Even numbers of negative integers will have a positive product.

**Evaluate each quotient.**

Question 22.

125 ÷ (-25)

Answer:

125 ÷ (-25) = -5

The quotient is **-5**.

Explanation:

Perform division operation on above two numbers. Divide 125 by -25 the quotient is -5. Odd numbers of negative integers will have negative quotient.

Question 23.

300 ÷ (-15)

Answer:

300 ÷ (-15) = -20

The quotient is **-20**.

Explanation:

Perform division operation on above two numbers. Divide 300 by -15 the quotient is -20. Odd numbers of negative integers will have negative quotient.

Question 24.

-100 ÷ 25

Answer:

-100 ÷ 25 = **-4**

Explanation:

Perform division operation on above two numbers. Divide -100 by 25 the quotient is -4. Odd numbers of negative integers will have negative quotient.

Question 25.

-32 ÷ 4

Answer:

-32 ÷ 4 = **-8**

Explanation:

Perform division operation on above two numbers. Divide -32 by 4 the quotient is -8. Odd numbers of negative integers will have negative quotient.

Question 26.

-480 ÷ (-12)

Answer:

-480 ÷ (-12) = **40**

Explanation:

Perform division operation on above two numbers. Divide -480 by -12 the quotient is 40. Even numbers of negative integers will have positive quotient.

Question 27.

-144 ÷ (-24)

Answer:

-144 ÷ (-24) = **6**

Explanation:

Perform division operation on above two numbers. Divide -144 by -24 the quotient is 6. Even numbers of negative integers will have positive quotient.

Question 28.

0 ÷ (-8)

Answer:

0 ÷ (-8) = **0**

Explanation:

Perform division operation on above two numbers. Divide 0 by -8 the quotient is 0.

Question 29.

0 ÷ (-111)

Answer:

0 ÷ (-111) = **0**

Explanation:

Perform division operation on above two numbers. Divide 0 by -111 the quotient is 0.

**Solve. Show your work.**

Question 30.

While returning to the glider port, Laura descended at minute for 3 minutes. Calculate her change in altitude.

Answer:

Question 31.

A scuba diver took 6 minutes to rise to the surface at a minute. How far was he below sea level?

Answer:

Question 32.

An elevator descends 1,500 feet in 60 seconds. Find the change in height per second.

Answer:

**1,500 ÷ 60 = 25 feet/sec
**Explanation:

An elevator descends 1,500 feet in 60 seconds. Here descends represented with negative sign. The change in height per second is -25 feet/sec

Question 33.

A scientist measures the change in height per second of a diving osprey as -198 feet per second. Find the change in position of the osprey after 2 seconds.

Answer:

The change in height per second of a diving osprey as -198 feet per second.

1 sec = -198 feet

2 sec = ?

-198 • 2 = -396 feet

The change in position of the osprey after 2 seconds is -396 feet.

Question 34.

**Math Journal**

Margaret wrote -25 ÷ (-100) = \(\frac{-25}{-100}\) = –\(\left(\frac{1}{4}\right)\) and

-2 • (-2) = -4. Discuss and correct her mistakes.

Answer:

-25 ÷ (-100) =** 1/4**

Perform division operation on above two numbers. Divide -25 by -100 the quotient is 1/4. Even numbers of negative integers will have positive quotient.

-2 • (-2) = **4**

Perform multiplication operation on above two numbers. Multiply -2 with -2 the product is 4. The product of two integers with the same sign results ‘ + ‘ sign.

Question 35.

**Math Journal** Umberto has trouble solving -12 ÷ 3 • 2 ÷ (-4). Write an explanation to help him.

Answer:

To evaluate -12 ÷ 3 • 2 ÷ (-4)

Umberto can do it from left to right. Perform any two operations at one time, and use the rules for sign multiplication and division.

-12 ÷ 3 • 2 ÷ (-4)

= -4 • 2 ÷ (-4)

= -8 ÷ (-4)

= **2**