Multiplying and Dividing Integers
Know your Signs!
Practice A
Write the correct integer sign for each modeled product or quotient.
1)
+ × − =
2)
(−) ÷ (−) =
3)
(+) ÷ (+) =
4)
(−) × (+) =
5)
+ ÷ − =
6)
(−) × (−) =
7)
(−) ÷ (+) × (+) =
8)
(+) × (−) ÷ (−) ÷ (+) =
9)
− × − × − =
10)
(+) ÷ (−) ÷ (−) ÷ (+) × (−) × (−) =
Write an integer sign combination that will produce the sign of each product or quotient.
11)
÷
=+
12)
×
=−
13)
÷
=−
14)
×
÷
=−
15)
÷
×
=+
Answer the following questions.
16) How would you best describe the set of numbers called integers?
_______________________________________________________________________________ ________________________________________________________________________________
© Mike’s Math Mall 3
17) If you have to multiply or divide more than two integers, how can you determine the sign of your answer before you actually multiply or divide?
_______________________________________________________________________________ ________________________________________________________________________________
Multiplying Integers
Practice B
2) −9 × 4The signs are ____________________
The product will be ____________________ 1) 11 × 8
The signs are ____________________
The product will be ____________________
like
positive
3) −15 × (−7)The signs are ____________________
The product will be ____________________
4) 3 × (−20)
The signs are ____________________
The product will be ____________________
5) −2 × 5 =_________ 6) −7 ∙ −3 =_________ 7) 4 × −4 =_________ 8) −8 × 0 =_________ 9) −6 −1 =_________ 10) −9 ∙ 3 =_________ 11) −5 11 =_________ 12) 15 −3 =_________ 13) −10 × (−10)_________ 14) −4 × −5 × −2 =_________ 15) 8 × −2 × 1 × −2 =_________ 16) −1 −4 −2 −1 −5 −4 =_________ 17) −10 × −3 × 2 × −10 × −1 × −4 =____________ Multiply.
18) The temperature dropped 4°Fdegrees each hour for 9 straight hours. •Write a multiplication problem using integers to show the total drop in
temperature. Simplify and label your answer.
________________________________________________________________________
Brrrrrr…
Dividing Integers
Practice C
2) 12 ÷ (−3)The signs are ____________________
The quotient will be ___________________ 1) 16 ÷ 4
The signs are ____________________
The quotient will be ___________________
positive
3) −36 ÷ 6The signs are ____________________
The quotient will be ___________________
4) −45 ÷ (−5)
The signs are ____________________
The quotient will be ___________________
5) −24 ÷ 4 =_________ 6) −9 ÷ −3 =_________ 7) 16 ÷ −8 = _________ 8) −20 −4
=
_________ 9) 54 ÷ 6 = _________ 10) −14 14=
_________ 11) 63 ÷ −7 =_________ 12) 18 −1=
_________ 13) 0 ÷ (−10) _________ 14) −24 ÷ 3 ÷ −2 =_________ 15) 48 ÷ −2 ÷ 6 ÷ −4 =_________ 16) −100 ÷ −2 ÷ 2 ÷ 1 ÷ −5 =_________ 17) −148 −4=
________ Divide.© Mike’s Math Mall
18) A scuba diver collected water samples down to 35 feet below the surface. If he took samples every 5 feet below the surface, how many water samples did he take?
•Write a division problem using integers to show the number of samples taken. Simplify and label your answer.
________________________________________________________________________
5
Tell if the signs are “like” or “unlike” and if the result will be positive or negative.
Puzzler – Multiplying and Dividing Integers
Practice D
1) −7 × 2 2) 49 −7 3) 8 ∙ −5 4) −12 ÷ (−4) ____________ ____________ ____________ ______________ __ __ __ __ __ __ __ __ __ __
__ __ __ __ __ __ __ __ __
__ __ __ __ __ __ __ __ __ __ __ __
What’s the most important piece of information learned from this lesson?
2
Code Bank
40= D 69= O −14= F −3= T −4= S 27= A 3= H −2= N −64= R
−36= I 4= K 7= B −40= V 36= Y 64= L 2= E −7= P −120= C
Multiply or divide the following integers to help you decode the puzzle below. Number one has been completed for you.
11
7
16
11
14
18
1
6
15
17
4
17
15
13
18
14
9
10
17
3
16
13
F
8
18
10
18
5
16
12
18 13
–14 5) −27 9 6) −4 × (−10) 7) 3 × (−12) 8) −35 ÷ −5 ____________ ____________ ____________ ____________ 9) −3 ∙ (−3) ∙ 4 10) 48 ÷ (−6) ∙ (−8) 11) −5 × 10 ÷ 25 12) −64 ÷ 8 ÷ (−2) ____________ ____________ ____________ ____________ 13) 2 ∙ −22 ÷ 11 14) 128 −2 15) 100 ÷ 5 ∙ (−6) 16) −2 ∙ −8 ∙ −2 ÷ (−16) ____________ _____________ ____________ ____________ 17) 3 ∙ −10 ÷ 5 ÷ (−2) ∙ 23 18) −9 ∙ (9) ÷ 3 ÷ −3 ÷ 9 ∙ (−9) ∙ (−3) ____________ ____________ © M ike’s M ath M allGetting Real with
Multiplying and Dividing Integers
Practice E
1) A football team lost 9 yards on three consecutive plays. What was the teams total change in position after the three plays?
2) On a certain day, the temperature changed at a rate of −3°𝐹per hour. How long did it take for the change in temperature to reach −21°𝐹?
4) The water level in a well decreased by 6 inches every month due to evaporation. What is the change in the water level after a six month period of time?
3) The length of an island is eroding at the rate of −12inches per year. How many years will it take for the change in the length of the island to be −144inches?
Write a multiplication or division of integers expression for each of the following word problems. Simplify each expression and label all answers!
5) A hiker was climbing down a mountain at a rate of 400 feet per hour. After 8 hours, what is the hiker’s change in elevation?
6) The population of a town is decreasing by a rate of −9people per year. At this rate, how many years will it take the population change to be −225people?
Multiplying and Dividing Integers
Assessment
1) T or F The set of numbers known as integers contain only negative whole numbers. 2) T or F When you multiply or divide several integers in an expression, you should do sofrom left to right.
3) T or F Dividing one negative number by another negative number will give you a negative quotient.
4) T or F A fraction is really a division expression where you can divide the numerator by the denominator.
5) T or F The following expression will produce a negative answer: −7 × 1 × (−9) ÷ (−7)
Fill in the blanks. Use the words “positive” or “negative” to correctly complete each sentence.
6) Multiplying a positive integer by a negative integer will create a ________________________ product.
7) Dividing a negative integer by a negative integer will produce a ________________________ quotient.
8) Multiplying a negative integer by a positive integer and then dividing by a negative integer will result in a ________________________ answer.
9) Multiplying two integers with opposite signs will always result in a ________________________ answer.
10) Dividing two integers with like signs will always result in a ________________________ answer.
11) Look at the following expression:
−35 ÷ 7 × (−5) ÷ −5 × 12 × −1 ÷ 3
Explain how you can determine whether the sign of the answer to this expression will be positive or negative without actually simplifying the expression.
________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ Short answer.
Multiply and/or divide. 12) −20 ÷ (−5) =__________ 13) 0 × −8 = __________ 14) 6 × −5 =__________ 15) 26 2
=
__________ 16) −77 ÷ (−7) =__________ 17) −7 ∙ 8 = __________ 18) 24 −3=
__________ 19) 60 × (−3) = __________ 20) −9 ÷ (−9)_________ 21) −30 ÷ 3 ÷ −2 =__________ 22) 8 × −2 ÷ 4 × 7 =_________ 23) −120 ÷ −3 ÷ 2 × 3 ÷ −5 =__________Write a multiplication or division of integers expression for each of the following word problems. Simplify each expression and label all answers!
24) The height of an ice sculpture was decreasing by −11millimeters every hour. How long will it take the ice sculpture to show a change in height of −88millimeters?
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25) Ellie withdrew $15 from her bank account every week for 9 straight weeks? What integer shows the total amount of money withdrawn after the nine weeks?
__________________________________________________________________
Rules for Multiplying and Dividing Integers
Multiplying Integers
+ × + = +
− × − = +
+ × − = −
− × + = −
Dividing Integers
+ ÷ + = +
− ÷ − = +
+ ÷ − = −
− ÷ + = −
Notice! The rules for multiplying and dividing integers are exactly the same!
Remember!
When multiplying or dividing two integers with like
signs,
answers will always be positive.
a)
16 ÷ 4 = 4
b)
−7 × (−10) = 70
c)
−36 ÷ (−6) = 6
When multiplying or dividing two integers with
unlike
signs,
answers will always be
negative
.
d)
8 × (−8) = −64
e)
−24 ÷ 6 = −4
f)
−20 × 5 = −100
Something Else to Think About!
If there are an evennumber of negative signs in an expression, the answer will always be positive.
−2 × −4 × 1 × −5 × 3 ÷ −2 = 60
(4 negative signs = positive answer)
If there are an odd number of negative signs in an expression, the answer will always be negative.
