Prerequisite: Multiply Positive and Negative Integers
Study the example problem showing how to use repeated addition to multiply a positive and a negative integer. Then solve problems 1–6.
1 Complete the table and describe the pattern in the products
2 Rewrite the repeated addition expression as a multiplication expression and fi nd the product
a. (22) 1 (22) 1 (22) 1 (22) 1 (22) 5 • (22) 5
b. (23) 1 (23) 1 (23) 1 (23) 1 (23) 1 (23) 5
c. (25) 1 (25) 1 (25) 5
Example
Dues for the art club are $2 per week Noriko pays $2 each week from her bank account for her art club dues At the end of 5 weeks, what is the change in the amount of money in Noriko’s account?
You can think of this as 5 groups of (22)
5 groups of (22) 5 (22) 1 (22) 1 (22) 1 (22) 1 (22)
3 Write and simplify a multiplication expression for each problem Explain what the product means
a. The temperature dropped 8 degrees every hour What was the change in temperature after 4 hours?
b. Mae loses 3 points for each wrong answer on a test How does her score change if she has 7 wrong answers?
4 Carlo is playing a game with the cards shown He draws cards at random and multiplies the numbers
a. Give an example of two cards Carlo could draw that have a positive product Find the product
b. Give an example of two cards Carlo could draw that have a negative product Find the product
5 Each month Marla pays a $30 cell phone bill from her back account At the end of one year, what is the change in the amount of money in Marla’s account because of her cell phone bill? Write a multiplication equation to represent the problem Explain what the product represents
6 How many integers must be negative for the product of three integers to be negative? Explain Find two diff erent groups of three integers whose product is 212
Show your work.
Solution:
22 0 23 24 8
50
4 3 (28) 5 232; the temperature is 32 degrees colder.
230 • 12 5 2360; Her account balance decreased $360.
7 3 (23) 5 221; her test score drops by 21 points.
Possible answer: 22 3 (23) 5 6
Possible answer: 22 3 8 5 216
Possible work:
22 3 (22) 3 (23) 5 212
6 3 (22) 3 1 5 212
Possible answer: 22, 22, and 23; 6, 22, and 1; Either 1 or 3 of the integers must be
negative for the product to be negative. If all three integers were positive or only two of the
integers were negative, the product would be positive.
3 A pitcher contains 28 fl uid ounces of juice How many 4-ounce servings can you pour before the pitcher is empty? Complete the repeated subtraction to solve
228 5 (24) 1
I can pour four-ounce glasses of juice
4 A small infl atable pool holds 10 gallons of water A tiny leak causes the amount of water in the pool to change by 20 05 gallon each hour until the pool is empty
a Write the numbers that represent each quantity
change in amount of water per hour 5
total change in amount of water 5
b Will you multiply or divide to fi nd how many hours it will take for the pool to be empty? Will the answer be positive or negative?
c How many hours will it take for the pool to be
empty? hours
5 The temperature at 6 PM was 0°F At 10 PM the temperature was 211 2°F Write an expression that you can use to fi nd the average change in temperature per hour during that time Then evaluate the expression
6 Marlene is solving a number puzzle involving three rational numbers a, b, and c Here are her clues:
• The quotient of a and c is 8
• The product of a and c is 2
• The quotient of a and b is 216
• The product of a and b is 21
• The quotient of b and c is 20 5
What are the three numbers in Marlene’s puzzle?
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divide; positive; The quotient of two negative numbers is positive; also, the number of
hours the pool is leaking is a positive number.
211.2 4 4 5 22.8
a 5 24, b 5 0.25, c 5 20.5 or a 5 4, b 5 20.25, c 5 0.5
Study the example problem showing how to divide rational numbers. Then solve problems 1–6.
1 You can also use repeated addition to evaluate the quotient (22 5) 4 (20 5) Complete
22 5 5 (20 5) 1
There are groups of 20 5 in
It will take hours for the submersible’s position to change by 22 5 miles
2 Mariella’s bank statement shows a change of 2$2 50 in her account each week
a. Complete the table to see how many weeks it will be before the change in Mariella’s account is 2$20
Number of Weeks 1 2 3 4 5 6 7 8
Change in Account ($) 22 5 25 0 27 5
b. Why are the amounts in the table negative?
c. How many weeks will it take for the the amount
deducted to total 2$20?
Example
The position of a submersible water vehicle, relative to sea level, changes by 20 5 mile each hour After how many hours will the vehicle’s position have changed by 22 5 miles?
You can use a table to understand the problem
You can also use division to understand the problem
(22 5) 4 (20 5) 5 225 4 (25) 5 5
0
1
2
3
4
5
Time (h) Position
020.5
20.520.5
21.0
21.5
22.0
22.5
20.5
20.5
20.5
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Money is being removed from Mariella’s account, not added to it.
6 Martin chose two of the cards below When he found the
quotient of the numbers, his answer was 2 16 ·· 9 Write the
division problem that Martin solved
23
942 3
82 1225
Show your work.
Solution:
Solve.
4 Craig is making 3 recipes for his party He has a container of fl our on his kitchen scale The table shows the total change in weight of the fl our on the scale after each of the 3 recipes What is the average change in the amount of fl our, in ounces, used in the 3 recipes?
Flour Used After Recipe 1 After Recipe 2 After Recipe 3
Change in Weight (oz) 22 23 1 ·· 2 24 1 ·· 2
A 2 3 ·· 2 C 23 1 ·· 3
B 22 1 ·· 2 D 27 1 ·· 2
5 On the number line, a and b are rational numbers Tell whether each statement is True or False
0b a
a a ? b is negative u True u False
b a 4 b is greater than 0 u True u False
c b 4 a is greater than a 4 b u True u False
d a ? b 5 b ? a u True u False
How can you tell whether a product or quotient is positive or negative?
