This document contains notes and exercises on writing and evaluating expressions involving multiplication and division from real-world problems. It includes 4 practice problems with multiple parts each that have students write expressions, evaluate them for given values, and identify differences between parts that involve multiplication versus division. The problems cover topics like number of bags of apples based on number of apples, money returned from recycling cans based on number of cans, cost of subway rides based on number of rides, and time for a pendulum to complete a number of cycles. The document aims to help students develop expressions and evaluate them in applied math contexts.

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Problem Set Lesson 19 Answers

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MODULE 4 Expressions and Equations
Topic F: Writing and Evaluating Expressions and Formulas
Lesson 20: Writing and Evaluating Expressions—
Multiplication and Division
Student Outcomes
§ Students develop expressions involving multiplication and division from real‐world problems.
§ Students evaluate these expressions for given values.

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Classwork
Exercises
1. The farmers’ market is selling bags of apples. In every bag, there are 3 apples.
a. Complete the table.

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b. What if the market had 25 bags of apples to sell?
How many apples is that in all?
c. If a truck arrived that had some number, a , more apples on it, then how many
bags would the clerks use to bag up the apples?
d. If a truck arrived that had 600 more apples on it, how many bags would the clerks
use to bag up the apples?

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e. How is part (d) different from part (b)?
Part (d) gives the number of apples and asks for the number of
bags. Therefore, we needed to divide the number of apples by 3.
Part (b) gives the number of bags and asks for the number of
apples. Therefore, we needed to multiply the number of bags by
3.

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2. In New York State, there is a five‐cent deposit on all carbonated beverage cans and
bottles. When you return the empty can or bottle, you get the five cents back.
a. Complete the table.

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b. If we let C represent the number of cans, what is the expression that
shows how much money is returned?
c. Use the expression to find out how much money Brett would
receive if he returned 222 cans.
d. If Gavin needs to earn $4.50 for returning cans, how many cans does
he need to collect and return?

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Part (d) gives the amount of money and asks for the
number of cans. Therefore, we needed to divide the
amount of money b 0.05. Part (c) gives the number
of cans and asks for the amount of money. Therefore,
we needed to multiply the number of cans by 0.05.
e. How is part (d) different from part (c)?

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3. The fare for a subway or a local bus ride is $2.50.
a. Complete the table.

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b. If we let R represent the number of rides, what is the expression
that shows the cost of the rides?
c. Use the expression to find out how much money 60 rides would
cost.
d. If a commuter spends $175.00 on subway or bus rides, how many trips did the
commuter take?

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Part (d) gives the amount of money and asks for the
number of rides. Therefore, we needed to divide the
amount of money by the cost of each ride ($2.50). Part (c)
gives the number of rides and asks for the amount of
money. Therefore, we needed to multiply the number of
rides by $2.50.
e. How is part (d) different from part (c)?

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4. A pendulum swings though a certain number of cycles in a given time. Owen
made a pendulum that swings 12 times every 15 seconds.
a. Construct a table showing the number of cycles through which a pendulum
swings. Include data for up to one minute. Use the last row for C cycles, and write
an expression for the time it takes for the pendulum to make C cycles.

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b. Owen and his pendulum team set their pendulum in motion
and counted 16 cycles. What was the elapsed time?
c. Write an expression for the number of cycles a pendulum swings in S seconds.
d. In a different experiment, Owen and his pendulum team counted the cycles of
the pendulum for 35 seconds. How many cycles did they count?

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Closing
Please take out your exit ticket for Lesson 20, close your
binder, and complete the exit ticket. This will be collected.

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