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Illustrative Math
Grade 7
Lesson 13: Expressions with Rational Numbers
Let’s develop our signed number sense.
Illustrative Math Unit 7.5, Lesson 13 (printable worksheets)
Lesson 13 Summary
The following diagram shows how to add, subtract, multiply, divide, and evaluate expressions that involve rational numbers.
Lesson 13.1 True or False: Rational Numbers
Decide if each statement is true or false. Be prepared to explain your reasoning.
 (38.76)(15.6) is negative
 10,000  99,999 < 0
 (3/4)(4/3) = 0
 (30)(80)  50 = 50  (30)(80)
Lesson 13.2 Card Sort: The Same But Different
Your teacher will give you a set of cards. Group them into pairs of expressions that have the same value.
Lesson 13.3 Near and Far From Zero
 For each set of values for and , evaluate the given expressions and record your answers in the table.
 When a =  1/2 and b = 6, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
 When a = 1/2 and b = 6, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
 When a = 6 and b = 1/2, which expression:
has the largest value?
has the smallest value?
is the closest to zero?
Are you ready for more?
Are there any values could you use for a and b that would make all of these expressions have the same value? Explain your reasoning.

Show Answer
It is not possible.
Even if we set a = 0 and b = 0, we will still have the problem of dividing by 0.
Lesson 14.3 Seagulls and Sharks Again
A seagull has a vertical position a, and a shark has a vertical position b.
In the applet, you may choose to start by clicking on the open circles on the seagull and shark to drag them to new vertical positions. Once you have them in place, drag each of the other animals to the vertical axis to show its position, determined by the expression next to it.
Open Applet
 A dragonfly at d, where d = b
 A jellyfish at j, where j = 2b
 An eagle at e, where 4e = a.
 A clownfish at c, where c = a/2
 A vulture at v, where v = a + b
 A goose at g, where g = a  b
Lesson 13 Practice Problems
 a. A coffee maker’s directions say to use 2 tablespoons of ground coffee for every 6 ounces of water. How much coffee should you use for 33 ounces of water?
b. A runner is running a 10 km race. It takes her 17.5 minutes to reach the 2.5 km mark. At that rate, how long will it take her to run the whole race?
 The price of an ice cream cone is $3.25, but it costs $3.51 with tax. What is the sales tax rate?
 Find the value of each expression.
a. 22 + 5
b. 22  (5)
c. (22)(5)
d. (22) ÷ 5
 Two students are both working on the same problem: A box of laundry soap has 25% more soap in its new box. The new box holds 2 kg. How much soap did the old box hold?
 Here is how Jada set up her double number line.
 Here is how Lin set up her double number line.
Do you agree with either of them? Explain or show your reasoning.
 The value of x is 1/4. Order these expressions from least to greatest:
 Here are four expressions that have the value 1/2:
Write five expressions: a sum, a difference, a product, a quotient, and one that involves at least two operations that have the value 3/4.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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