AnswersCommon Core Math 7 A-ICUsing Properties of Operations

Using Properties of Operations Answers

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Carlos is using the distributive property to evaluate the expression by using friendlier numbers. His work is shown below.Carlos’s Work Step 1Step 2Step 3Step 4569What was the first error that Carlos made?

Question illustration
A
Step 1 should have been 14(7 + 7).
B
Step 2 should have been 14(40) + 14(9).
C
Step 3 should have been 23(40).
D
Step 4 should have been 5,040.
2
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Morgan rewrote the expression as . How will this change the work that is needed to evaluate the expression?

Question illustration
A
4.8 is now multiplied by 90 and 10.
B
4.8 is now added to 10 before adding 90.
C
4.8 is now added after finding the sum of 90 and 10.
D
4.8 is now added to both 90 and 10.
3

Liz is using the distributive property to evaluate the expression by using friendlier numbers. Her work is shown below.Liz’s Work 27(36)Step 1 Step 2Step 3 Step 4405What was the first error that Liz made?

Question illustration
A
Step 1 should have been 27(6 + 30).
B
Step 2 should have been 27(3) + 12.
C
Step 3 should have been 27(30)(12).
D
Step 4 should have been 16,244.
4

What is the value of ?

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A
287
B
395
C
387
D
540
5

What is the value of ?

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A
105
B
204
C
357
D
864
6

What is the value of ?

Question illustration
A
11
B
14
C
17
D
19
7

Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel?

A
The numbers can be added in any order.
B
The number 45 must be the first addend, and 35 must be the last addend.
C
The numbers must be added in the order 45, 90, 70, 20, and 35.
D
The numbers must be added in either the order 45, 90, 70, 20, and 35 or the order 35, 20, 70, 90, and 45.
8

Which statement is true about the expression ?

Question illustration
A
The expression is equivalent to because of the associative property.
Option A
B
The expression is equivalent to because of the associative property.
Option B
C
The expression is equivalent to because of the commutative property.
Option C
D
The expression is equivalent to because of the commutative property.
Option D
9

Madison and Tyler each wrote an expression that is equivalent to . The expressions they created are shown in the table.Expressions Madison and Tyler CreatedStudentExpressionMadisonTylerWhich statement is true?

Question illustration
A
Madison used the associative property.
B
Madison used the distributive property.
C
Tyler used the associative property.
D
Tyler used the distributive property.
10

The figure below shows the route that Maya traveled home from the library this afternoon.Maya wrote the expression to represent the total distance that she traveled. Which statement best describes Maya’s expression?

Question illustration
A
Maya’s expression will generate the correct sum because of the associative property.
B
Maya’s expression will generate the correct sum because of the commutative property.
C
Maya’s expression will generate the wrong sum because she violated the associative property.
D
Maya’s expression will generate the wrong sum because she violated the commutative property.

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