Which property is illustrated by the following (9 + 1) + 4 = 9 + (1 + 4)

Associative Property of Addition

Commutative Property of Addition

Properties Of Algebra

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| By Ahumphreys

Ahumphreys

Community Contributor

Quizzes Created: 1 | Total Attempts: 1,609

Questions: 8 | Attempts: 1,610 | Updated: Oct 3, 2023

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This quiz is a review of the properties we have studied this year.

Questions and Answers

1.

The commutative property works with subtraction.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The commutative property states that the order of the numbers does not affect the result of addition or multiplication. However, it does not hold true for subtraction. The order of the numbers does affect the result of subtraction. For example, 5 - 3 is not the same as 3 - 5. Therefore, the statement "The commutative property works with subtraction" is false.

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2.

Which property is illustrated by the following (9 + 1) + 4 = 9 + (1 + 4)
- A.
  
  Distributive Property
- B.
  
  Commutative Property of Addition
- C.
  
  Associative Property of Addition
- D.
  
  Identity of Addition
Correct Answer
C. Associative Property of Addition

Explanation
The given equation (9 + 1) + 4 = 9 + (1 + 4) demonstrates the Associative Property of Addition. This property states that the grouping of numbers being added does not affect the sum. In the equation, the numbers are grouped differently on both sides of the equation, but the sum remains the same. This illustrates the associative property, as the grouping of numbers can be changed without changing the result.

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2
0
3.

Which of the following operations can be associative?
- A.
  
  Division
- B.
  
  Addition
- C.
  
  Subtraction
- D.
  
  Multiplication
Correct Answer(s)
B. Addition
D. Multiplication

Explanation
Addition and multiplication can be associative operations. This means that the order in which the operations are performed does not affect the result. For example, (2 + 3) + 4 is equal to 2 + (3 + 4), and (2 * 3) * 4 is equal to 2 * (3 * 4). However, division and subtraction are not associative operations. The order in which these operations are performed does affect the result. Therefore, the correct answer is addition and multiplication.

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1
0
4.

What is another word for inverse?
- A.
  
  Random
- B.
  
  Absolute value
- C.
  
  Opposite
Correct Answer
C. Opposite

Explanation
Another word for inverse is opposite.

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1
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5.

The following is an example of the associative property of addition: 7 + (3 +4) = (4 + 7) + 3
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The statement "7 + (3 + 4) = (4 + 7) + 3" is true and demonstrates the associative property of addition. This property states that you can group numbers in an addition operation differently, and the result will remain the same. In this case, you can change the grouping of the numbers and still get the same sum on both sides of the equation.

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2
4
6.

Which of the following is an example of the identity property of multiplication:
- A.
  
  7 + 1 = 8
- B.
  
  7 x 1 = 7
- C.
  
  7 + 0 = 7
- D.
  
  7 - 0 = 7
Correct Answer
B. 7 x 1 = 7

Explanation
The identity property of multiplication states that any number multiplied by 1 equals the original number. In the given options, the only example that demonstrates this property is 7 x 1 = 7.

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0
1
7.

Apply the distributive property to the following expression: 2(9 + 4)
- A.
  
  2 x 13
- B.
  
  2 x 9 + 2 x 4
- C.
  
  2 +9 x 2 + 4
- D.
  
  9 x 4 x 2
Correct Answer
B. 2 x 9 + 2 x 4

Explanation
The expression "2(9 + 4)" can be simplified by applying the distributive property. The distributive property states that when a number is multiplied by a sum, it can be distributed to each term within the parentheses. In this case, the number 2 can be distributed to both 9 and 4. Therefore, the expression simplifies to "2 x 9 + 2 x 4". This can be further simplified to "18 + 8", which equals 26.

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8.

Which of the following are NOT the commutative property?
- A.
  
  6 x 7 = 7 x 6
- B.
  
  4 + 9 + 3 = (4 + 9) + 3
- C.
  
  8/3 x 3/8 = 1
Correct Answer(s)
B. 4 + 9 + 3 = (4 + 9) + 3
C. 8/3 x 3/8 = 1

Explanation
The commutative property states that the order of the numbers does not affect the result of addition or multiplication. In the given options, both 6 x 7 = 7 x 6 and 8/3 x 3/8 = 1 satisfy the commutative property because the order of the numbers is switched without changing the result. However, 4 + 9 + 3 = (4 + 9) + 3 does not satisfy the commutative property because changing the grouping of the numbers changes the result of the addition. Thus, 4 + 9 + 3 = (4 + 9) + 3 is NOT the commutative property.

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Current Version
Oct 03, 2023

Quiz Edited by
ProProfs Editorial Team
Oct 13, 2011

Quiz Created by
Ahumphreys

Properties Of Algebra

The commutative property works with subtraction.

Which property is illustrated by the following (9 + 1) + 4 = 9 + (1 + 4)

Which of the following operations can be associative?

What is another word for inverse?

The following is an example of the associative property of addition: 7 + (3 +4) = (4 + 7) + 3

Which of the following is an example of the identity property of multiplication:

Apply the distributive property to the following expression: 2(9 + 4)

Which of the following are NOT the commutative property?