Pre-Algebra : Identities and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

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Example Question #1 : Identities And Properties

What property can be applied to the following expression?

Possible Answers:

Additive Inverse

Associative of Addition

Commutative of Multiplication

Commutative of Addition

Additive Identity

Correct answer:

Commutative of Addition

Explanation:

The rule for Commutative Property of Addition is 

Expression given in the question is: 

Hence the property is Commutative of Addition.

Example Question #1 : Identities And Properties

Identify the property being applied.

Possible Answers:

Additive Property of Addition

Associative Property of Addition

Associative Inverse Property

Order of Operations

Communitive Property of Addition

Correct answer:

Communitive Property of Addition

Explanation:

Correct Answer: Communitive Property of Addition

This property states that any set of terms can be added together in any order to achieve the same solution.

Example Question #3 : Commutative Property Of Addition

Which of the following statements demonstrates the commutative property of addition?

Possible Answers:

None of the examples in the other responses demonstrates the commutative property of addition.

Correct answer:

Explanation:

The commutative property of addition states that two numbers can be added in either order to obtain the same sum. Of the given responses, only

demonstrates this property, so it is the correct choice.

Example Question #4 : Commutative Property Of Addition

Which of the following best represents the commutative property of addition?

Possible Answers:

Correct answer:

Explanation:

The property is defined as:

Switching the order of the numbers and adding the numbers will yield the same result.

The only answer is:  

Example Question #5 : Commutative Property Of Addition

Which of the following choices best represent the commutative property of addition?

Possible Answers:

Correct answer:

Explanation:

Write the rule for the commutative property of addition, letting  and  be any number.

Changing the order of these two numbers will not affect the final answer.

The best choice is:  

Example Question #1 : Commutative Property Of Multiplication

Which property is illustrated by the example:

Possible Answers:

Multiplicative identity property

Commutative property of multiplication

Associative property of multiplication

Distributive property

Correct answer:

Commutative property of multiplication

Explanation:

The commutative property of mulitplication states that the order in which 2 numbers are multiplied does not affect the result:

Or in this case,

 

 

Example Question #1 : Commutative Property Of Multiplication

Use the Commutative Property of Multiplication to write the below expression in a different way.

Possible Answers:

Correct answer:

Explanation:

The rule for Commutative Property of Multiplication is 

Using this rule, the expression  can be written as 

Example Question #3 : Commutative Property Of Multiplication

Which of the following equations correctly shows the commutative property of multiplication?

Possible Answers:

Correct answer:

Explanation:

The commutative property states that factors can be multiplied in any order and the product is always the same. While each of our answer choices are real equations, only one correctly displays this property:

 

Example Question #4 : Commutative Property Of Multiplication

Evaluate the following expression without using a calculator

Possible Answers:

Correct answer:

Explanation:

This problem could easily turn into some super heavy calculations, but nobody has time for that.  Instead, we can make this problem very easy by utilizing the commutative property of multiplication, which in essence says that numbers can be multiplied in any order.  

In other words,     and    

That means that rather multiplying our numbers in their orginal order, which can actually change the order of the numbers without affecting the final product.  At this point we should notice that one of our numbers is  while another is .  Similarly the fractions  and  are each accompanied by their recripocals  and  respecitively.  At this point we must also remember the multiplicative inverse property, which tells us that the product of a number and its reciprocal will always be 1.  With that in mind, the strategic way to order the multiplication is as follows:

Doing this pairs each number up with its reciprocal.  Finally, we can utlize the associative properpty of multiplication, which tells us that we can multiply any two numbers at a time.

In other words, .  This allows us to pair off the multiplication as follows.

Within each parentheses we now have a number multiplied by its reciprocal.  Remembering that this always equals 1, we can simplify, giving

Our answer is 1.

Example Question #5 : Commutative Property Of Multiplication

Which answer shows the communitive property of multiplication to the equation below?

Possible Answers:

Correct answer:

Explanation:

The communitive property of multiplication is a property that states that the numbers can be multiplied in any combination. To show which answer is correct simply regroup the numbers in a different or and you will have your answer.

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