ISEE Middle Level Quantitative : How to find the distributive property

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

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Example Question #1 : How To Find The Distributive Property

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is greater

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

Apply the distributive and commutative properties to the expression in (a):

The two expressions are equivalent.

Example Question #2 : How To Find The Distributive Property

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

Correct answer:

(b) is greater

Explanation:

Apply the distributive property to the expression in (a):

, so  regardless of .

Therefore, 

Example Question #1 : How To Find The Distributive Property

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

Correct answer:

(b) is greater

Explanation:

Apply the distributive property to the expression in (a):

Since , and therefore, regardless of 

Example Question #4 : How To Find The Distributive Property

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

Correct answer:

It is impossible to tell from the information given

Explanation:

We show that there is at least one value of  that makes the (a) greater and at least one that makes (b) greater:

Case 1: 

(a) 

(b) 

(b) is greater here

Case 2: 

(a) 

(b) 

(a) is greater here

Example Question #5 : How To Find The Distributive Property

Which of the following is equivalent to  ?

Possible Answers:

Correct answer:

Explanation:

We can best solve this by factoring 4 from both terms, and distributing it out:

Example Question #2 : How To Find The Distributive Property

 and  are positive integers.

Which of the following is greater?

(A) 

(b) 

Possible Answers:

(B) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) is greater

Correct answer:

(A) and (B) are equal

Explanation:

(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of  and .

Example Question #7 : How To Find The Distributive Property

Simplify the below: 

Possible Answers:

Correct answer:

Explanation:

In order to simiplify we must first distribute the -2 only to what is inside the ( ): 

Now, we must combine like terms: 

This gives us the final answer:

Example Question #3 : How To Find The Distributive Property

Simplify the below: 

Possible Answers:

This does not simplify

Correct answer:

Explanation:

We must use the distributive property in this case to multiply the 4 by both the 3x and 5. 

Example Question #4 : How To Find The Distributive Property

 and  are positive numbers. Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

It is impossible to determine which quantity is the greater from the information given

Correct answer:

(b) is the greater quantity

Explanation:

Since  is positive, and , then, by the properties of inequality,

and

.

Example Question #10 : Distributive Property

 is the additive inverse of . Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

 is the additive inverse of , so, by definition, .

.

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