ISEE Middle Level Quantitative : How to multiply variables

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 Multiply Variables

Mulitply:

Possible Answers:

Correct answer:

Explanation:

The FOIL method works nicely here:

Example Question #1 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

It is not possible to tell from the information given

  is greater

and are equal

  is greater

Correct answer:

  is greater

Explanation:

  is the greater amount.

Example Question #3 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

 is greater

is greater

and are equal

It is not possible to tell from the information given

Correct answer:

is greater

Explanation:

 

is the greater amount.

Example Question #2 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

is greater

It is not possible to tell from the information given

is greater

and are equal

Correct answer:

and are equal

Explanation:

  and are equal.

Example Question #5 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

is greater

and are equal

is greater

It is not possible to tell from the information given

Correct answer:

is greater

Explanation:

Use the distributive property to expand.

 

To compare the expressions, we can remove common factors. and are common in both expressions, so they can be removed:

Example Question #6 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

and are equal

is greater

It is not possible to tell from the information given

is greater

Correct answer:

is greater

Explanation:

Use the distributive property to evaluate and .

Since , we get:

is the greater quantity.

Example Question #7 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

is greater

and are equal

is greater

It is not possible to tell from the information given

Correct answer:

is greater

Explanation:

Use the distributive property to evaluate each quantity.

 

 

 and  are common in both expressions, so we can write:

is the greater quantity

Example Question #3 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

is greater

It is not possible to tell from the information given

and are equal

is greater

Correct answer:

and are equal

Explanation:

  and are equal.

Example Question #4 : How To Multiply Variables

Which quantity is greater?

Possible Answers:

It is not possible to tell from the information given

is greater

 is greater

and are equal

Correct answer:

 is greater

Explanation:

 

is the greater amount.

Example Question #5 : How To Multiply Variables

Which of the following is equivalent to  ?

Possible Answers:

All four of the expressions given in the other responses are correct.

Correct answer:

All four of the expressions given in the other responses are correct.

Explanation:

We demonstrate that all four of the expressions are equivalent to .

By the associative property of multiplication,

and

By combining like terms, and applying the distribution property:

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