# ISEE Middle Level Quantitative : How to multiply variables

## Example Questions

### Example Question #41 : Algebraic Concepts

Which of the following is equivalent to  ?

Explanation:

Use the commutative and associative properties to reorder the expression and group like-terms together.

### Example Question #42 : Algebraic Concepts

Define an operation on the real numbers as follows:

For all real values of  and ,

is a positive number. Which is the greater quantity?

(a)

(b)

(b) is the greater quantity

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

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

Explanation:

, so

Since  is positive,

and by the addition property of inequality,

and

### Example Question #43 : Algebraic Concepts

Which of the following is equivalent to

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

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:

### Example Question #1 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Explanation:

To solve this problem, we multiply  by the ones position and the tens position.

### Example Question #2 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Explanation:

To solve this problem, we multiply  by the ones position and the tens position.

### Example Question #3 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Explanation:

To solve this problem, we multiply  by the ones position and the tens position.

### Example Question #4 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Explanation:

To solve this problem, we multiply  by the ones position and the tens position.

### Example Question #5 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Explanation:

To solve this problem, we multiply  by the ones position and the tens position.

### Example Question #6 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Solve the following:

Explanation:

To solve this problem, we multiply  by the ones position and the tens position.