# ISEE Middle Level Math : Algebraic Concepts

## Example Questions

### Example Question #71 : Operations

Simplify the following statement

Explanation:

Simplify the following statement

To multiply these terms, first multiply the 2 and the 14

Next, we can combine the b's and the t's by adding together their exponents.

### Example Question #71 : Algebraic Concepts

Combine the following terms:

Explanation:

Combine the following terms:

Let's begin by multiplying the coefficients (numbers out in front)

So our answer must have 360 in front.

Next, let's multiply our q's. To do so, we need to add up our exponents.

So, put it together to get:

### Example Question #72 : Algebraic Concepts

. Evaluate .

Explanation:

, so either  or .

If the former is true,

.

If the latter is true, then, since an even-numbered power of any number is positive,

.

### Example Question #74 : Algebraic Concepts

Simplify the following expression

Explanation:

Simplify the following expression

Let's begin by grouping our x's and our coefficients

We can combine our coefficents by multiplying them, and we can combine the x's by adding the exponents

### Example Question #71 : Variables

Evaluate .

Explanation:

First, use the given equations to solve for both the individual variables.

Now that both variables have been solved for, find their product.

### Example Question #1 : How To Divide Variables

Explanation:

First convert each mixed number into and improper fraction

Then convert the operation to multiplication and flip the second fraction

Reduce where possible and multiply to solve:

Simplify:

Explanation:

### Example Question #1 : How To Divide Variables

Solve for B

Not enough information provided.

Explanation:

This problem looks strange since it mostly contains variables, in particular unknown variables. Still remember the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. We still use those operations in this case. All we must do is move the variables around to solve for .

In this case we can subtract (additive inverse)  to the other side first.

Rewrite our problem.

Stop for a moment and look at the progress. Go back to the original question, solve for . Our problem shows  about to be multiplied to , but we do not necessarily have to multiply because we can divide by  to both sides of the equation, which would save us a step as well as have B by itself.

### Example Question #1 : How To Divide Variables

Suppose you know the values of , and , and you want to evaluate the expression below.

Which of the following is the first step you must complete?

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Evaluate .

Explanation:

Use the order of operations, PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

In our expression, there are no parentheses, so square  first.

Divide: