# ISEE Upper Level Math : Operations

## Example Questions

### Example Question #11 : Operations

Simplify:

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify. The negative in the fraction can be applied to either the numerator or the denominator, but not both; we will apply it to the numerator.

The fraction cannot be simplified further.

Solve for :

Explanation:

### Example Question #12 : Operations

If the product of three consecutive numbers is 990, what is the smallest number?

Explanation:

If the product of three consecutive numbers is 990, then the smallest number can be found by plugging in each answer choice into the scenario to see whether it is correct.

If we plug in 9 as the smallest number, then the two consecutive numbers would be 10 and 11.

Given that 9 times 10 times 11 equals 990, that is the correct answer.

### Example Question #13 : Operations

What is the simplified version of the expression below?

Explanation:

The first step is to simplify the values in the parentheses:

### Example Question #14 : Operations

Simplify:

Explanation:

Reorder the expression to group like-terms together.

Simplify by combining like-terms.

### Example Question #15 : Operations

If  is a positive number, what is a possible value of ?

Explanation:

If x is equal to , then the equation could be written as follows:

Given that  is a positive number,  is a possible value of

### Example Question #16 : Operations

Megan teaches a cooking class. Every time a student takes a class, the student receives a 10% discount off of the price he paid for the previous class. The first class that Jose took cost $50. What will be the first class in which Jose pays less than$38?

Explanation:

In order to solve this problem, the price of $50 must be discounted by 10% until we get to a price of$38 or less.

The first class is 50.

The second class, being 10 percent less than the previous one, is

The third class, being 10 percent less than the previous one, is

The fourth class, being 10 percent less than the previous one, is

### Example Question #17 : Operations

Simplify the following expression

Explanation:

Simplify the following expression

Let's begin by multiplying our coefficients:

Next, we need to realize that we can combine our x's by adding the exponents.

Put it all together to get:

### Example Question #18 : Operations

Simplify the following:

Explanation:

Simplify the following:

To begin, our coefficient will not change. We have just one integer (the 9) and nothing to multiply it by.

To combine our exponents, we will add them. This is because we are multiplying them

Put it together to get:

### Example Question #19 : Operations

and  are both positive.

Evaluate .

Explanation:

Multiply the binomials using the FOIL method - first, outer, inner, last - then combine like terms:

and ; also, by the Power of a Product Principle:

.

and  are both positive, so, substituting:

.

Again, using substitution: