How to multiply variables

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ISEE Upper Level Quantitative Reasoning › How to multiply variables

Questions 1 - 10
1

Multiply:

Explanation

2

Simplify the following:

Explanation

Simplify the following:

To multiple this out, we need to recall how to multiple variables with exponents, and how to multiply coefficients.

To multiple the coefficients (numbers in front) simply treat them like regular multiplications.

So far so good.

To combine our x's, we will add the exponents. Recall that multiplying variables means you add the exponents.

Now, put those two together to get:

3

Solve for \dpi{100} x:

\dpi{100} \frac{1}{3}x-14=7

\dpi{100} 63

\dpi{100} 21

\dpi{100} 3

\dpi{100} 7

Explanation

\dpi{100} \frac{1}{3}x-14=7

\dpi{100} \frac{1}{3}x-14+14=7+14

\dpi{100} \frac{1}{3}x=21

\dpi{100} 3\cdot \frac{1}{3}x=21\cdot 3

\dpi{100} x=63

4

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.

5

Multiply:

Explanation

Use the FOIL method:

6

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. Remember that fractional exponents can be written as roots.

Simplify by taking the roots and canceling common factors.

7

Brian has 3 siblings. When his family orders pizza, each of the 4 children is given \dpi{100} \frac{1}{4} of the pizza. Brian does not feel well so he only finishes \dpi{100} \frac{1}{3} of his pizza. If the original pizza consisted of 12 slices of pizza, how many slices did Brian eat?

\dpi{100} 1

\dpi{100} 3

\dpi{100} 4

\dpi{100} 6

Explanation

Brian eats \dpi{100} \frac{1}{3}\times \frac{1}{4}\times 12\ slices\ of\ pizza.

So Brian eats

\dpi{100} \frac{1}{12}\cdot 12=1\ slice\ of\ pizza.

8

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

Therefore, the answer is 4.

9

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:

10

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:

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