Operations

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ISEE Upper Level Quantitative Reasoning › Operations

Questions 1 - 10
1

Multiply:

Explanation

2

Multiply:

Explanation

3

Add:

Explanation

In order to simplify this expression, we will need to add like terms.

There is a lone positive three.

Combine all the terms.

The answer is:

4

Add:

Explanation

In order to simplify this expression, we will need to add like terms.

There is a lone positive three.

Combine all the terms.

The answer is:

5

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

6

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

7

Simplify the following expression:

Explanation

Simplify the following expression:

We can only subtract variables with the same exponent.

In this case, we can only combine the first two terms.

To do so, keep the exponents the same and subtract the coefficients.

So our answer is:

8

Simplify:

Explanation

To simplify this problem we need to combine like terms.

9

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:

10

Simplify the following expression:

Explanation

Simplify the following expression:

We can only subtract variables with the same exponent.

In this case, we can only combine the first two terms.

To do so, keep the exponents the same and subtract the coefficients.

So our answer is:

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