Operations

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ISEE Middle Level Quantitative Reasoning › Operations

Questions 1 - 10
1

Simplify:

Explanation

Remember, when there is a subtraction outside of a group, you should add the opposite of each member. That is:

That is a bit confusing, so let's simplify. When you add a negative, you subtract:

Now, group your like variables:

Finally, perform the subtractions and get:

2

Simplify:

Explanation

Remember, when there is a subtraction outside of a group, you should add the opposite of each member. That is:

That is a bit confusing, so let's simplify. When you add a negative, you subtract:

Now, group your like variables:

Finally, perform the subtractions and get:

3

Simplify:

Explanation

Begin by distributing the through the group:

Next, perform the multiplications:

Group the like terms:

Combine like terms:

Rearrange the terms to get the answer as it appears in the answer choices.

4

Simplify:

Explanation

Begin by distributing the through the group:

Next, perform the multiplications:

Group the like terms:

Combine like terms:

Rearrange the terms to get the answer as it appears in the answer choices.

5

Simplify the following expression

Explanation

Simplify the following expression

We can begin by grouping like terms:

Next, combine the like terms. In this case, simply treat them like two subtraction problems.

So our answer is:

6

Simplify the following expression

Explanation

Simplify the following expression

We can begin by grouping like terms:

Next, combine the like terms. In this case, simply treat them like two subtraction problems.

So our answer is:

7

Simplify:

Explanation

Begin by rewriting the subtracted group as a set of added negative numbers:

Now, simplify that a little by rewriting the additions of negatives as being mere subtractions:

Next, move the like terms next to each other:

Finally, combine like terms:

8

Simplify:

None of these

Explanation

We can solve it using the pattern for the square of a binominal or by using FOIL:

9

Simplify:

Explanation

We can apply the power of a power property:

10

Simplify:

Explanation

We can apply the power of a power property:

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