ISEE Middle Level Math : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #23 : How To Divide Variables

Possible Answers:

Correct answer:

Explanation:

Separate each part of the division problem. When dividing, exponents are subtracted.

Example Question #27 : How To Divide Variables

Simplify the following statement.

Possible Answers:

Correct answer:

Explanation:

Simplify the following statement.

TO divide variables, we need to subtract the exponents. The coefficients (numbers out in front) can be divided as you would normally divide.

So we get our answer of two x cubed.

Example Question #1 : How To Subtract Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Expressions & Equations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Expressions & Equations

Simplify:

Possible Answers:

Correct answer:

Explanation:

This problem is just a matter of grouping together like terms.  Remember that terms like  are treated as though they were their own, different variable:

The only part that might be a little hard is:

If you are confused, think of your number line.  This is like "going back" (more negative) from 15.  Therefore, you ranswer will be:

Example Question #1 : How To Subtract Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

This problem really is a trick question.  There are no common terms among any of the parts of the expression to be simplified.  In each case, you have an independent variable or set of variables:  and .  Therefore, do not combine any of the elements!

Example Question #1 : How To Subtract Variables

Simplify:

Possible Answers:

Correct answer:

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: 

Example Question #102 : Algebraic Concepts

Simplify:

Possible Answers:

Correct answer:

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:

Example Question #6 : Expressions & Equations

Simplify:

Possible Answers:

Correct answer:

Explanation:

You need to begin by distributing the minus sign through the whole group .  This gives you:

Simplifying the double negative, you get:

Now, you can move the like terms next to each other:

Finally, simplify:

Example Question #103 : Algebraic Concepts

Simplify:

Possible Answers:

Correct answer:

Explanation:

This problem is as simple as it appears.  All that you need to do is group together like terms:

The only like terms are the  terms.  Therefore, the simple answer is a matter of subtracting 3 from 4:

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