ISEE Middle Level Math : How to add variables

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

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Example Questions

Example Question #11 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by distributing the  through the parentheses:

Next, move the like terms next to each other.  Remember, treat  like it is its own, separate variable.

Finally, combine like terms:

Example Question #12 : How To Add Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Combine like terms:

Example Question #13 : How To Add Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Combine like terms:

Example Question #14 : How To Add Variables

Evaluate 

Possible Answers:

Correct answer:

Explanation:

 

Example Question #21 : How To Add Variables

Possible Answers:

Correct answer:

Explanation:

Add the numbers and keep the variable:

Answer:

Example Question #161 : Algebraic Concepts

Simplify:

Possible Answers:

Correct answer:

Explanation:

First we should simplify the first expression. We can first apply the power of a product rule and then apply the power of a power rule. So we can write:

 

Return to the original expression:

Since the variables have the same exponents we can write:

 

Example Question #12 : Algebra

Gina's mom baked 12 cookies. 8 were cinnamon and 4 were chocolate chip. If Gina eats one of the cinnamon cookies, how many more cinnamon cookies are there than chocolate chip?

Possible Answers:

Correct answer:

Explanation:

Gina's mom baked 12 cookies; 8 were cinnamon and 4 were chocolate chip. If Gina then eats a cinnamon cookie, there will be 7 cinnamon cookies left.

After she eats the cookie, we need to find the difference between the number of cinnamon cookies and chocolate chip cookies.

There are 3 more cinnamon cookies than chocolate chip cookies.

Example Question #18 : How To Add Variables

Add  in modulo 13 arithmetic.

Possible Answers:

Correct answer:

Explanation:

In modulo 13 arithmetic, a number is congruent to the remainder of the divison of that number by 13. Since 

and 

,

making the correct response 0.

 

Example Question #41 : Variables

Suppose you know the values of all variables in the expression 

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Adding, subtracting, multiplying

Multiplying, adding, subtracting

Subtracting, adding, multiplying

Adding, multiplying, subtracting

Multiplying, subtracting, adding

Correct answer:

Adding, multiplying, subtracting

Explanation:

By the order of operations, the operation within parentheses, which is addition, is carried out first; of the remaining two, multiplication precedes subtraction.

Example Question #21 : How To Add Variables

Suppose you know the values of all variables in the expression 

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Multiplying, squaring, adding

Squaring, multiplying, adding

Adding, multiplying, squaring

Multiplying, adding, squaring

Squaring, adding, multiplying

Correct answer:

Squaring, multiplying, adding

Explanation:

By the order of operations, in the absence of grouping symbols, exponentiation (squaring here) takes precedence, followed by, in order, multiplication and addition.

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