Operations - ISEE Middle Level Math

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

Now we have

Add the numbers and keep the variable:

Answer:

Add the numbers and keep the variable:

Answer:

Add the numbers and keep the variable:

Answer:

First, group together your like variables:

The only like variables needing to be combined are the x-variables. You can do this in steps or all at once:

First, move the like terms to be next to each other:

Now, combine the x-variables and the y-variables:

Let's begin by moving the like terms toward each other. Notice the following: zy is the same as yz. (Recall the commutative property of multiplication.)

Now, all you have to do is combine the x-variables and the yz-terms:

Notice that you do not end up with any exponent changes. That would only happen if you multiplied those variables.

Remember, when you have exponents like this, you will treat each exponented variable as though it were its own "type." Likewise, pairs of variables are to be grouped together. Therefore, group the problem as follows:

Notice that the only thing to be combined are the terms.

Therefore, your answer will be:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable. Therefore, you can group your problem as follows:

Then, all you need to do is to combine the terms:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable. Therefore, you can group your problem as follows:

Now, just combine like terms:

You should begin by distributing through the whole group that it precedes:

Now, move your like variables next to each other:

Finally, combine the like terms:

Begin by distributing the to its entire group:

Next, group the like terms:

Finally, combine the like terms:

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:

Combine like terms:

Combine like terms:

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:

The algebraic way to solve this problem is to set up an equation, however, students can also solve using guess-and-check from the answer options.

When setting up an equation, sequential numbers are equal to , , , and . We know the sum of these sequential numbers to be 62, allowing us to set up the following equation:

Combine like-terms by reordering.

Subtract 6 from each side of the equation, then divide each side by 4 in order to isolate the variable.

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.