SSAT Middle Level Quantitative › How to add variables
Simplify:
Combine like terms and
by subtracting their coefficients; do not combine either with the 7.
Simplify the following:
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
Simplify:
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:
Bob and Anita drove cross country together. If Bob drove miles on the trip, and Anita drove twice as many miles as Bob, how many miles total did they drive together?
If Bob drove miles, and Anita drove twice as many miles as Bob, then Anita drove
miles; therefore, the sum of the miles that they drove together would be 3J.
Thus, the correct answer is .
To simplify this expression,
combine like terms.
In this expression, the only terms that can be combined are the ones that have as the variable.
Rewrite in simplest form.
Simplify:
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.
Simplify:
Combine like terms:
Add in modulo 15 arithmetic.
In modulo 15 arithmetic, a number is congruent to the remainder of the divison of that number by 15. Since
and
,
.
This makes 10 the correct choice.
Write in base ten:
In base five, each place value is a power of five, starting with 1 at the right, then, going to the left, .
can be calculated in base ten as
.
Write in base ten:
In base five, each place value is a power of five, starting with 1 at the right, then, going to the left,
can be calculated in base ten as
.