How to subtract variables - ISEE Upper Level: Quantitative Reasoning

Group and collect like terms:

Group and collect like terms:

To simplify this problem we need to combine like terms.

To simplify this problem we need to combine like terms.

To simplify this problem we need to combine like terms.

Simplify the following expression:

We can only subtract variables with the same exponent.

In this case, we can only combine the first two terms.

To do so, keep the exponents the same and subtract the coefficients.

So our answer is:

Simplify the following expression:

Now, to complete this, we need to realize that we can only subtract variables with the same exponent.

In this case, we can only combine our first two terms, because they both have an exponent of 7. The third term has an exponent of 8, so it cannot be combined and must be left as is.

So, our answer must be:

,

So by the multiplication property of inequality, when each is multiplied by the negative number ,

.

Also,

,

so by the addition property of inequality,

or

This makes (B) greater.

Multiplication and division take precedence over subtraction in the order of operations, so these two operations are performed first. The two must be performed from left to right, so the division is worked first, followed by the multiplication. The subtraction is last.

The order of operations is as follows:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

The expression

is therefore evaluated by multiplying, then dividing, then adding. The net result is that the product is added to the quotient .

If we examine (I), we see that, since the multiplication is in parentheses, it is worked first. The division is worked second, then the addition. The order of operations has not changed, so the expressions are equivalent.

If we examine (II), we see that the order of operations has changed so that the addition is worked first. We see through example that the expressions can have different values:

If we examine (III), we see that, since the division is in parentheses, it is worked first. The multiplication is worked second, then the addition. The upshot is the same as in the main expression, however - the product is added to the quotient . Therefore, the expressions are equivalent.

The correct response is (I) and (III)

In the order of operations, any operations in parentheses must be performed first - there are two, the leftmost addition and the middle subtraction. What remains are the leftmost subtraction, the rightmost subtraction, and the rightmost addition. Since additions and subtractions are performed from left to right, the next, or third, operation performed is the leftmost subtraction.

Group and collect like terms:

Group and collect like terms: