Negative Numbers - SAT Math

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

Anytime a positive number is divided by a negative number, or vice versa, the end result is a negative number. Find the common factors.

In order to divide, it is necessary to simplify the numerator and denominator first.

Divide both negative numbers. Two negatives divided will result in a positive number.

The answer is .

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

Anytime a positive number is divided by a negative number, or vice versa, the end result is a negative number. Find the common factors.

In order to divide, it is necessary to simplify the numerator and denominator first.

Divide both negative numbers. Two negatives divided will result in a positive number.

The answer is .

Let's reductively consider what this data tells us.

Consider each group (a,b,c) as a group of signs.

From abc < 0, we know that the following are possible:

(–, +, +), (+, –, +), (+, +, –), (–, –, –)

From ab > 0, we know that we must eliminate (–, +, +) and (+, –, +)

From bc > 0, we know that we must eliminate (+, +, –)

Therefore, any of our answers must hold for (–, –, –)

This eliminates immediately a > 0, b > 0

Likewise, it eliminates a – b > 0 because we do not know the relative sizes of a and b. This could therefore be positive or negative.

Finally, ac is a product of negatives and is therefore positive. Hence ac < 0 does not hold.

We are left with a + b < 0, which is true, for two negatives added must be negative.

Anytime a negative number is added, it is similar to subtraction. Recovert the expression to the correct form. Simplify.

The correct answer is .

In order to add the negative numbers, we need to eliminate the double signs and the parentheses. A positive and a negative sign will result in a negative sign.

Evaluate the terms on the right.

The answer is:

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

Anytime a positive number is divided by a negative number, or vice versa, the end result is a negative number. Find the common factors.

In order to divide, it is necessary to simplify the numerator and denominator first.

Divide both negative numbers. Two negatives divided will result in a positive number.

The answer is .

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

Anytime a positive number is divided by a negative number, or vice versa, the end result is a negative number. Find the common factors.

In order to divide, it is necessary to simplify the numerator and denominator first.

Divide both negative numbers. Two negatives divided will result in a positive number.

The answer is .

Because is positive, must be negative since the product of two negative numbers is positive.

Because is also positive, must also be negative in order to produce a prositive product.

To check you answer, you can try plugging in any negative number for .