SAT Math : Negative Numbers
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Example Questions
Example Question #1 : How To Multiply Negative Numbers
Solve the following equation:
If there are two negative signs, then the answer will be positive. If there were only one negative sign, the answer will be negative.
Example Question #41 : Integers
Simplify the following expression:
Simplify the following expression:
Let's begin by expanding the inside of the parentheses.
Now, it is important to use all three negative signs. The first two will cancel out, but the third one will remain, ensuring our final answer will be negative.
Example Question #1 : How To Divide Negative Numbers
What is 
45
A negative number divided by a negative number always results in a positive number. 
Example Question #1 : How To Divide Negative Numbers
Solve for 
Begin by isolating your variable.
Subtract 
Next, subtract 
Then, divide both sides by 
Recall that division of a negative by a negative gives you a positive, therefore:
Example Question #42 : Integers
Divide:
Anytime a positive number is divided by a negative number, or vice versa, the end result is a negative number. Find the common factors.
Example Question #2 : How To Divide Negative Numbers
Divide:
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 
Example Question #1 : How To Add Negative Numbers
Add:
Anytime a negative number is added, it is similar to subtraction. Recovert the expression to the correct form. Simplify.
The correct answer is 
Example Question #2 : How To Add Negative Numbers
Add the negative numbers:
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:
Example Question #1 : Negative Numbers
a, b, c are integers.
abc < 0
ab > 0
bc > 0
Which of the following must be true?
a + b < 0
a > 0
ac < 0
b > 0
a – b > 0
a + b < 0
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.
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