A Guide to the GRE/Positives and Negatives

Positives & Negatives
Subtracting a negative is the same as adding a positive.

5 - -3 = 5 + 3 = 8

Adding a negative is the same as subtracting a positive.

2 + -5 = 2 – 5 = -3

Multiplying a negative and a positive equals a negative.

5(-3) = -15

Multiplying a negative and a negative equals a positive.

-7(-3) = 7(3) = 21

Thus, multiplying any odd number of negatives together equals a negative, while multiplying any even number of negatives together equals a positive.

Practice
1. What is the value of 8(-4)?

2. If -2 - y is positive, then is y negative or positive?

3. x^77 is positive. Is x negative or positive?

Answers to Practice Questions
1. -32

Multiplying a positive by a negative equals a negative.

2. y must be negative (and must be less than -2)

Subtracting a negative is the same as adding a positive. For example, y could equal -3. -2 - -3 = -2 + 3 = 1.

3. x must be positive.

A negative multiplied by a negative equals a positive (e.g., -1 ✕ -1 = 1), while a positive multiplied by a negative equals a negative (e.g., (-1 ✕ -1) ✕ -1 = 1 ✕ -1 = -1). Therefore, -1(-1)(-1) is negative, while -1(-1)(-1)(-1) is positive. Thus, any time an odd number of negatives are multiplied together, they equal a negative - meaning x must be positive, since 77 xs multiplied together are positive.