The term “signed numbers” refers to numbers that include either a positive or negative sign, and are therefore marked as being either greater than 0 (positive) or less than 0 (negative). Zero has no sign. For our purposes, the term usually refers to negative numbers, since you already know instinctively how to think about positive numbers.

Here’s a look at negative numbers on a number line:

Students who are comfortable with positive numbers sometimes get confused when dealing with negative numbers. For example, while positive numbers become larger as they move farther away from 0, negative numbers become smaller: –10 is a smaller number than –1. When dealing with negative numbers, be careful not to see the 10 in  –10 and just assume that it is a larger number than –1.

Negative numbers behave differently from positive numbers when you perform various operations on them. In terms of addition and subtraction, negative numbers invert the operations.

When a negative number is added to another number, the sum will be a smaller number. In fact, adding a negative number is the same as subtracting a positive number of the same value.

When a negative number is subtracted from another number, the difference will be a larger number. In fact, subtracting a negative number is the same as adding the inverse positive number.

Negative numbers also follow different rules when you multiply or divide them.

Negative numbers also follow different rules when you include them in multiplication or division.

Because negative numbers act in such different ways from positive numbers, whenever you plug a positive number into a QC question to try to determine which of the two columns is bigger, you must also plug in a negative number. Often, you’ll discover that positive and negative numbers will yield different answers, meaning that the relative size of the columns cannot be determined.