Negative numbers exist to the left of zero on the number line. Positive numbers exist to the right of zero on the number line. Therefore zero is neither negative nor positive.
The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero.
Given some number [latex]a[/latex], [latex]-a[/latex] means the opposite value on the number line from the number [latex]a[/latex], and is read the opposite of a.
The absolute value of a number [latex]n[/latex] is written as [latex]\lvert n\rvert[/latex], and [latex]\lvert n\rvert\ge0[/latex] for all [latex]n[/latex]
To add integers, if the signs are the same, combine the numbers and keep the sign. If the signs are different, take the difference between the numbers and keep the sign of the number having the larger absolute value.
Subtracting a number is the same as adding its opposite.
To multiply or divide two integers together, if the signs are the same, the result will be positive. If the signs are different, the result will be negative.
Key Equations
[latex]a+(-a)=0[/latex]
[latex]a \cdot \left(-1 \right)=-a[/latex]
.[latex]a \div \left(-1 \right)=-a[/latex]
Glossary
absolute value
the absolute value of a number is its distance from 0 on the number line
difference
the result of subtraction
integers
the set of counting numbers, their opposites, and [latex]0[/latex]
opposite notation
indicated by a negative sign in front of a variable or a number
