Integers, absolute value, adding and subtracting

Numbers below zero

A temperature of \(5\) degrees below zero, a bank balance that's \(20\) dollars overdrawn, a submarine \(300\) feet below sea level: all of these need numbers less than zero.

On a number line, negative numbers sit to the left of \(0\). The rule for comparing is the same as always: farther right means greater.

• Every positive number is greater than every negative number: \(1 > -100\).
• Between two negatives, the one closer to zero is greater: \(-2 > -9\).

Opposites and absolute value

Two numbers the same distance from \(0\) on opposite sides, like \(6\) and \(-6\), are opposites. A number plus its opposite always equals \(0\).

Adding integers

Think of positive numbers as money you have and negative numbers as money you owe.

Owing \(5\) and then owing \(8\) more means you owe \(13\). Having \(5\) but owing \(8\) means you still owe \(3\) after paying.

Subtracting integers

Subtraction can always be turned into addition.

Some teachers call this "keep, change, change": keep the first number, change subtraction to addition, change the sign of the second number.

Longer sums

When there are several terms, it helps to add all the positives, add all the negatives, and then combine the two results.

Practice