Integers extend whole numbers to include values below zero. They are useful for temperature, elevation, and money balances.

Directed numbers on a number line

Positive numbers are to the right of zero, negative numbers are to the left. Moving right increases value; moving left decreases value.

Absolute value and opposites

Absolute value is distance from zero: \(|-7|=7\). Opposites have equal distance from zero and opposite signs, such as \(+5\) and \(-5\).

Adding and subtracting integers

You can think of addition and subtraction as movement on the number line.

• \(a+b\): start at \(a\), move by \(b\).
• \(a-b = a+(-b)\): subtracting is adding the opposite.

Example: \(6-(-4)=6+4=10\).

Zero principle with tiles

A positive tile and a negative tile form a zero pair. Add or remove zero pairs to simplify without changing value.

Checkpoint: evaluate \(-3 + 8\)

\(-3 + 8 = 5\). Start at \(-3\), move 8 units right.

Checkpoint: evaluate \(4 - 9\)

\(4 - 9 = -5\). Equivalent to \(4 + (-9)\).

Checkpoint: explain why \(2-(-2)=4\)

Subtracting \(-2\) means adding its opposite \(+2\), so \(2-(-2)=2+2=4\).