The Four Operations with Confidence

Adding a positive number moves right on the number line; subtracting a positive number moves left. Adding a negative is the same as subtracting its absolute value.

Addition and subtraction as movement

Adding a positive number moves right on the number line; subtracting a positive number moves left. Adding a negative is the same as subtracting its absolute value.

When signs differ, subtract the smaller absolute value from the larger and keep the sign of the larger absolute value.

Multiplication and division

Multiplication is repeated addition; division asks how many equal groups fit. Sign rules are identical for both: same signs → positive result; different signs → negative result.

Positive × positive = positive; negative × negative = positive.
Positive × negative = negative.
Division by zero is undefined — there is no number that multiplies by 0 to give a non-zero result.
Order of operations: parentheses, exponents, multiply/divide left-to-right, add/subtract left-to-right (PEMDAS/BODMAS).

Worked example

Evaluate 12 − 3 × (2 + (−4))².

Inside parentheses: 2 + (−4) = −2. Square: (−2)² = 4. Multiply: 3 × 4 = 12. Subtract: 12 − 12 = 0.