Clock Arithmetic

Clock arithmetic: how to work it out

Clock arithmetic means you work modulo a fixed number of hours or units. After each operation, you bring the result back into the allowed clock range by wrapping around.

1) Identify the clock size

Find the number of positions on the clock. A 12-hour clock uses values from 0 to 11 or 1 to 12 depending on the convention; in many math exercises, the key idea is that values repeat after the full cycle.

2) Add or subtract normally

Carry out the operation as you would with ordinary numbers.

3) Wrap around

If the result goes past the maximum value, subtract one full cycle until it fits back on the clock. If the result is negative, add one full cycle until it becomes valid.

4) Simplify the final answer

Write the reduced value in the expected clock form.

Check your work

A good check is to see whether your answer is in the correct range and whether adding or subtracting a full cycle gives an equivalent result. For example, if the clock size is 12, then numbers that differ by 12 represent the same position.

Common mistake

Do not keep the ordinary arithmetic result if it lies outside the clock range. Always reduce it to the clock.