Modular multiplication

(Modular Arithmetic)

In standard arithmetic, \(5 \times 10\) is equal to \(50\), but in Modular Arithmetic it is equal to \(2\), since this is the remainder of the divison of \(50\) by \(12\). This is usually expressed as \[5 \times 10=2\,(\mbox{mod }12).\]

What about modulus \(9\) instead of modulus \(12\)? Likewise, since \(50 = 5 \times 9 + 5\), we say that \[5 \times 10=5\,(\mbox{mod }9).\]

In order to check your ability with modular multiplication, see this applet.



Modular multiplication has the following properties:


Check these and other properties of multiplication in the following "couloured" Multiplication Table .