Converting Negative Integers - SS1 Mathematics Lesson Note

Example: Convert \(- 51\) to its equivalent in \(mod\ 10\)

Solution

Using the formula, \(n = q.m + R\), we search for a value for \(q\) where the product with the mod \(m\) is JUST bigger than the number \(n\) we are converting. Its best for beginners to start with \(- 1,\ - 2,\ - 3,\ - 4,\ \ldots\) in that progression.

For \(- 51 = \mathbf{x}\ (mod\ 10)\)

\(- 51 = q.10 + \mathbf{x}\), here \(q\) must be \(- 6\) since its product with \(10\) will be \(- 60\), which is the just above \(- 51\)

\[- 51 = \ - 6(10) + \mathbf{x}\]

\[- 51 = \ - 60 + \mathbf{x}\]

\[- 51 + 60 = \mathbf{x}\]

\[\mathbf{9} = x\]

\[x = \mathbf{9}\]

Thus, \(- 51 \equiv \mathbf{9}(mod\ 10)\)