Division

Multiplication and division are inverse operations. This means one operation undoes the other. The fact family for \(\textcolor{colordef}{3}\), \(\textcolor{colorprop}{2}\), and \(\textcolor{olive}{6}\) is: $$\begin{aligned}[t] \textcolor{colordef}{3} \times \textcolor{colorprop}{2} &= \textcolor{olive}{6} \\ \textcolor{colorprop}{2} \times \textcolor{colordef}{3} &= \textcolor{olive}{6} \end{aligned} \qquad \qquad \begin{aligned}[t] \textcolor{olive}{6} \div \textcolor{colordef}{3} &= \textcolor{colorprop}{2} \\ \textcolor{olive}{6} \div \textcolor{colorprop}{2} &= \textcolor{colordef}{3} \end{aligned}$$

Taking half of a number means sharing it into two equal parts.
To find half of an even number, split it into hundreds, tens and ones, take half of each part, then add. This works because sharing the whole into two means sharing each of its parts into two.
Half of \(46\): split \(46\) into \(40 + 6\); half of \(40\) is \(20\) and half of \(6\) is \(3\), so half of \(46\) is \(20 + 3 = 23\).
Half of \(470\): split \(470\) into \(400 + 70\).
Half of \(400\) is \(200\), and half of \(70\) is \(35\) (\(70 = 60 + 10\): \(30 + 5\)).
Add: \(200 + 35 = 235\). So half of \(470\) is \(235\).
When the hundreds digit is odd, first split off one hundred: \(500 = 400 + 100\); half of \(400\) is \(200\) and half of \(100\) is \(50\), so half of \(500\) is \(250\).

To divide a number that is beyond the times tables, split it into two parts that the divisor divides exactly: first as many tens of the divisor as possible (\(10\) times, \(20\) times, \(30\) times the divisor …), then the other part, a fact of the table. Divide each part, then add the two results. $$\begin{aligned}[t] 96 \div 8 &= (80 \div 8) + (16 \div 8) && {\scriptstyle\left(96 = 80 + 16\right)} \\ &= 10 + 2 \\ &= 12 \end{aligned}$$ Check with a multiplication: \(8 \times 12 = 96\). If nothing is left after the tens, the tens alone give the result: \(60 \div 3 = 20\).