6.11 Patterns with multiplication

Rewrite the addition as a multiplication in this form:

Number of groups \times amount in each group

We are adding 4 groups of 4.

4+4+4+4= 4 \times 4

Doubling is the same as multiplying by 2.

To multiply 16 by 2 we can use a vertical algorithm:

\begin{array}{c} & &1 &6 \\ &\times && 2 \\ \hline \\ \hline \end{array}

First we multiply 2 by 6 which is 12. So we put 2 in the units column and carry the 1:\begin{array}{c} & & {}^1 1 &6 \\ &\times && 2 \\ \hline &&&2 \\ \hline \end{array}

Multiply 2 by 1 and add the carried 1 to get 3. We put this in the tens column:\begin{array}{c} & & {}^1 1 &6 \\ &\times && 2 \\ \hline &&3&2 \\ \hline \end{array}

To multiply 32 by 2 we can use a vertical algorithm and multiply 2 by 2 to get 4 in the units column: \begin{array}{c} & & 3 &2 \\ &\times && 2 \\ \hline &&&4 \\ \hline \end{array}

Multiply 2 by 3 to get 6. We put this in the tens column: \begin{array}{c} & & 3 &2 \\ &\times && 2 \\ \hline &&6&4 \\ \hline \end{array}

The complete pattern is 8,\,16,\,32,\,64.