Doubling and halving

Halve one factor and double the other. The product does not change.

You divide one factor by 2 and multiply the other by 2, so the two changes cancel.

Here 4 rows of 6 become 2 rows of 12. Half as many rows, each twice as long, and the same 24 squares.

Start with 16 × 25. Halve the first factor, double the second, and read the next line.

Every line is worth the same. Stop when one factor becomes easy, like the 100 here.

Now try 35 × 12. The top bar shows it as 12 pieces of 35. The middle bar halves the 12 and doubles the 35. The bottom bar halves the 35 and doubles the 12.

When neither factor is even, halving brings in a fraction and this move does not help. For 35 × 13, split a factor into parts instead.