Trade a halving for a doubling
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.
Keep going until one factor is easy
Start with 16 × 25. Halve the first factor, double the second, and read the next line.
16 × 25
= 8 × 50
= 4 × 100
= 400
Every line is worth the same. Stop when one factor becomes easy, like the 100 here.
Choose the factor to halve
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.
Halving an odd number introduces a fraction, which may make mental arithmetic less convenient. Doubling the other factor still keeps the product equal. For 35 × 13, try splitting a factor into parts.
Try it
Which move makes 35 × 12 easier?
- Halve 12 and double 35: 6 × 70.
- Halve 35 and double 12: 17.5 × 24.
Show the answer
Halve 12 and double 35: 6 × 70.
Both numbers stay whole, and 6 × 70 = 420. The even factor is the one to halve.
Enable JavaScript to answer interactively and save your place.
Practice Mental math