Solving the calculation without pencil and paper requires breaking the numbers into manageable cognitive chunks. Mathematicians and speed-calculation competitors rely on arithmetic decomposition, applying the distributive property to bypass brain freeze.
The most efficient method splits the calculation into tens and units:
- Multiply the tens base: 10 x 5 = 50
- Multiply the remainder: 7 x 5 = 35
- Sum the sub-totals: 50 + 35 = 85
An alternate mental shortcut uses doubling and halving. Since 5 is half of 10, multiplying any integer by 5 equals half of that integer multiplied by 10. Half of 17 is 8.5; multiply 8.5 by 10, and you arrive at 85 instantly. This approach bypasses digit addition entirely, relying instead on spatial shifts along a decimal line.
