97 × 94
The trick, step by step
How far each is from 100: 97 is 3 below, 94 is 6 below.
Cross: 97 − 6 = 91 (or 94 − 3, the same). These are the hundreds.
Multiply the gaps: 3 × 6 = 18. These are the last two digits.
So 97 × 94 = 9118. Above 100 it is the same with +: 103 × 104 = 107|12 = 10,712.
given working answer taken away
Why it works
(100 − x)(100 − y) = 100(100 − x − y) + xy. The cross step gives 100 − x − y, the hundreds, and xy fills the last two digits (carry if it is 100 or more). Above 100 both gaps are added; with one above and one below, xy is taken away.
Practise this trick