Try the ages of your family and friends.
What happens?
Can you explain it?
Does this work for very old people over the age of 99? Why or why not?
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The product of two 2-digit numbers can be written as (10a+b)(10c+d). Notice that(1) in all the examples on the left, the tens digits are repeated so a = c
(2) the units digits add up to 10 so b + d = 10
(3) the product is given by 100a(a+1)+ bd, e.g. 100(7×8) + 4×6. Can you prove this result?
(4) Can you prove that the quick calculation method shown on the right always works?
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