What is the value of $142,857 \times 7^2$? 
What is the value of $142,857 \times 7^2$?

Obviously you could solve this with a calculator and be done. But is there a more clever way to calculate this?

Multipling by $7^2=49$ is the same as multiplying by $50$ then subtracting one copy.
So $$142,857*7^2=142,857*50-142857$$. 
Now,  multipling by 50 is the same as multiplying by 100 then dividing by 2.
so we have $$(142,857*100)/2-142857$$.
Multiplying by 100 is just adding 2 0s:
$$14285700/2-142857$$
Dividing by 2 is easy to do by hand: $$7142850-142857$$
And finally, subtracting two numbers is easy to do by hand: $$6999993$$
Hopefully that's actually right, because I'm not checking :)
