Does everyone really think I'm some sort of magic maths wizard who answers all your funny maths questions?

Earlier this year, my new class team colleague, instead of introducing me to the new class, asked me, "How much is 79 x 8 - 16 x 7 without paper or calculator?"

"Eh, 520. I'm Veronika, nice to meet you too."

Of course, I like such questions, even though it's a bit odd instead of a greeting, but I guess I earned some respect! =)

So how did I do it? By decomposing those numbers into nicer ones before multiplying. All could be done in your head, really:

Step One: 79 is 80 - 1. So, I multiply 80 x 8, which is like 8 x 8 x 10 = 64 x 10 = 640. Then, I subtract the "one 8 on top" (i.e., 1 x 8), so I have 640 - 8 = 632. I visualize this number and keep it stored in my head.

Written in "simple" maths: 79×8=(80−1)×8=(80×8)−(1×8)=640−8=632

Step Two: 16 is 15 + 1. 15 is 10 + 5, which is good as 5 is half of ten, and multiplying by ten is always easy, as is finding a half of (almost) any number. So I have 10 + 5 + 1 = 16. Multiplying all by 7 will give me 70 + 35 + 7 = (with a little reorganizing) 70 + 30 + 5 + 7 = 100 + 12 = 112.

Written in "simple" maths: 16×7=(10+5+1)×7=(10×7)+(5×7)+(1×7)=70+35+7=112 (Or, you can think of it as 10×7+(10×7)/2+1×7=70+70/2+7=70+35+7=112)

Step Three: Combine everything together – retrieve the first number from the back of your head. Remember, it was 632. The second one was 112. The original question was to subtract those two, therefore:

632−112=600−100+32−12=500+20=520.

...nice to meet you! =)