No tricks please

On YouTube you can find videos where they teach you tricks to multiply. “Only for numbers under 100” they claim. Which is not true, of course, but what the heck.

It goes like this:

    \[32\cdot 14=3\cdot 1 \text{ and }2\cdot 4=3 \text{ ## } 8\]

now cross-multiply

    \[3\cdot 4+2\cdot 1=12+2=14\]

Then put the 4 in the middle between the 3 and the 8, then add the 1 to the 3 to make it 4 and you have 448.

Keep it simple. Instead of learning a trick, perform the above operation in the understandable format

    \[(30+2)(10+4)=30\cdot 10+30\cdot 4+2\cdot 10+2\cdot 4= 300+120+20+8=448\]

and you know what you’re doing.

So let’s look at 113\cdot 245.

    \[(100+13)(200+45)=20000+4500+2600+450+135=24500+3050+135=27550+135=27685\]

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