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While tutoring students who are in the process of multiplying two numbers, I sometimes challenge myself by trying to do the multiplication in my head instead of using a calculator. I don’t know where I learned it, but I usually take a divide-and-conquer approach to multiplying large numbers, a large number for me being anything greater than 12, save for a few exceptions.^{*} In general, my strategy has been to break the original multiplication problem into simpler parts that I can then solve easily and combine for the answer. I’ve noticed that I usually either “round down” a multiplying number to the nearest ten, break it apart and add up the resulting products or I “round up” a multiplying number, break it apart and subtract the resulting products.

That last sentence is probably impossible to parse without an example, so let’s look at **42 x 8**, first using the round-down strategy.

**Method 1: Round 42 down to nearest ten and add** ^{†}

Here, the implied first step is to round 42 to 40, but that doesn’t mean we forget about the 2. Instead, we recognize that 40 + 2 = 42 and rewrite the equation with 42 broken up. Then it’s a question of solving 40 x 8 and 2 x 8, both of which should be easy enough to do mentally.^{‡} The final step is to add the products, 320 and 16 together.

Continue reading “Two (perhaps) quick(ish) ways to multiply two digit numbers in your head” →