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Welcome to part 2 of our Fast Math series! In Part 1, I acquainted you with the fact that I’m a lazy math person: I don’t want to do any more than I have to in order to answer the question. And this series shows you how! ☺
Principle #2: Learn shortcuts for when you do have to do the math.
You already saw the first example of this in Principle #1:
Shortcut #1: When multiplying a string of numbers, pair off the 5’s and 2’s and multiply them first.
Let’s say that that problem hadn’t had a 20 in it. If we had to multiply 5 and 81…how would you do that?
You could do long multiplication, of course. But you’re lazy like me, right? So we aren’t going to do that.
There are various shortcuts for multiplication, but here’s my favorite one specifically for multiplying by 5:
Take the non-5 number (in this case, 81) and halve it: 81 → 40.5
Move the decimal one place to the right: 40.5 → 405
Really. That’s it. Try it again: what is 5 × 37?
I don’t know about you, but this one’s a bit harder for me to divide by 2. The number 36 divided by 2 is 18…ah, so 37 divided by 2 must be 18.5.
Finally, move the decimal one place to the right: 18.5 becomes 185.
Shortcut #2: If division involves an annoying number, start from a nearby easier number and then work to the annoying number from there.
Shortcut #3: To multiply by 5, first halve the other number, then make it bigger again by moving the decimal one place to the right.
What if you need to divide by 5 instead? Check it out! Let’s do 81 / 5:
Take the non-5 number (in this case, 81) and double it: 81 → 162
Move the decimal one place to the left: 162 → 16.2
Try it again: what is 896 / 5?
Hmm. 900 × 2 = 1,800, so 896 is 8 less than that, or 1,792.
Then, move the decimal one place to the left to make the number smaller: 1,792 → 179.2.
Shortcut #4: To divide by 5, first double the other number, then make it smaller again by moving the decimal one place to the left.
What do you think so far? We’re just getting started; next time, we’ll dive into Principle #3. And start looking for other Fast Math opportunities during your studies! 📝
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Stacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California. Stacey has been teaching the GMAT, GRE, and LSAT for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. Check out Stacey’s upcoming GMAT courses here.