How to Do Math Faster

The ability to do math quickly and accurately is inordinately prized by consulting firms.

If I had to guess why, I’d say it was because it makes you seem extremely sharp if you do a mental calculation faster than everybody else in the room (especially helpful when you’re dealing with clients that you need to impress quickly).

Now, I’d say that the ability to do math quickly is not really a proxy for your raw intelligence, but rather your knowledge of certain shortcuts, a pinch of misdirection, scientific notation, and practice, practice, practice.

And I’m going to teach these shortcuts to you today. 🙂

Shortcuts

First, read this blog post if you haven’t already, then come back here.

1. Modify / Round Your Numbers.

2. Shift Around Powers of 10.

3. Break Numbers Up into Easier Pieces.

4. Turn Decimals to Fractions (and Simplify).

Modify your Numbers

Let’s say I asked you to multiply 345 x 120 right now, without any paper. This calculation isn’t trivial. The #1 easiest thing you can do is ask if you can round the number and how accurate you need to be.

If you’re going for accurate you could change the calculation to 350 x 120. If you don’t mind being a little of you could made it 350 x 100 (which is extremely straightforward because you just have to add two 0’s onto the end of 350 and you have your answer).

However, I’m going to assume you need to be exact so we won’t use this trick. Just always make it the first thing you do.

Shift Around Powers of 10

345 x 120 is a strange calculation, but what if we could make it easier by making one of the numbers smaller? It turns out, that’s usually always possible if both numbers are > 10.

We can pull 10 out of 120 to make it 12, and pull 10 out of 12 to make it 1.2. So this means 345 x 120 is the same as 345 x 1.2 x 10 x 10. Now I know that doesn’t seem easier but look at what you can do next:

345 x 10 x 10 x 1.2 becomes 34,500 x 1.2

Break Numbers Up into Easier Pieces

The next step on my agenda is to break up one of the numbers in my calculation into its parts to make the calculation easier.

The way this looks is that 34,500 x 1.2 becomes 34,500 x (1 + 0.2). Which means all we’re left with is 34,500 + 34,500 x 0.2.

Turn Decimals Into Fractions (and Simplify)

I’ve always found decimals cumbersome. They’re useful because they are closely related to percentages but they aren’t easy for multiplication.

On the other hand, fractions are extremely useful for mathematical operations but it’s harder to tell what percent a fraction is. For the sake of calculations I always turn decimals into fractions.

So, 34,500 x 0.2 becomes 34,500 x 1/5.

By the way, you can apply the previous step at each point in the calculation. I’d break up 34,500 x 1/5 into (35,000 – 500) x 1/5 which becomes 7000 – 100 = 6900.

So we end up getting 34,500 + 6900. I’d again break up 6900 into (7000 – 100) So we get 34,500 + 7000 – 100 = 41,500 – 100 = 41,400.

Not bad, right 🙂

Also, sometimes you get decimals that aren’t as easy to convert into fractions as 0.2. In that case I’d simplify the fractions or round the decimals as quickly as possible.

For example, 0.55:

0.55 = 55/100 = 11/20

You could either work with 0.55 directly or just round it to 1/2 depending on how accurate you need to be.

Misdirection

People think you’re quick at math not depending on how fast you do a calculation, but how fast it feels to them. I usually take advantage of this cognitive bias by doing most of my math out loud and writing very little.

For example, if I was doing 345 x 120 out loud here is what I’d say:

1. 345 x 120 is the same as 3450 x 12 which is the same as 34,500 x 1.2.

2. 34,500 x 1.2 is the same as 34,500 + 34,500/5

3. 34,500/5 is the same as (35,000 – 500) / 5 = 6900

4. 34,500 + 6900 = 41,500 – 100 = 41,400.

If you were to hear me doing the calculation it would sound extremely fast, though if you were to time me you’d realize that it probably wasn’t all the fast at all. It’s just that communicating it ties up the mind of the listener and makes them feel like time has passed faster.

Scientific Notation

Sometimes you’re just given huge numbers, like 120 million x 600,000. These are actually much, much easier to do if you utilize scientific notation.

Here is a site that explains how convert numbers into scientific notation, and here’s a site that explains how to use it to multiply or divide.. I’ll just summarize what I do, (but read those links first):

1. Convert your numbers into scientific notation:

120 million x 600,000

120 million = 120 x 10^6 = 1.2 x 10^8

600,000 = 6 x 10^5

By the way, anything followed by million is multiplied by 10^6, billion is 10^9, and trillion is 10^12.

2. Add exponents if multiplying, subtract if dividing:

1.2 x 10^8 x 6 x 10^5 = (6 x 1.2) x (10^8 x 10^5) = 7.2 x 10^13

3. If your answer is large, pull out the appropriate power of 10 and turn it into millions, billions, or trillions:

7.2 x 10^13 =

7.2 x 10 x 10^12 = 72 trillion

Practice

This one goes without saying. Practice makes perfect. Being able to do math quickly in an actual interview is a whole different ballgame than drilling it by yourself or practicing with a friend.

Either do a lot of cases or do mental math practice while you’re waiting for class to start, sitting on the bus, when you have downtime at work, etc. Every little bit pays off.

Conclusion

The secret to quick and accurate math is:

1. Modifying / Rounding Your Numbers.

2. Shift Around Powers of 10.

3. Break Numbers Up into Easier Pieces.

4. Turning Decimals to Fractions (and Simplifying).

Good luck!

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