What’s important these days is being able to think about approximately what size answer you expect. That way if you mistype the digits, or hit divide when it should be multiply, you have a chance to catch it.

By the way, if a number is divisible by three, it will end in 3,6,9,2,5,8,1,4,7 or 0.

Reminds me of a situation a number of years ago; I bought seven of the same item. When the cashier rang it up, it didn’t sound right. I told the cashier and she said, That’s what the register says," I insisted that she check the tape and she found that she had entered one more than I had bought. Many people have not idea how to estimate an answer.

To address the question in panel 2 with an actual answer, just observe that you dont actually need the sum of all the digits. You can ignore all of the zeroes, threes, sixes, and nines. As you sum the digits that remain, every time you hit a sum that is a multiple of three, forget the sum and start over. You can do a very big number quickly, maybe quicker than punching all of those digits into a calculator #nerd

Actually, if there’s a digit or two left over is kinda important if trying to see if a number is prime. Multiples of 2 and 5 are the easiest to eliminate and with 3 you have the relatively easy way to check.

Carl Friedrich Gauss (1777-1855) would eventually be known as one of the world’s greatest mathematicians, but even he went to elementary school. When he was about 9 years old, his teacher gave the class some busy work to keep them occupied: add up all the numbers from 1 to 100. Less than a minute later, Gauss was looking for something else to do, and the teacher, irritated, asked why he wasn’t working on the problem. Gauss said he already had the answer: 5,050. The teacher was sure he was bluffing — or maybe just being a smartass — but it turned out that he was right!

What Gauss had done was notice that he could start at opposite ends of the number line and make pairs that would always add up to 101 — 100+1, 99+2, 98+3, … 51+50 — and there were 50 of them, so 101 × 50 = 5,050, voilà.

You add up the digits, then you add up the digits of the number you got from that, and so on until you get a number you know is or isn’t divisible by three. Time-consuming, though.

“Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense — or deciding whether the method is the right one to use in the first place — requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.” —Jordan Ellenberg, professor of mathematics, University of Wisconsin–Madison, How Not To Be Wrong: The Power of Mathematical Thinking (2014)

The trick for multiples of 7 is lesser known: Divide it by 10, subtract twice the remainder, and see whether you recognize the result as a multiple of 7 (which could be 0 or a negative number). Take 161, for instance: 16 – 2(1) = 14, so it qualifies.

Frazz15 hrs · I totally stole this punch line from Ed Hoogterp, my friend and co-worker at the Booth Capital Bureau. The staff was in a news meeting, and one story under discussion was about how few students in the state were showing sufficient proficiency in math. There was much outrage, wrapped around the story in general and among the staff in particular, and that’s when Ed dropped the perspective bomb, “yeah, we can’t ALL be journalists.” Some 20 years later, I think the statute of limitations has expired, so I helped myself.

The thing is, for all the jokes, a good journalist really is good at everything, including math. Better yet, a good journalist knows what he or she is NOT good at, a crucial and distressingly rare thing.

Take all the potshots you want at The Media, but dismiss journalists at your peril. Cartoonists, well, hell. Fire away.

## GreasyOldTam 10 months ago

Those rules were useful before calculators. Now that everyone has a pretty good calculator on their phone, it’s faster to just do the division.

## Concretionist 10 months ago

What’s important these days is being able to think about

approximatelywhat size answer you expect. That way if you mistype the digits, or hit divide when it should be multiply, you have a chance to catch it.By the way, if a number is divisible by three, it will end in 3,6,9,2,5,8,1,4,7 or 0.

## RAGs 10 months ago

Reminds me of a situation a number of years ago; I bought seven of the same item. When the cashier rang it up, it didn’t sound right. I told the cashier and she said, That’s what the register says," I insisted that she check the tape and she found that she had entered one more than I had bought. Many people have not idea how to estimate an answer.

## sandpiper 10 months ago

Why single out math?

## matzam Premium Member 10 months ago

isn’t any # divisible 3

## DutchUncle 10 months ago

See Isaac Asimov, “The Feeling of Power”, 1958, about the rediscovery of arithmetic

https://en.wikipedia.org/wiki/The_Feeling_of_Power

https://urbigenous.net/library/power.html

## cervelo 10 months ago

Because, sweetie, that ain’t math, it’s more like philosophy… you learn it through experience or hear about it in college.

## nos.nevets 10 months ago

Is that true only in base 10?

Or is it true for the number 3 in any Base?

Is it because (3×3)+1 = 100 in Decimal base?

So will that 3-Rule work for any number N(baseB) if N(baseB)xN(baseB) + 1 = B ?

Show your work(of course).## brianbeattie 10 months ago

To address the question in panel 2 with an actual answer, just observe that you dont actually need the sum of all the digits. You can ignore all of the zeroes, threes, sixes, and nines. As you sum the digits that remain, every time you hit a sum that is a multiple of three, forget the sum and start over. You can do a very big number quickly, maybe quicker than punching all of those digits into a calculator #nerd

## nos.nevets 10 months ago

The difference between

accurate&precise.Sometimes a precise calculator answer is misleading. It tells you more than you really know.

## poppacapsmokeblower 10 months ago

That is true of nine as well.All prime numbers, other than two and three, are 6n +1, or 6n -1, though not all the numbers formed that way are primes.

## patriots_aren't_partisan 10 months ago

Never heard this “trick” before, but since it doesn’t work for all numbers that are divisible by 3, I don’t understand how it’s particularly useful?

## geneking7320 10 months ago

I was over 18 when I first learned what she said in the first panel. I am 65 now. I frequently wondered why we were not taught that in school.

## The Wolf In Your Midst 10 months ago

If something is divisible by 3, I’m

stillnot sharing. Get your own!## Al Nala 10 months ago

DIVIDE….and Conquer!

## zmech13 Premium Member 10 months ago

Actually, if there’s a digit or two left over is kinda important if trying to see if a number is prime. Multiples of 2 and 5 are the easiest to eliminate and with 3 you have the relatively easy way to check.

## Richard S Russell Premium Member 10 months ago

Carl Friedrich Gauss (1777-1855) would eventually be known as one of the world’s greatest mathematicians, but even he went to elementary school. When he was about 9 years old, his teacher gave the class some busy work to keep them occupied: add up all the numbers from 1 to 100. Less than a minute later, Gauss was looking for something else to do, and the teacher, irritated, asked why he wasn’t working on the problem. Gauss said he already had the answer: 5,050. The teacher was sure he was bluffing — or maybe just being a smartass — but it turned out that he was right!

What Gauss had done was notice that he could start at opposite ends of the number line and make pairs that would always add up to 101 — 100+1, 99+2, 98+3, … 51+50 — and there were 50 of them, so 101 × 50 = 5,050, voilà.

Math is riddled with little tricks like this.

## genghis.shaman 10 months ago

You add up the digits, then you add up the digits of the number you got from that, and so on until you get a number you know is or isn’t divisible by three. Time-consuming, though.

## Jan C 10 months ago

I DID learn that in school.

## Richard S Russell Premium Member 10 months ago

“Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense — or deciding whether the method is the right one to use in the first place — requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.” —Jordan Ellenberg, professor of mathematics, University of Wisconsin–Madison,

How Not To Be Wrong: The Power of Mathematical Thinking(2014)## Stephen Gilberg 10 months ago

The trick for multiples of 7 is lesser known: Divide it by 10, subtract twice the remainder, and see whether you recognize the result as a multiple of 7 (which could be 0 or a negative number). Take 161, for instance: 16 – 2(1) = 14, so it qualifies.

## Night-Gaunt49 10 months ago

Jef Mallet’s BlogPostsFrazz15 hrs · I totally stole this punch line from Ed Hoogterp, my friend and co-worker at the Booth Capital Bureau. The staff was in a news meeting, and one story under discussion was about how few students in the state were showing sufficient proficiency in math. There was much outrage, wrapped around the story in general and among the staff in particular, and that’s when Ed dropped the perspective bomb, “yeah, we can’t ALL be journalists.” Some 20 years later, I think the statute of limitations has expired, so I helped myself.

The thing is, for all the jokes, a good journalist really is good at everything, including math. Better yet, a good journalist knows what he or she is NOT good at, a crucial and distressingly rare thing.

Take all the potshots you want at The Media, but dismiss journalists at your peril. Cartoonists, well, hell. Fire away.

## Daeder 10 months ago

♪ Three…is a magic number!…♪