Tag Archives: Proof by Nine

Why Don’t They Teach Our Kids “Proof by Nine” As A Part Of Math?

by Anura Guruge

“Proof by Nine” (I have always called it (possibly incorrectly) “Proof of Nine”) is a clever and totally foolproof way to check your multiplication — without having to rely on a calculator or an electronic device. I was taught it, in Ceylon, at school, probably when I was around 6 or 7, as an integral part of learning to do multiplication. We are talking the early 1960s. We did NOT, especially in Ceylon, have calculators or for that matter even slide rules. So “Proof of Nine” was the ONLY way we had — and even our teachers — of checking the correctness of multiplication.

The 3rd image below (albeit purely scanned) in its first paragraph spells out EVERYTHING as it pertained to I. I would do “Proof of Nine”, by rote, as soon as I did a multiplication by hand. I still do it TODAY, for the fun of it. I have tried to teach the kids but they don’t fully grasp it.

The two articles I show here try to explain it very well. I did this diagram to show you the basic mechanics AND I KNOW that most of you are going to say that it is totally confusing.

Shame that they don’t teach it in school. Because all of us would know how to do it.

PLEASE look it up. It is very neat and awfully handy if you don’t have any other means to check a multiplication.

prrofby9anuMy diagram. So I want to check whether 7826 x 43 = 336518.

I start by drawing the slanted ‘X’. The I come up with the two vertical numbers, in this case 5 & 7. I do that by repeatedly adding the digits until I have but one digit. I ALWAYS throw out any 9 I encounter — and even digits that together add up to nine.

I multiply 5 x 7. That is 35. Add the digits. 8.

I add up the digits in 336518. I notice two obvious pairings that come to 9. 3+6 & 1+8. I throw those out. Actually it will still work IF I didn’t throw them out! All comes out in the wash. Well it adds up to 8.

The same ‘8’ I got when I multiplied 5×7 and got 35. The two ‘8’s match. The multiplication was RIGHT.


First article. Click to ENLARGE and read here. Use link below to access original.

Click here to access original.


Second article. Click to ENLARGE and read here. Use link below to access original.

Click here to access original.


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by Anura Guruge