I was born on Sept. 9 in the 1990s and my first name has nine letters, and my first initial is the 19th letter of the alphabet. So naturally, I have some personal interest in the number nine. Biases aside, I can prove that nine is objectively the best number, and in the process teach you some cool mental math. After reading what I have to say, you’ll be able to pull a multiple of nine from the air next time you have to make between 200 and 300 pancakes for nine swinish friends who insist they each get an equal share. Or, you can wow your friends with some really random, but cool, facts about nine.
1. September, the ninth month of the year, is the only month in the English language whose number of letters in the name corresponds to the number of the month. Ninth month, nine letters.
2. Nine is the highest single digit Arabic numeral. You can’t go any higher without tacking on an extra digit. Nine has the last say, every time.
3. The sum of the digits of any multiple of nine is nine.
18: 1+8=9 5112: 5+1+1+2=9 99,112,041: 9+9+1+1+2+0+4+1=27
27: 2+7=9
4. The digits within any number that is divisible by nine can be rearranged in any orientation, and the resulting number will still be divisible by nine. This follows from the property that the sum of the digits of any product of nine is nine.
567, 576, 657, 675, 756, and 765 are all divisible by nine.
Feel free to toss in as many zeros as you like. The number is still a multiple of nine!
50,000,600,000,007 is STILL divisible by nine (5,556,222,223 times).
5. It’s easy to mentally compute multiples of nine in a given hundred.
Find a multiple of nine in the 700s (x=7).
1. Take any two digit multiple of nine:
27
2. Deduct x from the two-digit multiple,
27-7= 20
3. And put the number x to the result in Step 2.
720
720 is a multiple of nine in the 700s! The property carries on for double digit hundreds. For a multiple in the 2100s (x=21):
1. 72
2. 72-21=51
3. 2,151 is a multiple of nine.
To find numbers in the thousands, add digits to Step 1 so that Step 2 does not yield a negative answer. For example, to find a multiple of nine in the ten thousands,
x=100
Step 1 now needs to include a three digit number, since no two digit multiple of nine is greater than 100.
1. 144
2. 144-100= 44
3. 10,044
Alternately, you can keep x as two digits, but find a number in the thousands by lengthening the number in Step 1. For a number, again, in the ten-thousands:
Keep x as 10.
1. 144
2. 144-10= 134
3. 10,134
6. OR for a reverse take, find a random multiple of nine like this:
1.Multiply nine by any number, X. x=8:
72
2.Then subtract that number from the product.
72-8=64
3.Place the number you subtracted in the leftmost place, and the result of the subtraction to its left, filling the places to the right of X.
864
And, don’t forget that if 864 is a multiple of nine, so are 846, 468, etc.
7. Putting the digit nine into any number does not change the sum of the digits of that number.
53: 5+3=8
593: 5+9+3=17; 1+7=8.
From this property, follows:
8. Toss a nine into any multiple of nine, in any part of the number, and the resulting number will still be a multiple of nine.
72 (multiple of nine)
729 (likewise a multiple of nine)
Feel free to dump multiple nines into the mix to get a more mixed-up multiple.
79299 (still a multiple of nine)
And don’t forget the zeros. Is 92,990,007 a multiple of nine? Better believe it!
