Nifty Number Nine & Its Multiples
This trick isn't just about the number 9 & its multiples, but also about 2-digit numbers. 9 & its multiples have the power to swap the digits of 2-digit numbers! All it takes is some addition or subtraction.
If the bigger number is to the left of 9x, then you should subtract; if the smaller number is to the left of 9x, then you should add.
This next example uses 18, which is 9 × 2.
35 + 18 = 53
53 - 18 = 35
There's something you have to do with the digits of the 2-digit numbers to know which multiple of 9 you have to add or subtract to swap the ones digit & tens digit of the 2-digit number you picked: simply multiply the absolute value of the difference of the 2 digits by 9.
9(|T - D|) = M
T = tens digit, D = ones digit, M = the multiple of 9 that swaps the digits!
|3 - 5| = 2
|5 - 3| = 2
(With the bigger number to the left, the absolute value line symbols are unnecessary, but I put them there anyway to make a point.)
9 × 2 = 18
...And there's the multiple of 9 that had to be used in the previous example!
But I'll show you a few more!
58 + 27 = 85
85 - 27 = 58
(|5 - 8| = |8 - 5| = 3; 9 × 3 = 27)
16 + 45 = 61
61 - 45 = 16
(|1 - 6| = |6 - 1| = 5; 9 × 5 = 45)
29 + 63 = 92
92 - 63 = 29
(|2 - 9| = |9 - 2| = 7; 9 × 7 = 63)
19 + 72 = 91
91 - 72 = 19
(|1 - 9| = |9 - 1| = 8; 9 × 8 = 72)
09 + 81 = 90
90 - 81 = 09
(|0 - 9| = |9 - 0| = 9; 9 × 9 = 9^2 = 81)
What's up with the zeroes in this final example, you ask? Simple! Have you ever heard of padding zeroes? They're zeroes that are put into a number although they're unnecessary! But still, 09 = 9. In fact, no matter how many zeroes you print behind the number, the number remains the same value; so, 25 = 025 = 0025 = 00025 = et cetera. You can also print the decimal point & many zeroes in front of it ad infinitum, but the number's value remains the same; 7 = 7.0 = 7.00 = 7.000 = et cetera.
Hit counters use padding zeroes all the time!
Source of Reference: "Ones & Zeroes" by John Gregg.
Back to Index Page Back to Math Trick Menu
© Derek Cumberbatch