# 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 9*x*, then you should subtract; if the smaller number is to the left of 9*x*, 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.

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© Derek Cumberbatch