Quick division by 9

Before we go into the division technique, let s take a closer look at the number 9. In the number system base "10", number 9 =(base system no-1) ie it s one less than the base number. This observation leads us to its another property ie the divisibility rule of 9. To check if a number is divisible by 9, we just add up the digits of the number. If that sum is divisible by 9, the original number is also divisible by 9. Another corollary to this is, if we get a remainder when we divide the sum of digits by 9, then that remainder would be the remainder when we divide the original number by 9.

Example : 558 / 9

5+5+8 = 18 is the sum of the digits

now, divide this by 9 => 18/9 gives remainder 0, hence 558 is divisible by 9.

278 /9

2+7+8 = 17 is the sum of the digits

now,divide this by 9 => 17/9 gives remainder 8, hence 278/9 will also give a remainder of 8.

Now, that we are done with the remainder concept, how do we find the quotient then ???

That is lot more easy than the above method.

Example : 132/9

Write down the digits of the number 132.

On the next line, write the first digit of the number, next digit will be this number plus the next digit(add diagonally), and this pattern continues.

1    3    2

↓➚↓➚↓

1    4    6

In this 14 is the quotient and 6 is the remainder !

5    5    8

↓➚↓➚↓

5 10 18

Since the second digit in the result is 10, add 1 to the 5, hence it ll be like

6 0 18

18 is still divisible by 9, giving 2 as the quotient, add it to 60 giving 60+2 =62 this is the quotient and 0 is the remainder !

Squaring a 2 digit number - revisited

When my husband and I were playing around with the nos, he discovered a new smart shortcut to find squares of nos.

Example : 69

1. Add the unit digit '9' to the no itself

9+69= 78

2. Multiply this with the ten s digit '6' of the original no

6*78=468

3. Square the unit s digit of the original no and append at the end after shifting it once to left

4680 || 9^2 = 4680 || 81 = 4761

This method can very well be extended to higher digit nos too !

Squaring a no ending with 5

In this post,let s learn how to square a number that ends with the digit '5'.

Using examples to learn a method is always easy, so let s consider the squaring of the no '45'.

For all the nos ending with 5, the squared resultant no will have 25 as its last 2 digits. So, resultant must in the pattern _____25, what comes in the blank is calculated as follows. Remove the '5' from '45', we are left with '4', multiply it with its consecutive no, being '5', which gives 4*5=20. This '20' is filled in the above blank, hence giving the resultant to be 2025 !!!

Another example : 75

Pattern : ____ 25

7*8=56, hence resultant would be 5625.