# Playing with Numbers

Summary of playing with numbers

Let us begin it with a popular system of counting

# Summary

The Decimal Number system

The Decimal number system has ten symbols to represent all the possible numbers we would want to write. They are 0,1,2 ,3 ,4 ,5, 6, 7, 8,9.

To represent anything higher than 9, we add 0 to the original place and add 1 to its left side.

In our number system, we have the idea of place value; the value of a digit depends on its place or position in the number. Beginning with one’s place at the right, each place value is multiplied by increasing powers of 10.

#### General form of numbers.

A number is said to be in a General form if it is expressed as the sum of the product of its digits with their respective place values. Numbers can be written in general form, thus a 2 digit number a, b will be written as

```ab = 10 X a + b = 10a + b
ba = 10 X b + a = 10b + a```

Three digit numbers

A 3- digit number abc made up of digits a, b and c is written as

```Abc  = 100 X a + 10 X b + c
= 100a + 10b + c```

#### Order of arithmetic operators

Generally the acronym PEMDAS is common. It stands for

#### Number game trick for dividing by 11,

For any given two-digit number reverse the number and add it to the original number then on dividing it by 11, the remainder is always zero.

The steps followed

Step 1 select any two digit number ab which can be expressed as 10a + b.

```ab = (10xa)+(1xb) = 10a+b
```

step 2 reverse its digit that is a b will become BA which can be expressed as 10 b + a.

`ba = (10xb)+(1xa) = 10b+a`

Step 3 Add both the numbers that is AB + BA

```ab+ba = (10a+b)+(10b+a)
= 10a+a+10b+b
= 11a+11b
= 11(a+b)```

step 4 divide the number by 11 and that is 11 (A + B) divided by 11. 11 and 11 gets canceled and we have a + b hence remainder will be zero under any case.

```11(a+b)
-------  = a+b => Zero remainder
11```

#### Trick for dividing by 9.

for a given, a two-digit number reverses the number and subtracts the smaller number from the bigger number.

on dividing it by 9 will always result in a zero remainder.

the steps followed to understand the trick are

Step 1

select any two digit number ab and express 10a + b

step 2

reverse the number ab to ba which can be expressed as 10 b + a

step 3

subtract both the numbers that is ab minus ba

so we get (10 a + b) – (10 b + a )

next step

it becomes 9 a minus b

divided by 9

9 and 9 get cancelled hence remainder will be zero under any case

Alpha numeral puzzles

#### Rules for Alpha numeral puzzles

• Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter.
• The first digit of a number cannot be zero

Finding the value Q

```  3     1     Q
+ 1     Q     3
------------------
5     0     1```

By inspection method