** Numbers and Numeration**

Here, we are going to look at the various numbers available in Mathematics. These includes:

**Even Numbers**: These are numbers divisible by 2 i.e. they are multiples of 2 e.g. 0, 2, 4, 6, 8, 48, 1000, 89264 etc.

**Odd Numbers**: These are numbers that give a remainder of 1 when divided by 2. e.g. 1, 3, 57, 81, 647, 1045 etc.

**Prime Numbers:** These are numbers that are divisible by only 1 and itself. e.g. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 etc. Apart from 1 and itself, no other number can divide these numbers.

**Natural Numbers**: These are positive whole numbers. e.g. 1, 2, 3, 4, 5, 17, 39, 500, 9457 etc.

**Integers:** These includes positive and negative whole numbers. -5, -2, 0, 1, 3, 234 etc. These numbers are also called directed numbers since they possess positive and negative sign.

**Perfect Squares:** These are numbers whose square roots give Integers. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 225, 400 etc.

Taking the square roots of these numbers gives us integers

√16 = +4 or – 4 written as ± 4 for short.

√(225 )= + 15 or - 15 written as ±15 for short.

**Consecutive Numbers:** Consecutive numbers are numbers that follow each other. e.g.

1, 2, 3, 4, 5, 6, 7, 8, 9 are consecutive numbers

2, 4, 6, 8, 10, 12, 14, 16 are consecutive even numbers

1, 3, 5, 7, 9, 11, 13, 15 are consecutive odd numbers

1, 4, 9, 16, 25, 36, 49, 64 are consecutive perfect squares

-2, -1, 0, 1, 2, 3, 4, 5, 6 are consecutive integers

**NUMBER PATTERN**

Patterns are formed when numbers written in such a way that they follow some rules. Once the pattern of the series is understood, you can easily predict the next number in the series.

** Example**

Study the patterns below:

1, 2, 3, 4, 5, ...

In the above series, the next is formed by adding 1 to the previous one.

1, 7, 13, 19, 25, ....

This involves adding 6 to the previous number.

65, 54, 43, 32, 21, ...

Subtract 11 from the previous to get the next.

1, 4, 9, 16, 25, 36, ...

This is a sequence of perfect squares, add the next perfect square to continue the sequence.

**EXERCISE A**

Find the next 3 numbers in the series below:

1. 1, 15, 29, 43, 57, ...

2. 89, 88, 84, 75, 59, …

3. 8, 9, 12, 17, 24, ...

4. 1, -2, 3, -4, 5,....

5. 20, 22, 25, 30, 37, ...

6. – 7, – 6, – 2, + 7, +23, …

7. 21, 21, 42, 63, 105, ...

**NEXT : **PLACE VALUE