MENTAL ADDITION

Addition is easier than Subtraction. Here we find a way how to make addition even easier.

We can easily add, 63 + 9 = 72, but how would you add this in your mind?

That is, to add 10 to any number, 16 + 10 is 26, 28 + 10 is 38, etc.,

In Mental addition, the basic is – To Add 9, Add 10 and Subtract 1; To Add 8, Add 10 and Subtract 2; To Add 7, Add 10 and Subtract 3; and so on.

Then, if you want to Add 49, Add 50 and Subtract 1; To Add 198, Add 200 and Subtract 2.
This makes it easy to hold numbers in your mind.

For example- 25 + 8 = ?; 33 + 7 = ?; 56 + 6 = ?;

Simple Principle for Mental Addition

If the units digit is high, round off to the next ten and then subtract the difference. If the units digit is low, add the tens, then the units.

For example,
47 + 26 = ?; 33 + 15 = ?; 95 + 38 = ?; 47 + 84 = ?; 56 + 75 = ?

We can use the same method for adding three digit numbers. You may prefer to add from left to right; adding hundreds, then the tens, and then the units.

Ex: 345 + 243 = ?; 586 + 654 = ?; 796 + 159 = ?;

In Adding larger numbers, When adding a column of numbers, add pairs of digits to make tens first then add other digits.

Ex: 1) 1236 + 1587 + 4598 = ? ; 2) 4587 + 8796 + 6879 = ?

Mental Addition is easier than the effort of finding a pen and paper or calculator.

NUMBERS – IMPORTANT FACTS

NUMBERS: We use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9 are called Digits, to represent any Number.

A Group of figures representing a number is called a Numeral.

Representation of a number in figures is called notation and expressing a number in words is called numeration.

Place value or Local value of a Digit in a Numeral:

Example: 657891232, in this Place value of 2 is (2X1) = 2; Place value of 3 is (3X10) = 30; Place value of 2 is (2X100) = 200; and so on.. then the place value of 6 is (6X10⁸ ) = 600000000

Face value: The face value of a digit in a numeral is the value of the digit itself at whatever place it may be. In the above example, the face value of 2 is 2, the face value of 3 is 3 and so on.

TYPES OF NUMBERS:

Natural Numbers : Counting numbers 1, 2, 3, …. are called Natural Numbers.

Whole Numbers: All Counting numbers together with zero form the set of Whole Numbers. Thus,

• 0 is the only whole number which is not a natural number.
• Every natural number is a whole number.

Integers: All Natural numbers, 0 and negatives of counting numbers (i.e.){…..,-3, -2, -1, 0, 1, 2, 3,….} together form the set of integers.

‘0’ is neither positive nor negative. So {0, 1, 2, 3,…} represents non-negative integers, while {0, -1, -2, -3 ….} represents the set of non-positive integers.

Even Numbers: A number divisible by 2 is called an even number. (Eg.) 2, 4, 6, …..

Odd Numbers: A number not divisible by 2 is called an odd number. (Eg.) 1, 3, 5, …..

Prime Numbers: A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself. Two numbers are said to be Co-Primes, if their H.C.F. is 1. Eg. : (2,3), (7,9), etc.,

Composite Numbers: Numbers greater than 1 which are not prime, are known as composite numbers. (Eg.) 4, 6, 8, 9, 10

• 1 is neither prime nor composite.
• 2 is the only even number which is prime.
• There are 25 prime numbers between 1 and 100.

Prime numbers upto 100 : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

How can we find prime numbers Greater than 100? :

Let p>100, First find a whole number nearly greater than the square root of p. Let k be the number which is greater than square root of p. Test whether p is divisible by any prime number less than k. If yes, then p is prime. Otherwise p is not prime.

In next we can see more about this.

I look forward your valuable comments.