# Number System class 1

We can categories number

Natural Numbers (Positive Integers) :- All numbers from 1 to infinity which are used for counting are called natural numbers. It is denoted by N.

Ex - 1, 2, 3, 4. . . . . ∞

Whole Numbers :- When 0 is included in natural numbers it s called whole numbers.

Ex - 0, 1, 2, 3 . . . .∞

Negative Integers :- Negative integers include all negative number from -∞ to -1.

Ex - -∞ . . . . -4, -3, -2, -1

Integers :- Group of natural number, zero and negative number is integer.

Ex - -∞ . . . . -4, -3, -2, -1, 0, 1, 2, 3 . . . .∞

Even Numbers :- Numbers which are divided by 2 is known as even numbers.

Ex - 2, 4, 6, 8. . . . , 1, 2, 3 . . . .∞

Odd Numbers :- Numbers which are not divided by 2 are called odd numbers.

Ex - 1, 3, 5,7 . . . . ∞

Composite Numbers :- Numbers which are divided by other than 1 and self are composite number.

Ex - 4, 6, 9, 10

Prime Numbers :- Number which are not divided by other than 1 and itself are prime number.

Ex - 2 , 3, 5

Co-prime Numbers :- A pair in which both numbers are prime is called co-prime.

Ex - (3, 5), (7, 11)

Rational Numbers :- Numbers in form of p/q and q ≠ 0 are rational number.

Ex - 7, 11, 3/4, 7/11

Irrational Numbers :- Numbers which can not be write in form of p/q are irrational number.

Ex - √2, √3, π

Real Numbers :- Numbers which contains both rational and irrational numbers are real number.

Ex - 7, 11, 3/4, 7/11,√2, √3, π

Consecutive Numbers :- Numbers that follow continuously from smallest to largest are consecutive numbers and difference between each number will be 1.

if one integer is X then other consecutive will be X+1, X+2 and so on.

Consecutive Even Numbers :- Even numbers that follow other continuously are consecutive even number and difference between two consecutive number always be 2. If one even number is X then others are X+2, X+4, and so on.

Consecutive Odd Numbers :- odd numbers that follow other continuously are consecutive odd number and difference between two consecutive number always be 2. If one odd number is X then others are X+2, X+4, and so on.

### Finding Sum of consecutive Numbers

if there are n consecutive number from 1

1+2+3+4+5 . . . . .n

sum = n(n+1)/2

watch video for detailed explanation

Some questions for practice

Q 1. Find sum of 1 + 2 + 3 + 4 + 5 . . . . . . . . . . . . + 100.

a. 2500 b. 5050 c. 10100 d. 4500

Q 2. Sum of 2 + 4 + 6 + 8 . . . . . . . . . . . + 80.

a. 5050 b. 1600 c. 3280 d. 1640

Q 3. Sum of first 10 multiple of 3.

a. 165 b. 44 c. 55 d. 330

Q 4. Sum of 101 + 102 + 103 + 104 . . . . . . . . .+ 200.

a. 1500 b. 15025 c. 15050 d. 25000

Q 5. if sum of 1 + 2 + 3 . . . . . . + 10 = 55 then sum of 5 + 10 + 15 + 20 . . . . . . + 50 is -

a. 250 b. 655 c. 275 d. 300

Q 6. 1 + 2 + 3 + 4 . . . . . . + 23 + 24 + 25 + 24 +23 . . . . . 2 + 1 is equal to -

a. 1500 b. 625 c. 350 d. 600

Q 7. Sum of 1 + 2 + 3 + 4 . . . . . . . + 200 is -

a. 20200 b. 10100 c. 5050 d. 20100

Q 8. Sum of all positive multiple of 7 less than 50 is

a. 196 b. 700 c. 392 d. 146

Q 9. Sum of how many terms in series 1 + 2 + 3 + 4 . . . is 1275

a. 25 b. 100 c. 51 d. 50

Q 10. Sum of how many terms in series 1 + 2 + 3 + 4 . . . is 5050

a. 50 b. 51 c. 100 d. 101

Q 1. b Q 2. d Q 3. a Q 4. c Q 5. c

Q 6. b Q 7. d Q 8. a Q 9. d Q 10. c

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