Number System - 1

Dividend = Divisor * Quotient + Remainder Even + Even = Even Odd + Odd = even Even + Odd = odd
LCM & HCF The common factors in the two numbers are HCF. LCM : The common factors in the two numbers + the remainders Example: 12, 80, 50 12 = 2 * 2 * 3 80 = 2 * 5 * 2 * 2 * 2 50 = 2 * 5 * 5 HCF = 2 LCM = 2 * 5 * 5 * 2 * 2 * 2 * 3 LCM * HCF = Product of 2 numbers.
Squares and Cubes 1 + 2 + 3 ………………..n = n * n+1 / 2 Sum of squares of 1st n natural numbers = n (n+1)(2n+1) / 6 Sum of cubes of 1st n natural numbers = [n (n+1)/2]^2
Number ( x ) Square ( x 2 ) Cube ( x 3 )
1 1 1
2 4 8
3 9 27
4 16 64
5 25 125
6 36 216
7 49 -
8 64 -
9 81 -
10 100 -
11 121 -
12 144 -
13 169 -
14 196 -
15 225 -
16 256 -
17 289
18 324
19 361
21 441
22 484
23 529
24 576
25 625
Fractions and Percentage:
Fraction Decimal Percentage
1 / 2 0.5 50
1 / 3 0.33 33 1/3
2 / 3 0.66 66 2/3
1 / 4 0.25 25
3 / 4 0.75 75
1 / 5 0.2 20
2 / 5 0.4 40
3 / 5 0.6 60
4 / 5 0.8 80
1 / 6 0.166 16 2/3
5 / 6 0.833 83 2 / 3
1 / 8 0.125 12 1 / 2
3 / 8 0.375 37 1 / 2
5 / 8 0.625 62 1 / 2
7 / 8 0.875 87 1 / 2
1 / 9 0.111 11
2 / 9 0.222 22
1 / 10 0.1 10
1 / 20 0.05 5
1 / 100 0.01 1
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