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1. Addition, Subtraction, Multiplication, Division for Two numbers
1. Find addition of 2760 and 796
 1 1 2 7 6 0 + 0 7 9 6 3 5 5 6
2. Find Subtraction of 2760 and 796
 16 15 10 1 6 5 0 2 7 6 0 - 0 7 9 6 1 9 6 4
3. Find multiplication of 2760 and 796
 2760 × 796 1932000 248400 16560 2196960
4. Find division of 276 and 6

6 |
 2 7 6
| 46
|
 2 4

|

|
 3 6

|
 3 6

|

|
 0

Here, Divisor = 6
Dividend = 276
Quotient = 46
Remainder = 0
 2. Pronounce a number In Indian currency format and Other currency format. In Indian currency format 12345678 = One Crore Twenty Three Lakh Forty Five Thousand Six Hundred Seventy Eight In Other currency format 12345678 = Twelve Million Three Hundred Forty Five Thousand Six Hundred Seventy Eight

3. Factors of a number
1. All Possible Factors of a number
Eg: All Possible factors of 456 are as follows...
1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

2. All Prime Factors of a number
Eg: Find Prime factors of 456

 2 | 456 | 2 | 228 | 2 | 114 | 3 | 57 | 19 | 19 | | 1

Or

456
= 2 × 228
= 2 × 2 × 114
= 2 × 2 × 2 × 57
= 2 × 2 × 2 × 3 × 19

Or

Prime factors in exponential form
= 23 × 31 × 191

Or

Prime factorization tree

 456 /  \ 2 228 /  \ 2 114 /  \ 2 57 /  \ 3 19
4. HCF and LCM of Two / Multiple Numbers
1. Find HCF, LCM of 30,50
Factor of 30,50 are as follows...
30 = 2 × 3 × 5
50 = 2 × 5 × 5

HCF = 2 × 5 = 10
LCM = 2 × 3 × 5 × 5 = 150

2. Find HCF of 30,50 using Division Method...

Find HCF of (30,50)

 1

30|
 5 0

|
 3 0

|

|
 2 0

 1

20|
 3 0

|
 2 0

|

|
 1 0

 2

10|
 2 0

|
 2 0

|

|
 0

∴ HCF of given nos (30,50) = 10

3. Find LCM of 30,50 using Division Method...

 2 | 30 -- 50 | 3 | 15 -- 25 | 5 | 5 -- 25 | 5 | 1 -- 5 | | 1 -- 1

LCM of 30,50 = 2 × 3 × 5 × 5 = 150

 5. Prime Numbers Prime numbers Gives you prime calculation in the following situation. 1. Check given number (45) is prime or not 45 is not prime. Because 45 is divisible by 3 2. Find the Nth (5th) prime number Prime : 5 = 11 3. Find all prime numbers between given two numbers (1 and 10) Prime:1 = 2 Prime:2 = 3 Prime:3 = 5 Prime:4 = 7 4. Find all prime numbers between Mth prime & Nth prime (1st prime and 10th prime) Prime:1 = 2 Prime:2 = 3 Prime:3 = 5 Prime:4 = 7 Prime:5 = 11 Prime:6 = 13 Prime:7 = 17 Prime:8 = 19 Prime:9 = 23 Prime:10 = 29
 6. Simplifying Numerical Expressions Simplifying Numerical Expressions : Gives you number crunching for a given numerical expressions with or without variables. Eg: Inupt Expression without variables is 4^2+(4+2)/2 * (5+2) = 4 2 + ( 4 + 2 ) / 2 × ( 5 + 2 ) = 16 + ( 4 + 2 ) / 2 × ( 5 + 2 ) = 16 + 6 / 2 × ( 5 + 2 ) = 16 + 3 × ( 5 + 2 ) = 16 + 3 × 7 = 16 + 21 = 37 Inupt Expression with variables is 4^2+(4+2)/2* (5+2)+s and Given Values are s=1 = 4 2 + ( 4 + 2 ) / 2 × ( 5 + 2 ) + 1 = 16 + ( 4 + 2 ) / 2 × ( 5 + 2 ) + 1 = 16 + 6 / 2 × ( 5 + 2 ) + 1 = 16 + 3 × ( 5 + 2 ) + 1 = 16 + 3 × 7 + 1 = 16 + 21 + 1 = 37 + 1 = 38

 7.1 Decimal To Fraction 1. For Non-Recurring number like 6.5 = 65/10 = (13 * 5)/(2 * 5) = 13/2 2. For Recurring number like 3.142857142857 = 22/7

 7.3 Rounding Numbers Rounding Numbers at several places like Round Off 744.636 at ten - 10 place = 740 744.636 at zero - 0 place = 745 744.636 at tenth - .01 place = 745.64
 8. Scientific Notation Conversion 1. Decimal number To Scientific notation like 0.008 = 8 × 10-3 2. Scientific notation To Decimal number like 8 × 10-3 = 0.008

 1.1 Reduced Terms Find Reduced terms of 63/6 (63)/(6) = (3 * 3 * 7)/(2 * 3) = (21)/(2)
 1.2 Improper Fraction To Mixed Number Find Improper Fraction to Mixed Number of 63/6 (63)/(6) = (3 * 3 * 7)/(2 * 3) = (21)/(2) = 10(1)/(2)

1.3 Fraction to decimal
Find Fraction to decimal of 1/8

(1)/(8) = (1 * 125)/(8 * 125) = (125)/(1000) = 0.125

 0 0.1 2 5

8|
 1 0 0 0

|
 8

|

|
 2 0

|
 1 6

|

|
 4 0

|
 4 0

|

|
 0

 2. Mixed Number To Improper Fraction Find Mixed Number to Improper Fraction of 3 4/5 3(4)/(5) = ((3 * 5) + 4)/(5) = (19)/(5)

 3. Compare Two Fraction Compare Two Fractions 3/4 and 4/5 Here, LCM of 4 and 5 = 20 3/4 = 15/20 4/5 = 16/20 15/20 < 16/20 so 3/4 < 4/5
 4. Addition, Subtraction, Multiplication and Division of Fraction Numbers Find 3/4 + 4/5 + 5/6 =(3)/(4)+(4)/(5)+(5)/(6) =(3 * 15 + 4 * 12 + 5 * 10)/(60) =(45 + 48 + 50)/(60) =(143)/(60)

10. Power: Square, Cube, Nth Power
1. Find Square of 100

 2 | 100 2 | 50 5 | 25 5 | 5 | 1

100
= 22 × 52
= 24 × 54 (Taking square)
= 10000
11. Radical: Square root, Cube root, Nth Root
1. Find Square Root of 100

 2 | 100 2 | 50 5 | 25 5 | 5 | 1

100
= 22 × 52
= 2 × 5 (Taking square root)
= 10

12. Square Root with all steps
1. Find Square Root of 4096 with all steps

 6 | 40 96 | 64 6 | 36 | 124 | 496 4 | 496 | 128 | 0 Dividend = 40 96 Square Root = 64 Remainder = 0
13. Cube Root with all steps
2. Find Cube Root of 4096 with all steps

 1 | 4 096 | 16 1 | 1 | 516 | 3096 516 = 300(=1^2 * 300) + 180(=1*30*6) + 36(=6^2) 6 | 3096 | --- | 0 Dividend = 4 096 CubeRoot = 16 Remainder = 0

12.1 Find the smallest no which must be Added from / to 180 to make it perfect Square

 1 | 1 80 | 13 1 | 1 | 23 | 80 3 | 69 | 26 | 11 Dividend = 1 80 Square Root = 13 Remainder = 11

∴ Number to be Added = 16
∴ Perfect Square No = 180 + 16 = 196
∴ √196 = 14
12.2 Find Least number of 4 digits which is a perfect Square

Least number of 4 digits = 1000
 3 | 10 00 | 31 3 | 9 | 61 | 100 1 | 61 | 62 | 39 Dividend = 10 00 Square Root = 31 Remainder = 39

∴ Number to be Added = 24
∴ Perfect Square No = 1000 + 24 = 1024
∴ √1024 = 32

 14. Divisibility test The given number is divisble by 2,4,8,16, 3,9, 5,10, 7,11,13,17,19,23,29 using divisibility rules 1. Check whether 100 is divisible by 2 or not?Last Digit of 100 is 0, which is divisible by 2 So 100 is divisible by 2 2. Check whether 123 is divisible by 3 or not? Sum of Digits of 123 is 6, which is divisible by 3 So 123 is divisible by 3
15. Number Series
Find the next number in the sequence
1. 3, 6, 18, 72, ___
2. 1, 3, 5, 7, 9, ___
3. 2, 4, 8, 16, 32, ___
4. 20, 19, 17, 14, 10, ___
5. 1, 4, 9, 16, 25, ___
6. 1, 9, 17, 33, 49, 73, ___
7. 10, 28, 82, 244, ___

1. Find Next Number in Series 3,6,18,72,?

The given series is 3,6,18,72,?

 3 6 18 72 360 xx2 xx3 xx4 xx5

:. The next number for given series 3,6,18,72 is 360

2. Find Next Number in Series 1,4,9,16,25,?

The given series is 1,4,9,16,25,?

Series are based on square of a number 1=1^2,4=2^2,9=3^2,16=4^2,25=5^2

:. The next number for given series 1,2,3,4,5 is 6

:. Next possible number is 6^2=36

:. The next number for given series 1,4,9,16,25 is 36

3. Find Next Number in Series 1,9,17,33,49,73,?

The given series is 1,9,17,33,49,73,?

 1 9 17 33 49 73 97 +8 +8 +16 +16 +24 +24

:. The next number for given series 1,9,17,33,49,73 is 97

 1. Angle to Degree, Minute & Second Conversion 1. Convert Angle 117.748 to Degree Minute & Second 117.748^circ = 117^circ + 0.748^circ = 117^circ + 0.748 xx (60')/(1 ^circ) = 117^circ + 44.88' = 117^circ + 44' + 0.88' = 117^circ + 44' + 0.88 xx (60text{"})/(1') = 117^circ + 44' + 52.8text{"} = 117^circ 44' 53text{"}
2. Degree Conversion

 "15 Radian"  xx ("180") / ("π") " = "  "15 Radian"  xx ("180") / ("3.1416") " = "  "859.4367 Degree"

 Degree = 859.437 Radian = 15

3. Length Conversion
kilometer to meter
meter to decimeter, centimeter
centimeter to millimeter
mile to yard
yard to feet, inches
foot to inches
inch to centimeters
any to any

1. Convert 10 Kilometers to Meters

 "10 kilometers"  xx ("1000 meters") / ("1 kilometer") " = "  "10000 meters"

 Kilometers = 10 Meters = 10000 Decimeters = 100000 Centimeters = 1e+06 Millimeters = 1e+07 Miles = 6.2137 Yards = 10936.1 Feet = 32808.4 Inches = 393701
4. Mass Conversion
kilogram to gram
gram to milligram,kilogram
metric ton to kilograms
metric ton to short ton
pound to ounces
kilogram to pounds
any to any

1. Convert 15 Kilograms to Grams

 "15 kilograms"  xx ("1000 grams") / ("1 kilogram") " = "  "15000 grams"

 Kilograms = 15 Grams = 15000 Milligrams = 1.5e+07 Metric tons = 0.015 Short Tons = 0.0165 Pounds = 33.069 Ounces = 529.104

5. Money Conversion
Rupee to Paise
Paise to Rupee

1. Convert 5 Rupees to Paise

 "5 Rupees"  xx ("100 Paise") / ("1 Rupees") " = "  "500 Paise"

 Rupees = 5 Paise = 500
6. Power Conversion
hoursepower to watt
watt to joule/second
hoursepower to joule/second
any to any

1. Convert 19 Horsepower to Watts

 "19 horsepower"  xx ("746 watts") / ("1 horsepower") " = "  "14174 watts"

 Horsepower = 19 Watt = 14174

7. Speed Conversion
Kilometer/Hour to Meter/Second
Kilometer/Hour to Mile/Second
Meter/Second to Kilometer/Hour
Miles/Hour to Feet/Hour
any to any

1. Convert 10 Kilometers/Hour to Meters/Second

("10 kilometer") / ("1 hour") xx ("1000 meters") / ("1 kilometer") xx ("1 hour") / ("3600 second") " = "  "2.7778 meters/second"

 kilometers/hour = 10 meters/hour = 10000 meters/second = 2.7778 miles/hour = 6.2137 feet/hour = 32808.3
8. Temperature Conversion
Celcius to Fernhit
Celcius to Kelvin
Fernhit to Celcius
any to any

1. Convert 19 C to F

We have Given, C = 19

We know that, F = (1.8 × C) + 32
=> F = (1.8 × 19) + 32
=> F = 34.2 + 32
=> F = 66.2

 Celcius = 19 Kelvin = 292.15 Fernhit = 66.2

9. Time Conversion
Year to Month
Month to Week
Week to Day
Day to Hour
Hour to Minute
Minute to Second
any to any

1. Convert 30 Days to Minutes

 "30 days"  xx ("24 hours") / ("1 day") xx ("60 minutes") / ("1 hour") " = "  "43200 minutes"

 Years = 0.0822 Months = 1 Weeks = 4.2857 Days = 30 Hours = 720 Minutes = 43200 Seconds = 2.592e+06
10. Volume Conversion
quart to pint
pint to cup
cup to fluid ounce
fluid ounce to cubic inch
cubic inches to cubic foot
cubic foot to liters
liter to milliliter, cubic decimeter
milliliter to cubic centimeter
any to any

1. Convert 17 Liters to Milliliters

 "17 liters"  xx ("1000 milliliters") / ("1 liter") " = "  "17000 milliliters"

 Gallons = 4.4904 Quarts = 17.9617 Pints = 35.9234 Cups = 71.8468 Fluid Ounces = 574.774 Cubic Inches = 1037.29 Cubic Feet = 0.6003 Liters = 17 Milliliters = 17000

1. Decimal to Binary
(42)10 = (__________)2
(124)10 = (__________)2
(24.625)10 = (__________)2
(42.5)10 = (__________)2

1. Convert Decimal number (42)10 to Binary number

(42)10 = (_______)2

 2 | 42 | 2 | 21 | 0 ↑ ↑ 2 | 10 | 1 ↑ ↑ 2 | 5 | 0 ↑ ↑ 2 | 2 | 1 ↑ ↑ 2 | 1 | 0 ↑ ↑ | 0 | 1 ↑

∴ (42)10 = (101010)2
2. Decimal to Octal
(425)10 = (__________)8
(1425)10 = (__________)8
(3445.865)10 = (__________)8
(1423.25)10 = (__________)8

1. Convert Decimal number (425)10 to Octal number

(425)10 = (_______)8

 8 | 425 | 8 | 53 | 1 ↑ ↑ 8 | 6 | 5 ↑ ↑ | 0 | 6 ↑

∴ (425)10 = (651)8

(1423)10 = (__________)16
(42356)10 = (__________)16
(4234.456)10 = (__________)16
(1234.567)10 = (__________)16

1. Convert Decimal number (1423)10 to Hexadecimal number

(1423)10 = (_______)16

 16 | 1423 | 16 | 88 | F ↑ ↑ 16 | 5 | 8 ↑ ↑ | 0 | 5 ↑

∴ (1423)10 = (58F)16
 4. Binary to Decimal (110101001)2 = (__________)10 (1100111101)2 = (__________)10 (11010.1001)2 = (__________)10 (11011.101001)2 = (__________)10 1. Convert Binary number (110101001)2 to Decimal number (110101001)2 = (_______)10110101001 = 1 × 20 + 0 × 21 + 0 × 22 + 1 × 23 + 0 × 24 + 1 × 25 + 0 × 26 + 1 × 27 + 1 × 28 = 1 × 1 + 0 × 2 + 0 × 4 + 1 × 8 + 0 × 16 + 1 × 32 + 0 × 64 + 1 × 128 + 1 × 256 = 425∴ (110101001)2 = (425)10

5. Binary to Octal
(11011001)2 = (__________)8
(11110101001)2 = (__________)8
(111101.01001)2 = (__________)8
(11110101.00101001)2 = (__________)8

1. Convert Binary number (11011001)2 to Octal number

(11011001)2 = (_______)8

 011 011 001 3 3 1

∴ (11011001)2 = (331)8
(11110101001)2 = (__________)16
(111101010110001)2 = (__________)16
(11110.101001)2 = (__________)16
(111101.1101001)2 = (__________)16

1. Convert Binary number (11110101001)2 to Hexadecimal number

(11110101001)2 = (_______)16

 0111 1010 1001 7 A 9

∴ (11110101001)2 = (7A9)16

 7. Octal to Decimal (1534)8 = (__________)10 (12340)8 = (__________)10 (127.32)8 = (__________)10 (432.12)8 = (__________)10 1. Convert Octal number (1534)8 to Decimal number (1534)8 = (_______)101534 = 4 × 80 + 3 × 81 + 5 × 82 + 1 × 83 = 4 × 1 + 3 × 8 + 5 × 64 + 1 × 512 = 860∴ (1534)8 = (860)10
8. Octal to Binary
(4321)8 = (__________)2
(12345)8 = (__________)2
(123.45)8 = (__________)2
(7012.053)8 = (__________)2

1. Convert Octal number (4321)8 to Binary number

(4321)8 = (_______)2

 4 3 2 1 100 011 010 001

∴ (4321)8 = (100011010001)2

(7012)8 = (__________)16
(123456)8 = (__________)16
(1234.567)8 = (__________)16
(703.056)8 = (__________)16

1. Convert Octal number (7012)8 to Hexadecimal number

First Method
(7012)8 = (_______)16

First Converting Base-8 to Base-2(7012)8 = (_______)2

 7 0 1 2 111 000 001 010

∴ (7012)8 = (111000001010)2

Now Converting Base-2 to Base-16(111000001010)2 = (_______)16

 1110 0000 1010 E 0 A

∴ (111000001010)2 = (E0A)16

∴ (7012)8 = (E0A)16

OR

Second Method
(7012)8 = (_______)16

First Converting Base-8 to Base-10(7012)8 = (_______)10

7012
= 2 × 80 + 1 × 81 + 0 × 82 + 7 × 83
= 2 × 1 + 1 × 8 + 0 × 64 + 7 × 512
= 3594
∴ (7012)8 = (3594)10

Now Converting Base-10 to Base-16(3594)10 = (_______)16

 16 | 3594 | 16 | 224 | A ↑ ↑ 16 | 14 | 0 ↑ ↑ | 0 | E ↑

∴ (3594)10 = (E0A)16
∴ (7012)8 = (E0A)16
(FC3A)16 = (__________)8
(ABCD)16 = (__________)8
(1524.03)16 = (__________)8
(BCF.52A)16 = (__________)8

1. Convert Hexadecimal number (FC3A)16 to Octal number

First Method
(FC3A)16 = (_______)8

First Converting Base-16 to Base-2(FC3A)16 = (_______)2

 F C 3 A 1111 1100 0011 1010

∴ (FC3A)16 = (1111110000111010)2

Now Converting Base-2 to Base-8(1111110000111010)2 = (_______)8

 001 111 110 000 111 010 1 7 6 0 7 2

∴ (1111110000111010)2 = (176072)8

∴ (FC3A)16 = (176072)8

OR

Second Method
(FC3A)16 = (_______)8

First Converting Base-16 to Base-10(FC3A)16 = (_______)10

FC3A
= A × 160 + 3 × 161 + C × 162 + F × 163
= 10 × 1 + 3 × 16 + 12 × 256 + 15 × 4096
= 64570
∴ (FC3A)16 = (64570)10

Now Converting Base-10 to Base-8(64570)10 = (_______)8

 8 | 64570 | 8 | 8071 | 2 ↑ ↑ 8 | 1008 | 7 ↑ ↑ 8 | 126 | 0 ↑ ↑ 8 | 15 | 6 ↑ ↑ 8 | 1 | 7 ↑ ↑ | 0 | 1 ↑

∴ (64570)10 = (176072)8
∴ (FC3A)16 = (176072)8

(A35)16 = (__________)2
(BBA)16 = (__________)2
(1085.FB)16 = (__________)2
(FC.3A)16 = (__________)2

1. Convert Hexadecimal number (A35)16 to Binary number

(A35)16 = (_______)2

 A 3 5 1010 0011 0101

∴ (A35)16 = (101000110101)2
 12. Hexadecimal to Decimal (7036)16 = (__________)10 (BCA)16 = (__________)10 (A0.36)16 = (__________)10 (100.35)16 = (__________)10 1. Convert Hexadecimal number (BCA)16 to Decimal number (BCA)16 = (_______)10BCA = A × 160 + C × 161 + B × 162 = 10 × 1 + 12 × 16 + 11 × 256 = 3018∴ (BCA)16 = (3018)10

13. Decimal to Other
(1536)10 = (__________)6
(5336)10 = (__________)14
(45236)10 = (__________)24
(155436)10 = (__________)18

1. Convert Decimal number (383)10 to Base 20 number (_______)20

(383)10 = (_______)20

 20 | 383 | 20 | 19 | 3 ↑ ↑ | 0 | J ↑

∴ (383)10 = (J3)20
 14. Other to Decimal (155436)7 = (__________)10 (BA012)12 = (__________)10 (GH012)20 = (__________)10 (1230321)4 = (__________)10 1. Convert (64X)35 means 64X where its Base 35 to Decimal number (64X)35 = (_______)1064X = X × 350 + 4 × 351 + 6 × 352 = 33 × 1 + 4 × 35 + 6 × 1225 = 7523∴ (64X)35 = (7523)10

 18. Tables 1. Addition table 2. Addition table 1 to 30 3. Multiplication table rows and columns 4. Multiplication table 1 to 30 5. Roman table 6. Square table 7. Cube table 8. Power table 9. Factorial table 10. Sin table 11. Cos table 12. Tan table 13. Sin, Cos, Tan table 14. Area formula 15. Volume formula 16. Factors formula 17. Number system conversion table

 6. Place Value Place Value Gives you the place value of a number in the given number Eg:- Given number = 123456 and find place value = 3 then We have given no is 123456 and the place value of 3 is (3 × 1000) = 3000
 7. Leap Year Leap Year Gives you the given year is leap year or not. Eg:- Year = 2005 is not a leap year. Also gives the list of leap years between given two years. Eg:- Find Leap Years between the years 1955 and 2055 Leap Years Between the years 1955 and 2055 are given below... 1 : 1956 2 : 1960 3 : 1964 4 : 1968 5 : 1972 6 : 1976 7 : 1980 8 : 1984 9 : 1988 10 : 1992 11 : 1996 12 : 2000 13 : 2004 14 : 2008 15 : 2012 16 : 2016 17 : 2020 18 : 2024 19 : 2028 20 : 2032 21 : 2036 22 : 2040 23 : 2044 24 : 2048 25 : 2052

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