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Mathematics

What is mathematics? Mathematics is the study of quantity, structure, space, and change. What is the difference between math, maths, and mathematics? Math is a synonym of mathematics. Maths is a primarily British term for math. What are the subdivisions of mathematics? Mathematics can be subdivided broadly into the study of quantity, structure, space, and change (i.e., arithmetic, algebra, geometry, and mathematical analysis). 1. Arithmetic 2. Algebra 3. Geometry 4. Mathematical analysis 5. Other There are at least 1,000 mathematics topics, and each fits into one or more of these mathematical subdivisions. Where is math useful? 1. Everyday life 2. Natural science 3. Engineering 4. Medicine 5. Social sciences 6. Applied mathematics 7. Computer Science 8. Cryptography 9. Economics and Mathematics 10. Other What is a number? A number is a mathematical object used to count, label, and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

Counting Chart: Numbers 1 to 100

1 one

2 two

3 three

4 four

5 five

6 six

7 seven

8 eight

9 nine

10 ten

11 eleven

12 twelve

13 thirteen

14 fourteen

15 fifteen

16 sixteen

17 seventeen

18 eighteen

19 nineteen

20 twenty

21 twenty- one

22 twenty- two

23 twenty- three

24 twenty- four

25 twenty- five

26 twenty- six

27 twenty- seven

28 twenty- eight

29 twenty- nine

30 thirty

31 thirty- one

32 thirty- two

33 thirty- three

34 thirty- four

35 thirty- five

36 thirty- six

37 thirty- seven

38 thirty- eight

39 thirty- nine

40 forty

41 forty- one

42 forty- two

43 forty- three

44 forty- four

45 forty- five

46 forty- six

47 forty- seven

48 forty- eight

49 forty- nine

50 fifty

51 fifty- one

52 fifty- two

53 fifty- three

54 fifty- four

55 fifty- five

56 fifty- six

57 fifty- seven

58 fifty- eight

59 fifty- nine

60 sixty

61 sixty- one

62 sixty- two

63 sixty- three

64 sixty- four

65 sixty- five

66 sixty- six

67 sixty- seven

68 sixty- eight

69 sixty- nine

70 seventy

71 seventy- one

72 seventy- two

73 seventy- three

74 seventy- four

75 seventy- five

76 seventy- six

77 seventy- seven

78 seventy- eight

79 seventy- nine

80 eighty

81 eighty- one

82 eighty- two

83 eighty- three

84 eighty- four

85 eighty- five

86 eighty- six

87 eighty- seven

88 eighty- eight

89 eighty- nine

90 ninety

91 ninety- one

92 ninety- two

93 ninety- three

94 ninety- four

95 ninety- five

96 ninety- six

97 ninety- seven

98 ninety- eight

99 ninety- nine

100 one hundred

200 two hundred

900 nine hundred

1,000 one thousand

2,000 two thousand

10,000 ten thousand

11,000 eleven thousand

20,000 twenty thousand

21,000 twenty-one thousand

30,000 thirty thousand

85,000 eighty-five thousand

100,000 one hundred thousand or one lakh

999,000 nine hundred and ninety-nine thousand nine hundred ninety-nine thousand

1,000,000 one million

10,000,000 ten million or one crore

Value	Name
0	Zero
1	One
2	Two
3	Three
4	Four
5	Five
6	Six
7	Seven
8	Eight
9	Nine
10	Ten
11	Eleven
12	Twelve
13	Thirteen
14	Fourteen
15	Fifteen
16	Sixteen
17	Seventeen
18	Eighteen
19	Nineteen
20	Twenty
21	Twenty-one
22	Twenty-two
23	Twenty-three
24	Twenty-four
25	Twenty-five
26	Twenty-six
27	Twenty-seven
28	Twenty-eight
29	Twenty-nine
30	Thirty
31	Thirty-one
40	Forty
50	Fifty
60	Sixty
70	Seventy
80	Eighty
87	Eighty-seven
90	Ninety
100	One hundred

101	One hundred [and] one
110	One hundred [and] ten
111	One hundred [and] eleven
120	One hundred [and] twenty
121	One hundred [and] twenty-one
144	One hundred [and] forty-four
169	One hundred [and] sixty-nine
200	Two hundred
300	Three hundred
400	Four hundred
500	Five hundred
600	Six hundred
666	Six hundred [and] sixty-six
700	Seven hundred
777	Seven hundred [and] seventy-seven
800	Eight hundred
900	Nine hundred
1 000	One thousand
1 001	One thousand [and] one
1 010	One thousand [and] ten
1 011	One thousand [and] eleven
1 024	One thousand [and] twenty-four
1 100	One thousand one hundred
1 101	One thousand one hundred [and] one
1 728	One thousand seven hundred [and] twenty-eight
2 000	Two thousand
3 000	Three thousand
10 000	Ten thousand
100 000	One hundred thousand (lakh)
500 000	Five hundred thousand
1 000 000	One million
1 048 576	One million forty-eight thousand five hundred [and] seventy-six
10 000 000	Ten million (crore)
100 000 000	One hundred million

How high can you count?

1 - One 10 - Ten 100 - One hundred 1,000 - One thousand 10,000 - Ten thousand 100,000 - One hundred thousand 1,000,000 - One million 10,000,000 - Ten million 100,000,000 - One hundred million 1,000,000,000 - One billion

Looking at the Words

Examples: 3 - Three 23 - Twenty-three 423 - Four hundred twenty-three (you could already do this) 1,423 - One thousand four hundred twenty-three (1 and 423) 7,423 - Seven thousand four hundred twenty-three (7 and 423) 37,423 - Thirty-seven thousand four hundred twenty-three (37 and 423) 637,423 - Six hundred thirty-seven thousand four hundred twenty-three (637 and 423) 5,637,423 - Five million six hundred thirty-seven thousand four hundred twenty-three (5 and 637 and 423)

1 Crore (1,00,00,000) ------ 100 Lakhs 1 Lakh (1,00,000) ------ 0.01 Crores 1 Million (1,000,000) ------ 0.1 Crores 1 Crore (1,00,00,000) ------ 10 Million 1 Billion (1,000,000,000) ------ 100 Crores 1 Crore (1,00,00,000) ------ 0.01 Billion

Cardinal Numbers 0 zero 1 one 2 two 3 three 4 four 5 five 6 six 7 seven 8 eight 9 nine 10 ten Ordinal Numbers 1st first 2nd second 3rd third 4th fourth 5th fifth 6th sixth 7th seventh 8th eighth 9th ninth 10th tenth

How could arithmetic handle two numbers? Let's use 2 and 5 as sample numbers. - Addition: 2 + 5 = 7 - Subtraction: 5 - 2 = 3 - Multiplication: 5 x 2 = 10 - Division: 6 ÷ 2 = 3 What is Addition? Addition puts values together. It's about bringing things from one area and combining them with another. It could be as simple as adding two (2) books to a stack of four (4) books. You wind up with a stack of six (6) books. It could also be as complex as assigning the masses of planets to determine the forces of gravity at different points in the solar system. Terms that tell you addition is happening: Put them together. Add them up. Combine them. Group them. This plus that. This and that.   0+0=0  0+1=1  0+2=2  0+3=3  0+4=4  0+5=5   1+0=1  1+1=2  1+2=3  1+3=4  1+4=5  1+5=6   2+0=2  2+1=3  2+2=4  2+3=5  2+4=6  2+5=7   3+0=3  3+1=4  3+2=5  3+3=6  3+4=7  3+5=8   4+0=4  4+1=5  4+2=6  4+3=7  4+4=8  4+5=9   5+0=5  5+1=6  5+2=7  5+3=8  5+4=9  5+5=10   6+0=6  6+1=7  6+2=8  6+3=9  6+4=10   7+0=7  7+1=8  7+2=9  7+3=10   8+0=8  8+1=9  8+2=10   9+0=9  9+1=10 10+0=10 8 + 5 = 13   3 + 9 = 12   5 + 9 = 14   6 + 8 = 14   7 + 9 = 16   9 + 6 = 15   7 + 6 = 13   8 + 6 = 14   6 + 5 = 11   8 + 4 = 12   3 + 8 = 11   5 + 8 = 13   9 + 4 = 13   7 + 4 = 11   6 + 6 = 12   4 + 9 = 13   4 + 8 = 12   6 + 9 = 15   8 + 9 = 17   4 + 7 = 11   5 + 7 = 12   6 + 7 = 13   9 + 3 = 12   9 + 2 = 11   7 + 7 = 14   7 + 8 = 15   9 + 5 = 14   9 + 8 = 17   7 + 5 = 12   2 + 9 = 11   9 + 7 = 16   8 + 7 = 15   5 + 6 = 11   8 + 3 = 11   8 + 8 = 16   9 + 0 = 9   8 + 0 = 8   0 + 6 = 6   0 + 3 = 3   0 + 0 = 0 Addition of Chains Addition of Equations Addition of Functions Addition of Numbers Addition of Sets Addition of Shapes Addition of Spaces Addition of Strings Addition of Vectors Here are further guidelines.

What is Subtraction? If addition is the act of putting things together, subtraction is about taking things away. It could be as simple as eating two (2) apples from a pile of six (6) apples. You would wind up with four (4) apples left over. It could also be as complex as figuring out the number of organisms that die each year in a specific ecosystem. Terms that tell you subtraction is happening: Take some away. Subtract an amount. Lose some. This minus that. Give up some. Examples: 1 - 1 = 0 2 - 1 = 1 2 - 2 = 0 5 - 1 = 4 5 - 2 = 3 5 - 3 = 2 5 - 4 = 1 5 - 5 = 0 9 - 1 = 8 9 - 2 = 7 9 - 3 = 6 9 - 4 = 5 9 - 5 = 4 9 - 6 = 3 9 - 7 = 2 9 - 8 = 1 9 - 9 = 0

What is Multiplication? 3 × 6 = 18. 6 × 3 = 18. 7 × 4 = 28. 7.2 × 10 = 72. 6 × 4 = 24   5 × 4 = 20   7 × 4 = 28   7 × 7 = 49   9 × 8 = 72   9 × 3 = 27   7 × 5 = 35   9 × 9 = 81   6 × 3 = 18   9 × 5 = 45   8 × 4 = 32   6 × 8 = 48   3 × 9 = 27   4 × 6 = 24   4 × 5 = 20   5 × 7 = 35   4 × 7 = 28   3 × 6 = 18   4 × 3 = 12   7 × 8 = 56   8 × 7 = 56   8 × 3 = 24   6 × 7 = 42   8 × 9 = 72   5 × 8 = 40   5 × 6 = 30   3 × 4 = 12   4 × 8 = 32   5 × 5 = 25   5 × 9 = 45   8 × 6 = 48   8 × 5 = 40   9 × 6 = 54   6 × 9 = 54   7 × 9 = 63   6 × 5 = 30   9 × 7 = 63   9 × 4 = 36   6 × 6 = 36   3 × 8 = 24   3 × 7 = 21   7 × 3 = 21   8 × 8 = 64   3 × 5 = 15   5 × 3 = 15   7 × 6 = 42   4 × 9 = 36   4 × 4 = 16 What comes after multiplication in math? Division.

What is Division? Division is the opposite of multiplication. It's a method of making equal groups. The division sign resembles a dash or double dash with a dot above and a dot below (÷). It is equivalent to the words "divided by." Mathematically, the division sign is equivalent to the forward slash. 18 ÷ 6 = 3. 18 ÷ 3 = 6. 15 ÷ 3 = 5. 72 ÷ 10 = 7.2