Can you sove this?
BODMAS
To simplify
arithmetic and algebraic expressions, we use the BODMAS method. We should carry
out the operation in the order of each letters of the word BODMAS where;
B Bracket [{()}]
O Of of
D Division /
M Multiplication X
A Addition +
S Subtraction -
Example:
12 – 4 x 5 +
4 + 8 = 12-4x5+4+8
=12-20+4+8
=24-20
=4
Units of measurement
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Measure of capacity
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10
milliliters = 1 centiliter
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10
centiliters = 1 deciliter
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10
deciliters = 1 liter
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10
liters = 1 decaliter
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10
decaliters = 1 hectoliter
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10
hectoliters = 1 kiloliter
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Measure of area
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100
square millimeters = 1 square centimeter
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100
square centimeters = 1 square decimeter
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100
square decimeters = 1 square meter
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100
square meter = 1 square decameters
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100
square decameters = 1 square hectometer
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100
square hectometers = 1 square kilometer
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1
hectare = 10,000 square meter
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Measure of volume
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1000
cubic millimeters = 1 cubic centimeter
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1000
cubic centimeter = 1 cubic decimeter
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1000
cubic decimeter = 1 cubic meter
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1000
cubic meters = 1 cubic decameter
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1000
cubic decameters = 1 cubic hectometer
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1000
cubic hectometers = 1 cubic kilometer
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Measure of length
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10
millimeters (mm) = 1 centimeter (cm)
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10
centimeters = 1 decimeter (dm)
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10
decimeters = 1 meter (m)
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10
meters = 1 decameter (da.m)
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10
decameters = 1 hectometer (hm)
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10
hectometers = 1 kilometer (Km)
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Measure of weight
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10
milligrams = 1 centigram
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10
centigrams = 1 decigram
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10
decigrams = 1 gram
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10
grams = decagram
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10
decagrams = 1 hectogram
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10
hectograms = 1 kilogram
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100
kilograms = 1 quintal
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10
quintals or 1000 kg = 1 metric ton
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Measure of time
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60
seconds = 1 minute
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60
minutes = 1 hour
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24
hours = 1 day
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7
days = 1 week
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15
days = 1 fortnight
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12
months = 1 year
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365
days = 1 year
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366
days = 1 leap year
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1
year = anniversary
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10
years = decade
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25
years = silver jubilee
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50
years = golden jubilee
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60
years = diamond jubilee
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75
years = platinum jubilee
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100
years = century
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1000
years = millennium
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Ramanujan number
1729
1729 is the natural number following 1728 and preceding 1730. 1729 is known as the Hardy- Ramanujan number after a famous anecdote of the British mathematician G.H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. As told by Hardy; " I remember once going to see him ( Ramanujan) when he was lying ill at Putney. i had ridden in taxi cab No. 1729, and remarked that the number seemed to be rather a dull one, and that i hoped it was not an favorable omen. "NO", he replied, "it is a very interesting number, it is the smallest number expressible as the sum of two [positive] cubes in two different ways." the number was also found in one of Ramanujan's notebooks dated years before the incident.some of the properties of 1729:
1. it can be represent as a product of 3 distinct prime numbers.
2. 1729 is divisible by sum of its digits. Hence its a Harshad number. 1729/19=91
3. 1729 is the smallest number expressible as the sum of two positive cubes in two different ways. the different ways are ;1729 = 13 + 123 = 93 + 103.
4.1729 is the third Carmichael number and the first absolute Euler pseudo prime.
5. 1729 is a Zeisel number. it is a centered cube number, as well as a dodecagonal number.
6. 1729 is one of four positive integer which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number.
1+ 7 + 2 + 9 = 19
19 x 91 =1729
Srinivasa Ramanujan
Birth
Srinivasa Ramanujan, an Indian mathematician was born in 22nd December, 1887 in Madras, India.
Like Sophie Germain,
he received no formal education in mathematics but made important contributions
to advancement of mathematics.
Contribution to Mathematics
His chief contribution in mathematics lies
mainly in analysis, game theory and infinite series. He made in depth analysis
in order to solve various mathematical problems by bringing to light new and
novel ideas that gave impetus to progress of game theory. Such was his
mathematical genius that he discovered his own theorems. It was because of his
keen insight and natural intelligence that he came up with infinite series for
Ï€.This series made up the basis of certain
algorithms that are used today. One such remarkable instance is when he solved
the bivariate problem of his roommate at spur of moment with a novel answer
that solved the whole class of problems through continued fraction. Besides
that he also led to draw some formerly unknown identities such as by linking
coefficients of and providing identities for hyperbolic secant.
He also described in detail the mock theta
function, a concept of mock modular form in mathematics. Initially, this
concept remained an enigma but now it has been identified as holomorphic parts
of mass forms. His numerous assertions in mathematics or concepts opened up new
vistas of mathematical research for instance his conjecture of size of tau function
that has distinct modular form in theory of modular forms. His papers became an
inspiration with later mathematicians such as G. N. Watson, B. M. Wilson and
Bruce Berndt to explore what Ramanujan discovered and to refine his work. His
contribution towards development of mathematics particularly game theory
remains unrivaled as it was based upon pure natural talent and enthusiasm. In
recognition of his achievements, his birth date 22 December is celebrated in
India as Mathematics Day. It would not be wrong to assume that he was first
Indian mathematician who gained acknowledgment only because of his innate
genius and talent.
His Publications
It was after his first publication in the
“Journal of the Indian Mathematical Society” that he gained recognition as
genius mathematician. With collaboration of English mathematician G.H. Hardy, with whom he
came in contact with during his visit to England, he brought forward his
divergent series that later stimulated research in that given area thus
refining the contribution of Ramanujan. Both also worked on new asymptotic
formula that gave rise to method of analytical number theory also called as
“Circle Method” in mathematics.
It was during his visit to England that he got
worldwide recognition after publication of his mathematical work in European
journals. He also achieved the distinction of becoming second Indian, who was
elected as Fellow of Royal Society of London in 1918.
Death
He died on 26 April 1920 at hands of dreadful disease of tuberculosis. Although he couldn’t get recognition of world at large but in field of mathematics, his contribution is duly recognized.
Composite numbers & Co-prime
Composite
number:
A number
greater than one and not a prime number is a composite number.
Co-prime:
Two numbers ‘a’ and ‘b’ are said to
be co-prime if the only common divisor of ‘a’ and ‘b’ is 1.
Prime numbers:
A positive integer p is considered a prime number, if p greater than 1 and p does not have factors other than 11 and p.
Prime numbers up to 500;
2
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3
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5
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7
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11
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13
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17
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19
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23
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29
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31
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37
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41
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43
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47
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53
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59
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61
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67
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71
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73
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79
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83
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89
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97
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101
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103
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107
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109
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113
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127
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131
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137
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139
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149
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151
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157
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163
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167
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173
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179
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181
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191
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193
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197
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199
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211
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223
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227
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229
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233
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239
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241
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251
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257
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263
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269
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271
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277
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281
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283
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293
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307
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311
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313
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317
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331
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337
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347
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349
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353
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359
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367
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373
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379
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383
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389
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397
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401
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409
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419
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421
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431
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433
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439
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443
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449
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457
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461
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463
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467
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479
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487
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491
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499
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Properties of arithmetics
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