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Now consider the numerators. The first fraction, two thirds, is twice as large as one third. Since one third of a quarter is one twelfth, two thirds of a quarter is two twelfth. The second fraction, three quarters, is three times as large as one quarter, so two thirds of three quarters is three times as large as two thirds of one quarter.
Once these strategies are eliminated for every player, 66 + 2 / 3 becomes the new highest possible average (that is, if everyone chooses 66 + 2 / 3 ). Therefore, any guess above 44 + 4 / 9 is weakly dominated for every player since no player will guess above 66 + 2 / 3 , and 2 / 3 of 66 + 2 / 3 is 44 ...
2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 2 ⁄ 5: 0.4 Vulgar Fraction Two Fifths 2156 8534 ⅗ 3 ⁄ 5: 0.6 Vulgar Fraction Three Fifths 2157 8535 ⅘ 4 ⁄ 5: 0.8 Vulgar Fraction Four Fifths 2158 8536 ⅙ 1 ⁄ 6: 0.166... Vulgar Fraction One Sixth 2159 8537 ⅚ 5 ⁄ 6: 0 ...
This system results in "two thirds" for 2 ⁄ 3 and "fifteen thirty-seconds" for 15 ⁄ 32. This system is normally used for denominators less than 100 and for many powers of 10 . Examples include "six ten-thousandths" for 6 ⁄ 10,000 and "three hundredths" for 0.03.
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
The most common tuplet [9] is the triplet (German Triole, French triolet, Italian terzina or tripletta, Spanish tresillo).Whereas normally two quarter notes (crotchets) are the same duration as a half note (minim), three triplet quarter notes have that same duration, so the duration of a triplet quarter note is 2 ⁄ 3 the duration of a standard quarter note.
Alternatively, and for greater numbers, one may say for 1 ⁄ 2 "one over two", for 5 ⁄ 8 "five over eight", and so on. This "over" form is also widely used in mathematics. Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 1 ⁄ 4 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths"
If the thousands digit is odd, the number formed by the last three digits must be 8 times an odd number. 3408: 408 = 8 × 51. Add the last two digits to four times the rest. The result must be divisible by 16. 176: 1 × 4 + 76 = 80, 1,168: 11 × 4 + 68 = 112. The last four digits must be divisible by 16. [2] [3] 157,648: 7,648 = 478 × 16. 17