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For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4 , or 20 / 5 = 4 . [ 2 ] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient.
1 / 6 45 / 32 and 64 / 45 (tritones) 32 / 55 −0.188801 9 / 5 = 1.80 55 1 / 5 16 / 15 and 15 / 8 (diatonic semitone and major seventh) 25 / 43 +0.0206757 7 / 4 = 1.75 43 1 / 4 5 / 4 and 8 / 5
6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.
A flat roof includes pitches as low as 1 ⁄ 2:12 to 2:12 (1 in 24 to 1 in 6), which are barely capable of properly shedding water. Such low-slope roofs (up to 4:12 (1 in 3)) require special materials and techniques to avoid leaks. [4] Conventional describes pitches from 4:12 (1 in 3) to 9:12 (3 in 4). [4]
For example, the ratio 4:5 can be written as 1:1.25 (dividing both sides by 4) Alternatively, it can be written as 0.8:1 (dividing both sides by 5). Where the context makes the meaning clear, a ratio in this form is sometimes written without the 1 and the ratio symbol (:), though, mathematically, this makes it a factor or multiplier .
This just ratio is also the difference between a minor third (6:5) and septimal minor third (7:6). Composer Ben Johnston , to accommodate the just septimal quarter tone, uses a small "7" ( ) as an accidental to indicate a note is lowered 49 cents, or an upside down " 7 " ( ) to indicate a note is raised 49 cents, [ 5 ] or a ratio of 36:35. [ 6 ]
The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯.The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...
Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n.It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number.