To calculate this sort of subtraction problem the two fractions have to be converted so that they share the same denominator - the number below the line.
This is done by calculating the lowest common denominator they share. As 11 is a prime and 63 is not a multiple of it, then the lowest common denominator will be 63 x 11 = 693.
* To convert the 46/63 to a fraction with 693 as its denominator we need to multiply both the numerator and the denominator by 11. This gives 506/693. * To convert the 3/11 to a fraction with 693 as its denominator we need to multiply both the numerator and the denominator by 63. This gives 189/693.
Now we can subtract 189 from 506. That gives 317.
* 317/693
As 317 is a prime, and 693 is not a multiple of it, that fraction can not be simplified.
(63/7) / (22/14) = (63/11) meaning that it equals 63 over 11
63/11 - 310/11 = 26/11 or 24/11
3, with 11 left over.
For 63 it is 3 and 7. For 99 it is 3 and 11.
(Assuming 100 is 100 degrees)cos 100 degrees is equal to - sin 10 degrees.In radians, this is - sin (pi/18).Approximating pi as 22/7, this is - sin (11/63)Using four terms of a Taylor series, this is approximately:- (11/63) + (11/63)^3 /6 - (11/63)^5 / 120 + (11/63)^7 / 5040.- (11/63) + (11^3/63^3) /6 - (11^5/63^5) / 120 + (11^7/63^7) / 5040.Rewriting the fractions with the common denominator 63^7:- (11*63^6/63^7) + (11^3*63^4/63^7) /6 - (11^5*63^2/63^7) / 120 + (11^7/63^7) / 5040.Rewriting again with common denominators of 5040:- 5040*(11*63^6/63^7)/5040 + 840*(11^3*63^4/63^7)/5040 - 42*(11^5*63^2/63^7) / 5040 + (11^7/63^7) / 5040.Now add it all up:[- 5040*11*63^6 + 840*11^3*63^4 - 42*11^5*63^2 + 11^7] / (5040*63^7)Now, some seriously long multiplication gives:(- 3466302962466960 + 17612440516440 - 26846879598 + 19487171) / 19852462421401680Some really easy addition:-3448717349342947 / 19852462421401680And finally, do the long division:-0.17371735939 ... and so on.The actual value is -0.17364817766693034885171662676931So, I got 3 decimal places right. Maybe use a better approximation of pi (like 355/113) and more terms of the Taylor series. But you get the picture.
21 = 3 x 7 85 = 5 x 17 63 = 32 x 7 46 = 2 x 23
46/3
3/7 = 27/635/9 = 35/6327/63 - 35/63 = -8/63
21/63 = 1/3
21
63/147 = 3/7
3/4