where do we get the answer for (1 - 1/6) + (1/2 - 1/7) + (1/3 - 1/8) + (1/95 - 1/100) =

Question

steps in solving

Answer 1

Work out each bracket:

1-1/6=(6-1)/6=5/6; 1/2-1/7=(7-2)/14=5/14; 1/3-1/8=(8-3)/24=5/24; 1/95-1/100=(100-95)/9500=5/9500=1/1900 or 1/95-1/100=(20-19)/1900=1/1900.

So now we have: 5/6+5/14+5/24+1/1900; 6=2*3; 14=2*7; 24=2*2*2*3; 1900=2*2*5*5*19. The LCM must be a product that contains 2*2*2*3*5*5*7*19. In this LCM we can see the factors we need to get 6, 14, 24 and 1900. The LCM=79800. So we have: (5*13300+5*5700+5*3325+42)/79800=(66500+28500+16625+42)/79800=(95000+16667)/79800=111667/79800=1 31867/79800 or 1.399336 approx.