Sohan decided to clean his school campus and asked his friend to help him. they agreed to clean 1/3,1/7,1/6 and 1/4 part of the campus. how much part of the campus will be left for sohan?
Answers
(3 / 28) parts of the campus will be left for sohan to clean.
• Let the total campus of the school be taken as 1.
• Given,
Parts of the campus cleaned by Sohan's friends = (1 / 3), (1 / 7), (1 / 6), and (1 / 4)
Therefore, total fraction of the campus cleaned by Sohan's friends = (1 / 3) + (1 / 7) + (1 / 6) + (1 / 4)
• L.C.M. of the denominators 3, 7, 6, and 4 = 84
Now,
[ {1 × (84 / 3)} + {1 × (84 / 7)} + {1 × (84 / 6)} + {1 × (84 / 4)} ] / 84
= { (1 × 28) + (1 × 12) + (1 × 14) + (1 × 21) } / 84
= ( 28 + 12 + 14 + 21 ) / 84
= 75 / 84
= 25 / 28
Therefore, part of the campus cleaned by Sohan's friends = 25 / 28
• Now, part of the campus left for Sohan to clean = Total campus - Part of the campus already cleaned by his friends
=> Part of the campus left for Sohan to clean = 1 - (25 / 28)
= { (1 × 28) - 25 } / 28
= (28 - 25) / 28
= 3 / 28
Therefore, Sohan has to clean (3 / 28) parts of the campus.