A cyclist takes part in a race with four stages. In the first stage he completes #5/12# of the entire course, in the second he complets #7/20# of the course #1/6# in the third . What fraction is the fourth stage?

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Answer 1 · 2018-03-08T16:56:07

# 1/15#

To solve find a common denominator so that all the fractions can be added.

# 5/12+ 7/20 + 1/6 + x = 1 # Use 60 as a common denominator

# ( 5 xx 5)/( 5 xx 12) + (3 xx 7)/(3 xx20) +(10xx 1)/(10xx6) + x = 1# so

# 25/60 + 21/60 + 10/60 + x = 1 add the numerators to give

# 56/60 + x = 1 # subtract 56/60 from both sides

# 56/60 - 56/60 + x = 1 - 56/60# Change 1 to# 60/60 #

# x = 60/60 -56/60#

# x = 4/60 divided both the denominator and numerator by 4

# x = (4/4) / ( 60/4)# which gives

# x = 1/15 #