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

$x = 1/15$

A cyclist takes part in a race with four stages. In the first stage he completes 5/125/12 of the entire course, in the second he complets 7/207/20 of the course 1/61/6 in the third . What fraction is the fourth stage?