# 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?

Mar 8, 2018

$\frac{1}{15}$

#### Explanation:

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

$\frac{5}{12} + \frac{7}{20} + \frac{1}{6} + x = 1$ Use 60 as a common denominator

$\frac{5 \times 5}{5 \times 12} + \frac{3 \times 7}{3 \times 20} + \frac{10 \times 1}{10 \times 6} + x = 1$ so

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

$\frac{56}{60} + x = 1$ subtract 56/60 from both sides

$\frac{56}{60} - \frac{56}{60} + x = 1 - \frac{56}{60}$ Change 1 to$\frac{60}{60}$

$x = \frac{60}{60} - \frac{56}{60}$

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

$x = \frac{\frac{4}{4}}{\frac{60}{4}}$ which gives

$x = \frac{1}{15}$