# Question #a3315

Sep 9, 2016

$\frac{3}{10}$

#### Explanation:

The only thing that is a bit confusing in this question is that we have to make a fraction using values that are already fractions.
If it had been a 1 mile straight section of a 4 mile circuit we would have been happy to give the fraction as $\frac{1}{4}$

The fraction will be $\frac{1 \frac{3}{4}}{5 \frac{5}{6}}$ But now to simplify that...

Method 1 $\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times}$ Method 2

$1 \frac{3}{4} \div 5 \frac{5}{6}$$\textcolor{w h i t e}{\times \times \times \times \times \times}$ note that $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a d}{b c}$

=$\frac{7}{4} \div \frac{35}{6}$$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times} \frac{\frac{7}{4}}{\frac{35}{6}} = \frac{7 \times 6}{4 \times 35}$

=$\frac{\cancel{7}}{\cancel{4}} ^ 2 \times {\cancel{6}}^{3} / {\cancel{35}}^{5} \textcolor{w h i t e}{\times \times \times \times \times \times \times} = \frac{\cancel{7}}{\cancel{4}} ^ 2 \times {\cancel{6}}^{3} / {\cancel{35}}^{5}$

=$\frac{3}{10} \textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times} = \frac{3}{10}$

(This is the same as saying that 30% of the circuit is straight)