Question

It takes $2\frac{3}{11}$ tons of bitumen to pave $5$ meters of road. How much of a road can be paved by using one ton of bitumen? (in meters)

• A. $\frac{5}{11}$
• B. $\frac{11}{5}$
• C. $\frac{125}{11}$

Answer 1

The correct option is B $\frac{11}{5}$

Road paved by $2\frac{3}{11}$ tons of bitumen = $5$ meter
Road paved by 1 ton of bitumen $=5÷2\frac{3}{11}$

First convert $2\frac{3}{11}$ to an improper fraction.

$2\frac{3}{11}=\frac{2\times 11+3}{11}=\frac{25}{11}$

$\therefore 5÷2\frac{3}{11}=5÷\frac{25}{11}$

Take a reciprocal of the second fraction and multiply that reciprocal by the first fraction as follows.

$=\frac{5}{1}\times \frac{11}{25}$

$=\frac{5\times 11}{1\times 25}$

$=\frac{55}{25}$

Now, we need to simplify the resulting fraction

$=\frac{5\times 11}{5\times 5}$

Cancel out the common factors of numerator and denominator of the fraction

$=\frac{11}{5}$

Hence, $\frac{11}{5}$ meters of road is paved by 1 ton of bitumen.