Chapter SH, Problem 6.1.5EP

To determine

To calculate: The fraction of the ratio in simplest form.

Answer to Problem 6.1.5EP

The required simplest form the fraction is $\frac{2}{5}$ .

Explanation of Solution

Given information:

The ratio = 18 boys out of 45 students

Calculation:

The ratio can be expressed in the fraction as,

  $\frac{18}{45}$

To find the simplest form of the above fraction, find the greatest common factor of the numerator and denominator that is, 18 and 45.

  $18=2\times 3\times 3$

  $45=3\times 3\times 5$

Thus, the greatest common factor of 18 and 45 is $3\times 3=9$

Divide the numerator and the denominator of the fraction by 9.

  $\begin{array}{c}\frac{\frac{18}{9}}{\frac{45}{9}}=\frac{\frac{\cancel{18}}{\cancel{9}}}{\frac{\cancel{45}}{\cancel{9}}}\\ =\frac{2}{5}\end{array}$

Hence, the required simplest form the fraction is $\frac{2}{5}$ .