Chapter SH, Problem 6.1.8EP

To determine

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

Answer to Problem 6.1.8EP

The required simplest form the fraction is $\frac{35}{3}$ .

Explanation of Solution

Given information:

The ratio = 140 dogs to 12 cats

Calculation:

The ratio can be expressed in the fraction as,

  $\frac{140}{12}$

To find the simplest form of the above fraction, find the greatest common factor of the numerator and denominator that is, 140 and 12.

  $140=2\times 2\times 5\times 7$

  $12=2\times 2\times 3$

Thus, the greatest common factor of 140 and 12 is $2\times 2=4$

Divide the numerator and the denominator of the fraction by 4.

  $\begin{array}{c}\frac{\frac{140}{4}}{\frac{12}{4}}=\frac{\frac{\cancel{140}}{\cancel{4}}}{\frac{\cancel{12}}{\cancel{4}}}\\ =\frac{35}{3}\end{array}$

Hence, the required simplest form the fraction is $\frac{35}{3}$ .