Chapter 6.1, Problem 30PPS

To determine

To compare: Following two ratios: (i) 8 girls out of 18 students (ii) 12 girls out of 22 students

Answer to Problem 30PPS

Ratio of 8 girls out of 18 students is less than the ratio of 12 girls out of 22 students, or,

  $\frac{4}{9}<\frac{6}{11}$(both ratios are taken in simplest form)

Explanation of Solution

Given information:Two ratios (i) 8 girls out of 18 students (ii) 12 girls out of 22 students.

Concept used: Each ratio will give a fraction and to compare them, their denominators are made equal by multiplying each fraction up and down by the denominator of other fraction.

Calculation: So, ratio of 8 girls out of 18 students $=\frac{8}{18}=\frac{4}{9}$

And ratio of 12 girls out of 22 students $=\frac{12}{22}=\frac{6}{11}$

Again $\frac{4}{9}=\frac{4\times 11}{9\times 11}=\frac{44}{99}$

And $\frac{6}{11}=\frac{6\times 9}{9\times 11}=\frac{54}{99}$

Conclusion: On observing the numerators of both fractions, when their denominators are same, it is found that $\frac{4}{9}<\frac{6}{11}$