Chapter 6.5, Problem 23E

To determine

To calculate:the order of ratios $15to9,35:25,\frac{44}{33},\frac{22}{20},8:3$ from least to greatest.

Answer to Problem 23E

The order of the ratios $15to9,35:25,\frac{44}{33},\frac{22}{20},8:3$ from least to greatest is $22:20,44:33,35:25,15:9,8:3$ .

Explanation of Solution

Given information :

  $15to9,35:25,\frac{44}{33},\frac{22}{20},8:3$ .

Calculation : to find the order of ratios from least to greatest , first write the ratio in the form of fraction then arrange in the order,

  $\frac{15}{9},\frac{35}{25},\frac{44}{33},\frac{22}{20},\frac{8}{3}$

First equal the denominator,

  $\begin{array}{l}\frac{15}{9},\frac{35}{25},\frac{44}{33},\frac{22}{20},\frac{8}{3}\\ \frac{5}{3},\frac{7}{5},\frac{4}{3},\frac{11}{10},\frac{8}{3}\text{ [simplify]}\\ \frac{50}{30},\frac{42}{30},\frac{40}{30},\frac{33}{30},\frac{80}{30}\text{ [equal the denominator]}\end{array}$

In order of least to greatest ,

  $\frac{22}{20}<\frac{44}{33}<\frac{35}{25}<\frac{15}{9}<\frac{8}{3}$

  $22:20,44:33,35:25,15:9,8:3$

Hence,The order of the ratios $15to9,35:25,\frac{44}{33},\frac{22}{20},8:3$ from least to greatest is $22:20,44:33,35:25,15:9,8:3$ .