Chapter 3.2, Problem 60HP

To determine

To explain:The method of comparing and ordering fractions and decimals number using examples.

Explanation of Solution

In order to compare fractions, it is required to make denominators same of all fractions and then compare the numerators and arrange them in ascending or descending order.

In order to compare the decimal numbers, it is required to plot decimal numbers on a number line.

Example: $\frac{1}{2},\frac{3}{4}and\frac{1}{3}$ could be compare by taking least common denominator 12 and convert each denominator as 12.

  $\frac{1}{2}=\frac{6}{12},\frac{3}{4}=\frac{9}{12}and\frac{1}{3}=\frac{4}{12}\text{.}$

Now, if we compare the numerators 6, 9 and 4, we could see that 4 is the least number and middle number is 6 and greatest number is 9.So, we could arrange 6, 9 and 4 in ascending order as 4, 6, 9.

Therefore, $\frac{6}{12},\frac{9}{12},\frac{4}{12}$ could be arrange in ascending order as $\frac{4}{12}<\frac{6}{12}<\frac{9}{12}$ .

Now, replacing original fractions for $\frac{4}{12},\frac{6}{12},\frac{9}{12}$ we get final ascending order of given fractions as $\frac{1}{3}<\frac{1}{2}<\frac{3}{4}.$