Chapter 0.4, Problem 8E

To determine

To calculate: The order of set of rational numbers $2\frac{1}{4},1\frac{7}{8},1.75,2.4$ from least to greatest.

Answer to Problem 8E

The correct order of rational numbers from least to greatest is $1.75<1\frac{7}{8}<2\frac{1}{4}<2.4$ .

Explanation of Solution

Given information:

The set of rational numbers $2\frac{1}{4},1\frac{7}{8},1.75,2.4$ .

Formula used:

Rational numbers are of the form $\frac{p}{q}$ where p and q are integers and $\text{q}\ne \text{0}$ .

Mixed fractions of the form $m\frac{p}{q}$ can be converted into proper fractions as,

  $m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

Calculation:

Consider the provided statement “ The set of rational numbers $2\frac{1}{4},1\frac{7}{8},1.75,2.4$ .”

Recall that the mixed fractions can be converted into proper fractions as,

  $m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

So, $2\frac{1}{4}$ will be written as,

  $\begin{array}{c}2\frac{1}{4}=\frac{\left(2\times 4\right)+1}{4}\\ 2\frac{1}{4}=\frac{9}{4}\end{array}$

And, $1\frac{7}{8}$ will be written as,

  $\begin{array}{c}1\frac{7}{8}=\frac{\left(1\times 8\right)+7}{8}\\ 1\frac{7}{8}=\frac{15}{8}\end{array}$

Now, convert $\frac{9}{4}$ and $\frac{15}{8}$ into decimal notation and then compare the set of rational numbers.

Decimal notation for $\frac{9}{4}$ is $2.25$ .

Decimal notation for $\frac{15}{8}$ is $1.875$ .

Thus, the set of rational number $2\frac{1}{4},1\frac{7}{8},1.75,2.4$ becomes $2.25,1.875,1.75,2.4$ .

Now, arrange this set of rational numbers from least to greatest as,

  $\begin{array}{c}1.75<1.875<2.25<2.4\\ 1.75<1\frac{7}{8}<2\frac{1}{4}<2.4\end{array}$

Hence, the correct order of rational numbers from least to greatest is $1.75<1\frac{7}{8}<2\frac{1}{4}<2.4$ .