Chapter 3.3, Problem 69SR

To determine

The find: the condition <,>, or = for numbers $0.3$ and $\frac{1}{4}$ .

Answer to Problem 69SR

  $0.3>\frac{1}{4}$

Explanation of Solution

Given:

The numbers are $0.3$ and $\frac{1}{4}$ .

Calculation:

Convert the decimal 0.3 into fraction as follows:

  $\begin{array}{l}\Rightarrow 0.3\\ \Rightarrow \frac{3}{10}\end{array}$

Take the LCM of denominator of fractions $\frac{3}{10}$ and $\frac{1}{4}$ as follows:

  $\begin{array}{l}10=5\times 2\\ 4=2^2\\ \text{LCM}=5\times 2^2=20\end{array}$

Multiply fraction $\frac{3}{10}$ by 2 in numerator and denominator as follows:

  $\begin{array}{l}\Rightarrow \frac{3\times 2}{10\times 2}\\ \Rightarrow \frac{6}{20}\end{array}$

Multiply fraction $\frac{1}{4}$ by 5 in numerator and denominator as follows:

  $\begin{array}{l}\Rightarrow \frac{1\times 5}{4\times 5}\\ \Rightarrow \frac{5}{20}\end{array}$

Thus, the fraction $\frac{6}{20}\text{or}0.3$ is greater than $\frac{5}{20}\text{or}\frac{1}{4}$ .

Thus, $0.3>\frac{1}{4}$ .