Chapter 3.3, Problem 70SR

To determine

The find: the condition <,>, or = for numbers $\frac{5}{8}$ and $0.65$ .

Answer to Problem 70SR

  $\frac{5}{8}<0.65$

Explanation of Solution

Given:

The numbers are $\frac{5}{8}$ and $0.65$ .

Calculation:

Convert the decimal 0.65 into fraction as follows:

  $\begin{array}{l}\Rightarrow 0.65\\ \Rightarrow \frac{65}{100}\\ \Rightarrow \frac{13\times \cancel{5}}{20\times \cancel{5}}\\ \Rightarrow \frac{13}{20}\end{array}$

Take the LCM of denominator of fractions $\frac{13}{20}$ and $\frac{5}{8}$ as follows:

  $\begin{array}{l}20=5\times 2^2\\ 8=2^3\\ \text{LCM}=5\times 2^3=40\end{array}$

Multiply fraction $\frac{13}{20}$ by 2 in numerator and denominator as follows:

  $\begin{array}{l}\Rightarrow \frac{13\times 2}{20\times 2}\\ \Rightarrow \frac{26}{40}\end{array}$

Multiply fraction $\frac{5}{8}$ by 5 in numerator and denominator as follows:

  $\begin{array}{l}\Rightarrow \frac{5\times 5}{8\times 5}\\ \Rightarrow \frac{25}{40}\end{array}$

Thus, the fraction $\frac{25}{40}\text{or}\frac{5}{8}$ is less than $\frac{26}{40}\text{or}0.65$ .

Thus, $\frac{5}{8}<0.65$ .