Chapter 0, Problem 13PRT

To determine

The true relation using $<,>,=$ sign between two numbers $\frac{7}{20},\frac{2}{5}$ .

Answer to Problem 13PRT

The true relation is $\frac{7}{20}<\frac{2}{5}$ .

Explanation of Solution

Given information:

Compare two numbers: $\frac{7}{20},\frac{2}{5}$ .

To compare two fractions, write the fractions with the same denominator.

Least common denominator is the same denominator for two fractions.

Factors of $20$ are

  $20=1\times 4\times 5$

Factors of $5$ are

  $5=1\times 5$

Greatest common factor in $20$ and $5$ is $5$

Product of denominators is

  $20\times 5=100$

Least common denominator of fractions $\frac{7}{20},\frac{2}{5}$ is the ratio of product of denominators $100$ and greatest common factor $5$

  $\begin{array}{l}=\frac{100}{5}\\ =20\end{array}$

The least common denominator of fractions $\frac{7}{20},\frac{2}{5}$ is $20$

Therefore,

  $\begin{array}{c}\frac{2}{5}=\frac{2\times 4}{5\times 4}\\ =\frac{8}{20}\end{array}$

And

  $\frac{7}{20}=\frac{7}{20}$

Since,

  $\begin{array}{c}7<8\\ \frac{7}{20}<\frac{8}{20}\end{array}$

Thus, the true relation is $\frac{7}{20}<\frac{2}{5}$ .