Chapter 0.4, Problem 6E

To determine

To find: The correct symbol to make the sentence true.

Answer to Problem 6E

The correct symbol is $<$ .

Explanation of Solution

Given:

The given sentence is $-\frac{7}{11}•-\frac{2}{3}$ .

Calculation:

Consider the given fractions,

$-\frac{7}{11}•-\frac{2}{3}$

Consider the prime factor of 11is,

$11=11\times 1$

Consider the prime factor of 3 is,

$3=3\times 1$

Then, the LCM of 11 and 3 is,

$11\times 3=33$

Convert each of the fraction in equivalent fraction as,

$\begin{array}{c}\frac{7}{11}=\frac{7\times 11}{11\times 3}\\ =\frac{77}{33}\end{array}$

Also,

$\begin{array}{c}\frac{2}{3}=\frac{2\times 11}{3\times 11}\\ =\frac{22}{33}\end{array}$

Consider the given sentence is,

$-\frac{77}{33}•-\frac{22}{33}$

Both the fractions are negative for the number $-\frac{22}{33}$ is more than $-\frac{77}{33}$ that is,

$-\frac{77}{33}<-\frac{22}{33}$