Chapter 3.1, Problem 32PPS

To determine

To replace $•$ in the sentence $\frac{5}{6}•\frac{7}{8}$ with $<,>,\text{or }=$ to make a true sentence.

Answer to Problem 32PPS

  $\frac{5}{6}<\frac{7}{8}$

Explanation of Solution

Given:

The sentence, $\frac{5}{6}•\frac{7}{8}$ .

Concept Used:

To convert a fraction into an equivalent decimal, use long division method and divide the numerator by the denominator.

Calculation:

In order to checkwhether the fraction on the left of $•$ is less than, greater than or equal to the number on the right of $•$ , first convert the fractions into equivalent decimals and then compare the numbers.

So, to convert the left fraction into decimal, divide the numerator by the denominator using long division as shown below,

  $6\begin{array}{c}\hfill 0.833\\ \hfill \overline{)\begin{array}{l}5.000\\ \underset{\_}{0}\\ 50\\ \underset{\_}{48}\\ 20\\ \underset{\_}{18}\\ 20\\ \underset{\_}{18}\\ 2\end{array}}\end{array}$

And similarly convert the right side fraction into equivalent decimal as

  $8\begin{array}{c}\hfill 0.875\\ \hfill \overline{)\begin{array}{l}7.000\\ \underset{\_}{0}\\ 70\\ \underset{\_}{64}\\ 60\\ \underset{\_}{56}\\ 40\\ \underset{\_}{40}\\ 0\end{array}}\end{array}$

So, in decimal form the given sentence can be written as $0.833•0.875$ .

Observe that the decimal number to the left of the symbol $•$ is less than the decimal number to the right. So, replace the symbol by $<$ sign.

Thus, the true sentence is $\frac{5}{6}<\frac{7}{8}$ .