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Exercises Numbers, fractions and percents

Example 1.115 from Elementary Algebra, 1.8 The Real Numbers

The Real Numbers: example 1.115

Locate and label the following on a number line: $4, \frac{3}{4}, - \frac{1}{4}, −3, \frac{6}{5}, - \frac{5}{2}, and \frac{7}{3} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Locate and plot the integers, $4, −3 .$

Locate the proper fraction $\frac{3}{4}$ first. The fraction $\frac{3}{4}$ is between 0 and 1. Divide the distance between 0 and 1 into four equal parts then, we plot $\frac{3}{4} .$ Similarly plot $- \frac{1}{4} .$

Now locate the improper fractions $\frac{6}{5}, - \frac{5}{2}, \frac{7}{3} .$ It is easier to plot them if we convert them to mixed numbers and then plot them as described above: $\frac{6}{5} = 1 \frac{1}{5}, - \frac{5}{2} = −2 \frac{1}{2}, \frac{7}{3} = 2 \frac{1}{3} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Locate and label the following on a number line: $−1, \frac{1}{3}, \frac{6}{5}, - \frac{7}{4}, \frac{9}{2}, 5, - \frac{8}{3} .$

How did it go?

PreviousThe Real Numbers: example 1.114 Next The Real Numbers: example 1.116

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 1.8, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.