Question

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. $$-1 \frac{5}{6} \text { and }-1 \frac{7}{9}$$

Short answer

The numbers plotted on a number line show that -11/6 is less than -16/9 and, conversely, -16/9 is greater than -11/6. Therefore, the inequalities are \(-\frac{11}{6} < -\frac{16}{9}\) and \(-\frac{16}{9} > -\frac{11}{6}\).

Step-by-step solution

Convert Mixed Numbers to Improper Fractions

Firstly, it’d be easier comparing the two numbers if they were both in a similar format. Since they are mixed fractions, it’s advisable to convert them into improper fractions. For -1 5/6, to convert, multiply the whole number by the denominator and add the numerator, giving you -11/6. Similarly, for -1 7/9, this gives -16/9.

Graph the Numbers on a Number Line

Draw a number line and plot the two numbers. Since these are negative numbers, they will be located to the left of zero. The larger a negative number, the farther left it will be from zero. Depending on conversion, -11/6 will occupy a space more to the left than -16/9.

Write Two Inequalities That Compare The Two Numbers

From the number line plot, -11/6 is less than -16/9 and -16/9 is greater than -11/6. Therefore, the inequalities are \(-\frac{11}{6} < -\frac{16}{9}\) and \(-\frac{16}{9} > -\frac{11}{6}\).