Question

which sign makes the statement true?
$-1 \frac{1}{5}$ $\boldsymbol{?}$ $\frac{-13}{30}$
$>$
$<$
$=$

Explanation:

Step1: Convert mixed number to improper fraction

\(-1\frac{1}{5}=-\frac{5\times1 + 1}{5}=-\frac{6}{5}\)

Step2: Find a common denominator

The common denominator of 5 and 30 is 30. So, \(-\frac{6}{5}=-\frac{6\times6}{5\times6}=-\frac{36}{30}\)

Step3: Compare the two fractions

We have \(-\frac{36}{30}\) and \(-\frac{13}{30}\). Since for negative numbers, the one with the larger absolute value is smaller. \(\vert-\frac{36}{30}\vert=\frac{36}{30}\) and \(\vert-\frac{13}{30}\vert=\frac{13}{30}\), and \(\frac{36}{30}>\frac{13}{30}\), so \(-\frac{36}{30}<-\frac{13}{30}\)

Answer:

\(<\)