Question

checking your understanding match each fraction to a reasonable estimate. (-6/11) (-3/13) (-7/9) (-3/4) (-1/2) (-1/4)

Explanation:

Step1: Analyze \(\frac{-6}{11}\)

We know that \(\frac{-6}{11}\approx - 0.545\), and \(-\frac{1}{2}=-0.5\). The value of \(\frac{-6}{11}\) is close to \(-\frac{1}{2}\) (the difference between \(\vert - 0.545\vert\) and \(\vert - 0.5\vert\) is \(0.045\)). So \(\frac{-6}{11}\) matches with \(-\frac{1}{2}\).

Step2: Analyze \(\frac{-3}{13}\)

\(\frac{-3}{13}\approx - 0.23\), and \(-\frac{1}{4}=-0.25\). The value of \(\frac{-3}{13}\) is close to \(-\frac{1}{4}\) (the difference between \(\vert - 0.23\vert\) and \(\vert - 0.25\vert\) is \(0.02\)). So \(\frac{-3}{13}\) matches with \(-\frac{1}{4}\).

Step3: Analyze \(\frac{-7}{9}\)

\(\frac{-7}{9}\approx - 0.778\), and \(-\frac{3}{4}=-0.75\). The value of \(\frac{-7}{9}\) is close to \(-\frac{3}{4}\) (the difference between \(\vert - 0.778\vert\) and \(\vert - 0.75\vert\) is \(0.028\)). So \(\frac{-7}{9}\) matches with \(-\frac{3}{4}\).

Answer:

\(\frac{-6}{11}\) matches with \(-\frac{1}{2}\); \(\frac{-3}{13}\) matches with \(-\frac{1}{4}\); \(\frac{-7}{9}\) matches with \(-\frac{3}{4}\)