Questions: Ordering Fractions and Decimals Quick Check Identify the numeric order of these fractions and mixed numbers from smallest to largest: 4/6, 2 5/6, 2 1/2, 2 3/4. (1 point) 5/2, 11/4, 17/6, 4/6 4/6, 2 1/2, 2 3/4, 2 5/6 2/5, 4/11, 6/17, 4/6 2 5/6, 2 3/4, 2 1/2, 4/6

Solution Steps

To order the given fractions and mixed numbers from smallest to largest, we need to convert all the numbers into a common format, such as decimals, to easily compare them. Once converted, we can sort them in ascending order and then map them back to their original forms.

First, we convert the mixed numbers to improper fractions:

• \(2 \frac{5}{6} = \frac{17}{6}\)
• \(2 \frac{1}{2} = \frac{5}{2}\)
• \(2 \frac{3}{4} = \frac{11}{4}\)

The fractions and mixed numbers are now:

• \(\frac{4}{6}\)
• \(\frac{17}{6}\)
• \(\frac{5}{2}\)
• \(\frac{11}{4}\)

Convert each fraction to a decimal for easy comparison:

• \(\frac{4}{6} \approx 0.6667\)
• \(\frac{17}{6} \approx 2.8333\)
• \(\frac{5}{2} = 2.5\)
• \(\frac{11}{4} = 2.75\)

Sort the decimals in ascending order:

• \(0.6667\)
• \(2.5\)
• \(2.75\)
• \(2.8333\)

Map the sorted decimals back to their original fractions:

• \(0.6667 \rightarrow \frac{2}{3}\)
• \(2.5 \rightarrow \frac{5}{2}\)
• \(2.75 \rightarrow \frac{11}{4}\)
• \(2.8333 \rightarrow \frac{17}{6}\)

Final Answer