Question

6a. place $2\frac{2}{5}$, $3\frac{1}{2}$, $\frac{8}{7}$, $\frac{7}{8}$, $\frac{4}{5}$ on the number line.
b. order them from greatest to least.

Explanation:

Step1: Convert mixed numbers to improper fractions or decimals

First, convert the mixed numbers to improper fractions or decimals for easier comparison.

• \( 5\frac{2}{5} = 5 + \frac{2}{5} = 5 + 0.4 = 5.4 \)
• \( 3\frac{1}{2} = 3 + \frac{1}{2} = 3 + 0.5 = 3.5 \)
• \( \frac{8}{7} \approx 1.14 \) (since \( 8\div7\approx1.14 \))
• \( \frac{7}{8} = 0.875 \) (since \( 7\div8 = 0.875 \))
• \( \frac{4}{5} = 0.8 \) (since \( 4\div5 = 0.8 \))

Step2: Compare the decimal values

Now we have the decimal equivalents: \( 5.4 \), \( 3.5 \), \( 1.14 \), \( 0.875 \), \( 0.8 \)

Arranging them from greatest to least: \( 5.4 > 3.5 > 1.14 > 0.875 > 0.8 \)

Step3: Convert back to original fractions

Converting back to the original forms, we get: \( 5\frac{2}{5} > 3\frac{1}{2} > \frac{8}{7} > \frac{7}{8} > \frac{4}{5} \)

Answer:

\( 5\frac{2}{5}, 3\frac{1}{2}, \frac{8}{7}, \frac{7}{8}, \frac{4}{5} \) (from greatest to least)