Question

1. use benchmarks and a number line to order this set of numbers from greatest to least. \\(\frac{7}{12}, \frac{5}{6}, \frac{3}{4}, \frac{2}{3}\\) from greatest to least: ________

Explanation:

Step1: Find a common denominator

To compare the fractions \(\frac{7}{12}\), \(\frac{5}{6}\), \(\frac{3}{4}\), and \(\frac{2}{3}\), we first find a common denominator. The least common denominator (LCD) of 12, 6, 4, and 3 is 12.

Step2: Convert each fraction to twelfths

• \(\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}\)
• \(\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}\)
• \(\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}\)
• \(\frac{7}{12}\) remains as \(\frac{7}{12}\)

Step3: Compare the numerators

Now that all fractions have the same denominator, we compare the numerators: \(10 > 9 > 8 > 7\). So, \(\frac{10}{12}>\frac{9}{12}>\frac{8}{12}>\frac{7}{12}\).

Step4: Substitute back the original fractions

Substituting back, we get \(\frac{5}{6}>\frac{3}{4}>\frac{2}{3}>\frac{7}{12}\).

Answer:

\(\frac{5}{6}\), \(\frac{3}{4}\), \(\frac{2}{3}\), \(\frac{7}{12}\)