Question

n7.2, n7.3, & n7.4

1. use a number line to order each set of numbers from least to greatest.

a) \\(\frac{7}{8}, \frac{5}{8}, \frac{3}{8}, \frac{10}{8}\\)
from least to greatest:

d) \\(\frac{11}{12}, \frac{1}{3}, \frac{7}{6}, \frac{5}{4}\\)

Explanation:

Step1: Analyze the fractions

We have the fractions \(\frac{3}{8}\), \(\frac{5}{8}\), \(\frac{7}{8}\), and \(\frac{10}{8}\). Since they have the same denominator, we can compare their numerators. The numerator represents the number of parts we have, so a larger numerator means a larger fraction when the denominator is the same.

Step2: Order the fractions

Comparing the numerators: \(3 < 5 < 7 < 10\). So, \(\frac{3}{8}<\frac{5}{8}<\frac{7}{8}<\frac{10}{8}\).

Step3: Verify on the number line

The number line is divided into eighths (since the denominator is 8). Plotting each fraction: \(\frac{3}{8}\) is 3 eighths from 0, \(\frac{5}{8}\) is 5 eighths, \(\frac{7}{8}\) is 7 eighths, and \(\frac{10}{8}=1\frac{2}{8}\) is 1 and 2 eighths from 0. From left to right (least to greatest), the order matches the numerator comparison.

Answer:

\(\frac{3}{8}\), \(\frac{5}{8}\), \(\frac{7}{8}\), \(\frac{10}{8}\)