Question

plot the following points on the number line without measuring.
i. \\(\frac{1}{3}\\) ii. \\(\frac{5}{6}\\) iii. \\(\frac{7}{12}\\)
(number line with 0, \\(\frac{1}{2}\\) marked)

b. use the number line in part (a) to compare the fractions by writing >, <, or = on the lines.
i. \\(\frac{7}{12}\\) __ \\(\frac{1}{2}\\) ii. \\(\frac{7}{12}\\) __ \\(\frac{5}{6}\\)

a. plot the following points on the number line without measuring.
i. \\(\frac{11}{12}\\) ii. \\(\frac{1}{4}\\) iii. \\(\frac{3}{8}\\)
(number line with 0, \\(\frac{1}{2}\\) marked)

b. select two fractions from part (a), and use the given number line to compare them by writing >, <, or =.

c. explain how you plotted the points in part (a).

Explanation:

Step1: Convert to common denominator

$\frac{1}{2} = \frac{6}{12}$, $\frac{5}{6} = \frac{10}{12}$, $\frac{1}{4} = \frac{2}{8}$

Step2: Compare numerators

$\frac{7}{12} > \frac{6}{12}$, $\frac{7}{12} < \frac{10}{12}$, $\frac{2}{8} < \frac{3}{8}$

Step3: Plot by fraction size

$\frac{1}{4}$ (0.25) left of $\frac{3}{8}$ (0.375); $\frac{7}{12}$ (~0.58) between $\frac{1}{2}$ (0.5) and $\frac{5}{6}$ (~0.83)

Step4: Explain plotting method

Use equivalent fractions to align with number line intervals (e.g., 12ths for first set, 8ths/4ths for second set) to place points without measuring.

Answer:

i. $\frac{7}{12} > \frac{1}{2}$
ii. $\frac{7}{12} < \frac{5}{6}$
$\frac{1}{4} < \frac{3}{8}$ (example for second part a)