Question

b) $2\frac{1}{12}$, $\frac{15}{8}$, $\frac{17}{6}$, $2\frac{3}{4}$
from least to greatest:
number line with marks at $1\frac{11}{12}$, 2, $2\frac{1}{2}$, 3

Explanation:

Step1: Convert to improper fractions

$2\frac{1}{12}=\frac{2\times12 + 1}{12}=\frac{25}{12}$; $\frac{15}{8}$; $\frac{17}{6}=\frac{17\times2}{6\times2}=\frac{34}{12}$; $2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}=\frac{11\times3}{4\times3}=\frac{33}{12}$; Also, find a common denominator (24 or 12, let's use 24 for clarity). $\frac{25}{12}=\frac{50}{24}$, $\frac{15}{8}=\frac{45}{24}$, $\frac{34}{12}=\frac{68}{24}$, $\frac{33}{12}=\frac{66}{24}$.

Step2: Compare numerators

Since denominators are same, compare numerators: 45 < 50 < 66 < 68. So $\frac{15}{8}<2\frac{1}{12}<2\frac{3}{4}<\frac{17}{6}$. Wait, wait, let's re - check. Wait, $2\frac{1}{12}=\frac{25}{12}\approx2.083$, $\frac{15}{8}=1.875$, $\frac{17}{6}\approx2.833$, $2\frac{3}{4}=2.75$. Oh! I made a mistake in common denominator earlier. Let's use decimal: $\frac{15}{8}=1.875$, $2\frac{1}{12}\approx2.083$, $2\frac{3}{4}=2.75$, $\frac{17}{6}\approx2.833$. So order from least to greatest: $\frac{15}{8}$, $2\frac{1}{12}$, $2\frac{3}{4}$, $\frac{17}{6}$.

Answer:

$\frac{15}{8}$, $2\frac{1}{12}$, $2\frac{3}{4}$, $\frac{17}{6}$