Ordering fractions from least to greatest worksheet for math practice.

To solve the problem of ordering fractions from least to greatest, we need to compare the values of the fractions in each set. Here's a step-by-step explanation for each row:

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Row 1:

#### Set 1: $\frac{5}{3}$, $\frac{4}{3}$, $\frac{2}{3}$
- All fractions have the same denominator (3). Compare the numerators:
- Numerators: $2 < 4 < 5$
- Therefore: $\frac{2}{3} < \frac{4}{3} < \frac{5}{3}$

#### Set 2: $\frac{3}{11}$, $\frac{3}{8}$, $\frac{3}{5}$
- All fractions have the same numerator (3). Compare the denominators:
- Denominators: $11 > 8 > 5$ (larger denominator means smaller fraction)
- Therefore: $\frac{3}{11} < \frac{3}{8} < \frac{3}{5}$

#### Set 3: $\frac{2}{7}$, $\frac{6}{7}$, $\frac{10}{7}$
- All fractions have the same denominator (7). Compare the numerators:
- Numerators: $2 < 6 < 10$
- Therefore: $\frac{2}{7} < \frac{6}{7} < \frac{10}{7}$

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Row 2:

#### Set 1: $\frac{2}{5}$, $\frac{3}{7}$, $\frac{4}{9}$
- Different numerators and denominators. Find a common denominator or convert to decimals:
- $\frac{2}{5} = 0.4$
- $\frac{3}{7} \approx 0.4286$
- $\frac{4}{9} \approx 0.4444$
- Therefore: $\frac{2}{5} < \frac{3}{7} < \frac{4}{9}$

#### Set 2: $\frac{15}{2}$, $\frac{13}{2}$, $\frac{17}{2}$
- All fractions have the same denominator (2). Compare the numerators:
- Numerators: $13 < 15 < 17$
- Therefore: $\frac{13}{2} < \frac{15}{2} < \frac{17}{2}$

#### Set 3: $\frac{13}{3}$, $\frac{16}{3}$, $\frac{5}{3}$
- All fractions have the same denominator (3). Compare the numerators:
- Numerators: $5 < 13 < 16$
- Therefore: $\frac{5}{3} < \frac{13}{3} < \frac{16}{3}$

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Row 3:

#### Set 1: $\frac{2}{19}$, $\frac{2}{17}$, $\frac{2}{13}$
- All fractions have the same numerator (2). Compare the denominators:
- Denominators: $19 > 17 > 13$ (larger denominator means smaller fraction)
- Therefore: $\frac{2}{19} < \frac{2}{17} < \frac{2}{13}$

#### Set 2: $2\frac{3}{5}$, $2\frac{1}{5}$, $3\frac{2}{5}$
- Convert mixed numbers to improper fractions:
- $2\frac{3}{5} = \frac{13}{5}$
- $2\frac{1}{5} = \frac{11}{5}$
- $3\frac{2}{5} = \frac{17}{5}$
- All fractions have the same denominator (5). Compare the numerators:
- Numerators: $11 < 13 < 17$
- Therefore: $2\frac{1}{5} < 2\frac{3}{5} < 3\frac{2}{5}$

#### Set 3: $\frac{3}{8}$, $\frac{6}{8}$, $\frac{5}{8}$
- All fractions have the same denominator (8). Compare the numerators:
- Numerators: $3 < 5 < 6$
- Therefore: $\frac{3}{8} < \frac{5}{8} < \frac{6}{8}$

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Row 4:

#### Set 1: $\frac{11}{14}$, $\frac{3}{14}$, $\frac{9}{14}$
- All fractions have the same denominator (14). Compare the numerators:
- Numerators: $3 < 9 < 11$
- Therefore: $\frac{3}{14} < \frac{9}{14} < \frac{11}{14}$

#### Set 2: $4\frac{1}{8}$, $5\frac{3}{8}$, $9\frac{5}{8}$
- The whole number parts are different. Compare them directly:
- Whole numbers: $4 < 5 < 9$
- Therefore: $4\frac{1}{8} < 5\frac{3}{8} < 9\frac{5}{8}$

#### Set 3: $7\frac{1}{6}$, $4\frac{5}{6}$, $2\frac{1}{6}$
- The whole number parts are different. Compare them directly:
- Whole numbers: $2 < 4 < 7$
- Therefore: $2\frac{1}{6} < 4\frac{5}{6} < 7\frac{1}{6}$

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Final Answer:

$$
\boxed{
\begin{array}{ccc}
\text{Row 1:} & \frac{2}{3} < \frac{4}{3} < \frac{5}{3}, & \frac{3}{11} < \frac{3}{8} < \frac{3}{5}, & \frac{2}{7} < \frac{6}{7} < \frac{10}{7} \\
\text{Row 2:} & \frac{2}{5} < \frac{3}{7} < \frac{4}{9}, & \frac{13}{2} < \frac{15}{2} < \frac{17}{2}, & \frac{5}{3} < \frac{13}{3} < \frac{16}{3} \\
\text{Row 3:} & \frac{2}{19} < \frac{2}{17} < \frac{2}{13}, & 2\frac{1}{5} < 2\frac{3}{5} < 3\frac{2}{5}, & \frac{3}{8} < \frac{5}{8} < \frac{6}{8} \\
\text{Row 4:} & \frac{3}{14} < \frac{9}{14} < \frac{11}{14}, & 4\frac{1}{8} < 5\frac{3}{8} < 9\frac{5}{8}, & 2\frac{1}{6} < 4\frac{5}{6} < 7\frac{1}{6}
\end{array}
}
$$