Math worksheet for ordering fractions, including positive and negative fractions, mixed numbers, and decimals.

Let's solve each problem step by step. The goal is to order the fractions from greatest to least or least to greatest, depending on what's indicated.

We'll convert all numbers to improper fractions, find a common denominator (or use decimals), and compare them.

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Problem 1:

Fractions:
$\frac{1}{2}, \frac{17}{6}, -\frac{17}{12}, -\frac{5}{4}, \frac{6}{10}$
Order: greatest → least

#### Step 1: Convert all to decimals:
- $\frac{1}{2} = 0.5$
- $\frac{17}{6} \approx 2.833$
- $-\frac{17}{12} \approx -1.4167$
- $-\frac{5}{4} = -1.25$
- $\frac{6}{10} = 0.6$

#### Step 2: Order from greatest to least:
$2.833 > 0.6 > 0.5 > -1.25 > -1.4167$

So:
$$
\frac{17}{6}, \frac{6}{10}, \frac{1}{2}, -\frac{5}{4}, -\frac{17}{12}
$$

✔ Answer: $\boxed{\frac{17}{6}, \frac{6}{10}, \frac{1}{2}, -\frac{5}{4}, -\frac{17}{12}}$

---

Problem 2:

Fractions:
$-\frac{7}{3}, -2, 2\frac{6}{20}, -\frac{13}{6}, 2\frac{1}{5}$
Order: greatest → least

#### Step 1: Convert to improper fractions and decimals:
- $-\frac{7}{3} \approx -2.333$
- $-2 = -2$
- $2\frac{6}{20} = 2 + \frac{3}{10} = 2.3$
- $-\frac{13}{6} \approx -2.1667$
- $2\frac{1}{5} = 2.2$

#### Step 2: Order from greatest to least:
$2.3 > 2.2 > -2 > -2.1667 > -2.333$

So:
$$
2\frac{6}{20}, 2\frac{1}{5}, -2, -\frac{13}{6}, -\frac{7}{3}
$$

✔ Answer: $\boxed{2\frac{6}{20}, 2\frac{1}{5}, -2, -\frac{13}{6}, -\frac{7}{3}}$

---

Problem 3:

Fractions:
$-2\frac{77}{100}, \frac{4}{5}, \frac{1}{2}, -\frac{3}{10}, -\frac{6}{3}$
Order: greatest → least

#### Step 1: Convert to decimals:
- $-2\frac{77}{100} = -2.77$
- $\frac{4}{5} = 0.8$
- $\frac{1}{2} = 0.5$
- $-\frac{3}{10} = -0.3$
- $-\frac{6}{3} = -2$

#### Step 2: Order:
$0.8 > 0.5 > -0.3 > -2 > -2.77$

So:
$$
\frac{4}{5}, \frac{1}{2}, -\frac{3}{10}, -\frac{6}{3}, -2\frac{77}{100}
$$

✔ Answer: $\boxed{\frac{4}{5}, \frac{1}{2}, -\frac{3}{10}, -\frac{6}{3}, -2\frac{77}{100}}$

---

Problem 4:

Fractions:
$-1\frac{97}{100}, \frac{45}{25}, -\frac{11}{5}, -1\frac{2}{12}, \frac{10}{8}$
Order: greatest → least

#### Step 1: Convert:
- $-1\frac{97}{100} = -1.97$
- $\frac{45}{25} = 1.8$
- $-\frac{11}{5} = -2.2$
- $-1\frac{2}{12} = -1\frac{1}{6} \approx -1.1667$
- $\frac{10}{8} = 1.25$

#### Step 2: Order:
$1.8 > 1.25 > -1.1667 > -1.97 > -2.2$

So:
$$
\frac{45}{25}, \frac{10}{8}, -1\frac{2}{12}, -1\frac{97}{100}, -\frac{11}{5}
$$

✔ Answer: $\boxed{\frac{45}{25}, \frac{10}{8}, -1\frac{2}{12}, -1\frac{97}{100}, -\frac{11}{5}}$

---

Problem 5:

Fractions:
$\frac{5}{3}, \frac{3}{4}, -1\frac{9}{10}, -1\frac{6}{8}, 2\frac{1}{2}$
Order: least → greatest

#### Step 1: Convert:
- $\frac{5}{3} \approx 1.6667$
- $\frac{3}{4} = 0.75$
- $-1\frac{9}{10} = -1.9$
- $-1\frac{6}{8} = -1\frac{3}{4} = -1.75$
- $2\frac{1}{2} = 2.5$

#### Step 2: Order from least to greatest:
$-1.9 < -1.75 < 0.75 < 1.6667 < 2.5$

So:
$$
-1\frac{9}{10}, -1\frac{6}{8}, \frac{3}{4}, \frac{5}{3}, 2\frac{1}{2}
$$

✔ Answer: $\boxed{-1\frac{9}{10}, -1\frac{6}{8}, \frac{3}{4}, \frac{5}{3}, 2\frac{1}{2}}$

---

Problem 6:

Fractions:
$\frac{60}{25}, -2\frac{4}{9}, \frac{3}{3}, \frac{107}{100}, -1\frac{34}{50}$
Order: greatest → least

#### Step 1: Convert:
- $\frac{60}{25} = 2.4$
- $-2\frac{4}{9} \approx -2.444$
- $\frac{3}{3} = 1$
- $\frac{107}{100} = 1.07$
- $-1\frac{34}{50} = -1.68$

#### Step 2: Order:
$2.4 > 1.07 > 1 > -1.68 > -2.444$

So:
$$
\frac{60}{25}, \frac{107}{100}, \frac{3}{3}, -1\frac{34}{50}, -2\frac{4}{9}
$$

✔ Answer: $\boxed{\frac{60}{25}, \frac{107}{100}, \frac{3}{3}, -1\frac{34}{50}, -2\frac{4}{9}}$

---

Problem 7:

Fractions:
$-1\frac{1}{3}, -2, -1\frac{16}{20}, -\frac{16}{6}, \frac{21}{10}$
Order: greatest → least

#### Step 1: Convert:
- $-1\frac{1}{3} \approx -1.333$
- $-2 = -2$
- $-1\frac{16}{20} = -1\frac{4}{5} = -1.8$
- $-\frac{16}{6} \approx -2.6667$
- $\frac{21}{10} = 2.1$

#### Step 2: Order:
$2.1 > -1.333 > -1.8 > -2 > -2.6667$

So:
$$
\frac{21}{10}, -1\frac{1}{3}, -1\frac{16}{20}, -2, -\frac{16}{6}
$$

✔ Answer: $\boxed{\frac{21}{10}, -1\frac{1}{3}, -1\frac{16}{20}, -2, -\frac{16}{6}}$

---

Problem 8:

Fractions:
$\frac{2}{3}, -\frac{11}{25}, -\frac{6}{10}, -1\frac{3}{12}, -\frac{6}{20}$
Order: least → greatest

#### Step 1: Convert:
- $\frac{2}{3} \approx 0.6667$
- $-\frac{11}{25} = -0.44$
- $-\frac{6}{10} = -0.6$
- $-1\frac{3}{12} = -1\frac{1}{4} = -1.25$
- $-\frac{6}{20} = -0.3$

#### Step 2: Order from least to greatest:
$-1.25 < -0.6 < -0.44 < -0.3 < 0.6667$

So:
$$
-1\frac{3}{12}, -\frac{6}{10}, -\frac{11}{25}, -\frac{6}{20}, \frac{2}{3}
$$

✔ Answer: $\boxed{-1\frac{3}{12}, -\frac{6}{10}, -\frac{11}{25}, -\frac{6}{20}, \frac{2}{3}}$

---

Problem 9:

Fractions:
$\frac{6}{6}, \frac{5}{4}, -\frac{2}{5}, \frac{2}{2}, -\frac{49}{50}$
Order: greatest → least

#### Step 1: Simplify and convert:
- $\frac{6}{6} = 1$
- $\frac{5}{4} = 1.25$
- $-\frac{2}{5} = -0.4$
- $\frac{2}{2} = 1$
- $-\frac{49}{50} = -0.98$

#### Step 2: Order:
$1.25 > 1 = 1 > -0.4 > -0.98$

Note: $\frac{6}{6}$ and $\frac{2}{2}$ both equal 1, so they are equal.

So:
$$
\frac{5}{4}, \frac{6}{6}, \frac{2}{2}, -\frac{2}{5}, -\frac{49}{50}
$$

✔ Answer: $\boxed{\frac{5}{4}, \frac{6}{6}, \frac{2}{2}, -\frac{2}{5}, -\frac{49}{50}}$

---

Problem 10:

Fractions:
$\frac{9}{10}, -2\frac{1}{4}, \frac{4}{4}, \frac{2}{3}, \frac{15}{20}$
Order: greatest → least

#### Step 1: Convert:
- $\frac{9}{10} = 0.9$
- $-2\frac{1}{4} = -2.25$
- $\frac{4}{4} = 1$
- $\frac{2}{3} \approx 0.6667$
- $\frac{15}{20} = 0.75$

#### Step 2: Order:
$1 > 0.9 > 0.75 > 0.6667 > -2.25$

So:
$$
\frac{4}{4}, \frac{9}{10}, \frac{15}{20}, \frac{2}{3}, -2\frac{1}{4}
$$

✔ Answer: $\boxed{\frac{4}{4}, \frac{9}{10}, \frac{15}{20}, \frac{2}{3}, -2\frac{1}{4}}$

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✔ Final Answers:

1) $\frac{17}{6}, \frac{6}{10}, \frac{1}{2}, -\frac{5}{4}, -\frac{17}{12}$
2) $2\frac{6}{20}, 2\frac{1}{5}, -2, -\frac{13}{6}, -\frac{7}{3}$
3) $\frac{4}{5}, \frac{1}{2}, -\frac{3}{10}, -\frac{6}{3}, -2\frac{77}{100}$
4) $\frac{45}{25}, \frac{10}{8}, -1\frac{2}{12}, -1\frac{97}{100}, -\frac{11}{5}$
5) $-1\frac{9}{10}, -1\frac{6}{8}, \frac{3}{4}, \frac{5}{3}, 2\frac{1}{2}$
6) $\frac{60}{25}, \frac{107}{100}, \frac{3}{3}, -1\frac{34}{50}, -2\frac{4}{9}$
7) $\frac{21}{10}, -1\frac{1}{3}, -1\frac{16}{20}, -2, -\frac{16}{6}$
8) $-1\frac{3}{12}, -\frac{6}{10}, -\frac{11}{25}, -\frac{6}{20}, \frac{2}{3}$
9) $\frac{5}{4}, \frac{6}{6}, \frac{2}{2}, -\frac{2}{5}, -\frac{49}{50}$
10) $\frac{4}{4}, \frac{9}{10}, \frac{15}{20}, \frac{2}{3}, -2\frac{1}{4}$

Let me know if you'd like this in printable format or with explanations for specific steps!