High School

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Order each set of fractions as indicated:

1) [tex]\left(\frac{1}{2}, \frac{17}{6}, -\frac{17}{12}, -\frac{5}{4}, \frac{6}{10}, \frac{10}{17}\right)[/tex]

2) [tex]\left(-\frac{7}{3}, -2, 2\frac{5}{20}, -\frac{13}{6}, 2\frac{15}{3}\right)[/tex]

3) [tex]\left(2\frac{5}{6}, \frac{9}{10}, \frac{1}{2}, -\frac{10\pi}{4}, -\frac{5}{12}\right)[/tex]

4) [tex]\left(-2\frac{6}{20}, 2\frac{1}{5}, -2, -2\frac{1}{61}, -2\frac{1}{3}\right)[/tex]

5) [tex]\left(-2\frac{77}{100}, \frac{4}{5}, \frac{1}{2}, -\frac{3}{10}, -\frac{6}{3}\right)[/tex]

Arrange from greatest to least:

6) [tex]\left(-1\frac{97}{100}, +\frac{45}{25}, -\frac{11}{5}, -1\frac{2}{12}, +\frac{10}{8}\right)[/tex]

Arrange from greatest to least:

[tex]\left(+\frac{45}{25}, +\frac{10}{81}, -\frac{97}{100}, -2\frac{1}{5}, \frac{2}{12}\right)[/tex]

7) [tex]\left(+\frac{4}{5}, +\frac{7}{2}, -\frac{3}{10}, -\frac{0}{10}, = \frac{77}{100}\right)[/tex]

8) [tex]\left(+\frac{5}{3}, +\frac{3}{4}, -\frac{19}{10}, -1\frac{8}{9}, +2\frac{1}{2}\right)[/tex]

9) [tex]\left(2\frac{10}{25}, +\frac{60}{25}, -2\frac{4}{9}, +\frac{3}{3}, \frac{107}{100}, -1\frac{34}{50}\right)[/tex]

Arrange from greatest to least:

[tex]\left(2\frac{10}{25}, 1\frac{7}{100}, 1, 1\frac{38}{50}, 2\frac{4}{9}\right)[/tex]

10) [tex]\left(-1\frac{9}{10}, -1\frac{8}{9}, \frac{3}{4}, \frac{2}{3}, 2\frac{1}{2}\right)[/tex]

11) [tex]\left(-1\frac{1}{3}, -2, -1\frac{16}{20}, -\frac{16}{6}, +\frac{21}{10}\right)[/tex]

Arrange from greatest to least:

[tex]\left(2, -1\frac{16}{20}, -1\frac{1}{3}, -2, 2\frac{4}{4}\right)[/tex]

12) [tex]\left(+\frac{2}{3}, -\frac{11}{25}, -\frac{6}{10}, -1\frac{3}{12}, -\frac{6}{20}\right)[/tex]

Arrange from least to greatest:

[tex]\left(-1\frac{3}{12}, \frac{6}{10}, \frac{6}{20}, 1\frac{1}{25}, +\frac{2}{3}\right)[/tex]

Answer :

Sure! Let's go through the steps to order the given fractions from each set as instructed.

### 1) Ordering Fractions

Here are the fractions provided for this first exercise:

- [tex]\( \frac{1}{2} \)[/tex]
- [tex]\( \frac{17}{6} \)[/tex]
- [tex]\(-\frac{17}{12} \)[/tex]
- [tex]\(-\frac{5}{4} \)[/tex]
- [tex]\(\frac{6}{10} \)[/tex]

To simplify fractions and convert them into decimal form:

1. [tex]\( \frac{1}{2} = 0.5 \)[/tex]
2. [tex]\( \frac{17}{6} \approx 2.833 \)[/tex]
3. [tex]\(-\frac{17}{12} \approx -1.416 \)[/tex]
4. [tex]\(-\frac{5}{4} = -1.25 \)[/tex]
5. [tex]\(\frac{6}{10} = 0.6 \)[/tex]

Order from least to greatest: [tex]\(-\frac{17}{12}\)[/tex], [tex]\(-\frac{5}{4}\)[/tex], [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{6}{10}\)[/tex], [tex]\(\frac{17}{6}\)[/tex]
Decimal Order: [tex]\(-1.416\)[/tex], [tex]\(-1.25\)[/tex], [tex]\(0.5\)[/tex], [tex]\(0.6\)[/tex], [tex]\(2.833\)[/tex]

### 2) Ordering Integers and Mixed Numbers

Here are the numbers provided for this second exercise:

- [tex]\(-\frac{7}{3} \approx -2.333 \)[/tex]
- [tex]\(-2 \)[/tex]
- [tex]\(2 + \frac{5}{20} = 2.25 \)[/tex]
- [tex]\(-\frac{13}{6} \approx -2.166 \)[/tex]
- [tex]\(2 + \frac{15}{3} = 7 \)[/tex]

Order from least to greatest: [tex]\(-\frac{7}{3}\)[/tex], [tex]\(-\frac{13}{6}\)[/tex], [tex]\(-2\)[/tex], [tex]\(2 + \frac{5}{20}\)[/tex], [tex]\(2 + \frac{15}{3}\)[/tex]
Decimal Order: [tex]\(-2.333\)[/tex], [tex]\(-2.166\)[/tex], [tex]\(-2\)[/tex], [tex]\(2.25\)[/tex], [tex]\(7\)[/tex]

### 3) Ordering Mixed Numbers and Fractions

Here are the numbers provided:

- [tex]\(-2 \frac{77}{100} = -2.77 \)[/tex]
- [tex]\(\frac{4}{5} = 0.8 \)[/tex]
- [tex]\(\frac{1}{2} = 0.5 \)[/tex]
- [tex]\(-\frac{3}{10} = -0.3 \)[/tex]
- [tex]\(-\frac{6}{3} = -2 \)[/tex]

Order from greatest to least: [tex]\(\frac{4}{5}\)[/tex], [tex]\(\frac{1}{2}\)[/tex], [tex]\(-\frac{3}{10}\)[/tex], [tex]\(-2\)[/tex], [tex]\(-2 \frac{77}{100}\)[/tex]
Decimal Order: [tex]\(0.8\)[/tex], [tex]\(0.5\)[/tex], [tex]\(-0.3\)[/tex], [tex]\(-2\)[/tex], [tex]\(-2.77\)[/tex]

### 5) Ordering Mixed Numbers and Fractions

- [tex]\(\frac{5}{3} \approx 1.666 \)[/tex]
- [tex]\(\frac{3}{4} = 0.75 \)[/tex]
- [tex]\(-\frac{19}{10} = -1.9 \)[/tex]
- [tex]\(-1 \frac{8}{9} = -1.889 \)[/tex]
- [tex]\(2 + \frac{1}{2} = 2.5 \)[/tex]

Order from least to greatest: [tex]\(-\frac{19}{10}\)[/tex], [tex]\(-1 \frac{8}{9}\)[/tex], [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{5}{3}\)[/tex], [tex]\(2 + \frac{1}{2}\)[/tex]
Decimal Value Order: [tex]\(-1.9\)[/tex], [tex]\(-1.889\)[/tex], [tex]\(0.75\)[/tex], [tex]\(1.666\)[/tex], [tex]\(2.5\)[/tex]

These steps provide a clear way to convert, compute, and order the fractions and numbers accordingly. Feel free to ask if you have any questions about this process!

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