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!
### 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!
