To solve this problem of ordering the given fractions from smallest to largest, we need to determine the decimal equivalents of each fraction and then arrange them accordingly. Here are the steps involved:
### Step 1: List the fractions
The given fractions are:
[tex]\[ \frac{4}{5}, \frac{3}{4}, \frac{9}{10}, \frac{17}{20}, \frac{3}{5} \][/tex]
### Step 2: Convert each fraction to a decimal
[tex]\[
\frac{4}{5} = 0.8
\][/tex]
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
[tex]\[
\frac{9}{10} = 0.9
\][/tex]
[tex]\[
\frac{17}{20} = 0.85
\][/tex]
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
### Step 3: List the fractions with their corresponding decimal values
- [tex]\( \frac{4}{5} = 0.8 \)[/tex]
- [tex]\( \frac{3}{4} = 0.75 \)[/tex]
- [tex]\( \frac{9}{10} = 0.9 \)[/tex]
- [tex]\( \frac{17}{20} = 0.85 \)[/tex]
- [tex]\( \frac{3}{5} = 0.6 \)[/tex]
### Step 4: Sort the decimal values from smallest to largest
Sorted decimals:
[tex]\[ 0.6, 0.75, 0.8, 0.85, 0.9 \][/tex]
### Step 5: Arrange the fractions according to their decimal values
Based on the sorted decimal values, the fractions in order from smallest to largest are:
1. [tex]\( \frac{3}{5} \)[/tex]
2. [tex]\( \frac{3}{4} \)[/tex]
3. [tex]\( \frac{4}{5} \)[/tex]
4. [tex]\( \frac{17}{20} \)[/tex]
5. [tex]\( \frac{9}{10} \)[/tex]
### Step 6: Extract the numerators and denominators from the sorted fractions
From the sorted list of fractions:
- The numerators are: [tex]\( 3, 3, 4, 17, 9 \)[/tex]
- The denominators are: [tex]\( 5, 4, 5, 20, 10 \)[/tex]
### Final Answer
The fractions ordered from smallest to largest are:
[tex]\[ \frac{3}{5}, \frac{3}{4}, \frac{4}{5}, \frac{17}{20}, \frac{9}{10} \][/tex]
Here are the numerators and denominators based on their sorted order:
- Numerators: [tex]\( 3, 3, 4, 17, 9 \)[/tex]
- Denominators: [tex]\( 5, 4, 5, 20, 10 \)[/tex]
