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Sagot :
Let's work through ordering the given fractions from least to greatest step-by-step.
### List of Fractions
The fractions we need to order are:
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{2}{6}\)[/tex]
### Step-by-Step Solution
#### Step 1: Simplify Fractions if Possible
First, simplify each fraction if it is not already in its simplest form:
- [tex]\(\frac{2}{3}\)[/tex] is already in its simplest form.
- [tex]\(\frac{1}{2}\)[/tex] is already in its simplest form.
- [tex]\(\frac{3}{4}\)[/tex] is already in its simplest form.
- [tex]\(\frac{2}{6}\)[/tex] can be simplified. By dividing the numerator and the denominator by their greatest common divisor (2), we get [tex]\(\frac{1}{3}\)[/tex].
So, after simplification, the fractions are:
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{1}{3}\)[/tex]
#### Step 2: Convert Fractions to Decimal Form (for Comparison)
Now, let's convert each fraction to its decimal equivalent to help compare them:
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{1}{3} \approx 0.3333\)[/tex]
#### Step 3: Compare and Order the Decimal Values
Now, we can compare these decimal values and order the fractions from least to greatest:
- [tex]\(\frac{1}{3} \approx 0.3333\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
#### Step 4: Write the Fractions in the Correct Order
Putting them back into their fractional forms, we have:
From least to greatest:
1. [tex]\(\frac{1}{3}\)[/tex] (which corresponds to [tex]\(\frac{2}{6}\)[/tex] in the original list)
2. [tex]\(\frac{1}{2}\)[/tex]
3. [tex]\(\frac{2}{3}\)[/tex]
4. [tex]\(\frac{3}{4}\)[/tex]
### Final Answer
The fractions in order from least to greatest are:
[tex]\[ \frac{2}{6}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4} \][/tex]
Thus, [tex]\(\frac{2}{6}\)[/tex], [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{3}{4}\)[/tex] are the fractions ordered from least to greatest.
### List of Fractions
The fractions we need to order are:
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{2}{6}\)[/tex]
### Step-by-Step Solution
#### Step 1: Simplify Fractions if Possible
First, simplify each fraction if it is not already in its simplest form:
- [tex]\(\frac{2}{3}\)[/tex] is already in its simplest form.
- [tex]\(\frac{1}{2}\)[/tex] is already in its simplest form.
- [tex]\(\frac{3}{4}\)[/tex] is already in its simplest form.
- [tex]\(\frac{2}{6}\)[/tex] can be simplified. By dividing the numerator and the denominator by their greatest common divisor (2), we get [tex]\(\frac{1}{3}\)[/tex].
So, after simplification, the fractions are:
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{1}{3}\)[/tex]
#### Step 2: Convert Fractions to Decimal Form (for Comparison)
Now, let's convert each fraction to its decimal equivalent to help compare them:
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{1}{3} \approx 0.3333\)[/tex]
#### Step 3: Compare and Order the Decimal Values
Now, we can compare these decimal values and order the fractions from least to greatest:
- [tex]\(\frac{1}{3} \approx 0.3333\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
#### Step 4: Write the Fractions in the Correct Order
Putting them back into their fractional forms, we have:
From least to greatest:
1. [tex]\(\frac{1}{3}\)[/tex] (which corresponds to [tex]\(\frac{2}{6}\)[/tex] in the original list)
2. [tex]\(\frac{1}{2}\)[/tex]
3. [tex]\(\frac{2}{3}\)[/tex]
4. [tex]\(\frac{3}{4}\)[/tex]
### Final Answer
The fractions in order from least to greatest are:
[tex]\[ \frac{2}{6}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4} \][/tex]
Thus, [tex]\(\frac{2}{6}\)[/tex], [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{3}{4}\)[/tex] are the fractions ordered from least to greatest.
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