To plot the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(1 \frac{2}{3}\)[/tex] on a number line, follow these steps:
### Step 1: Understand the Fractions
First, let's recognize the fractions we are working with:
1. [tex]\(\frac{5}{6}\)[/tex] is already a simple fraction.
2. [tex]\(1 \frac{2}{3}\)[/tex] is a mixed number. To make it easier, we can convert it to an improper fraction or a decimal number.
### Step 2: Convert [tex]\(\frac{5}{6}\)[/tex] to a Decimal
[tex]\(\frac{5}{6}\)[/tex] can be converted to a decimal to see its exact position on the number line:
[tex]\[
\frac{5}{6} \approx 0.8333
\][/tex]
### Step 3: Convert [tex]\(1 \frac{2}{3}\)[/tex] to a Decimal
[tex]\(1 \frac{2}{3}\)[/tex] means 1 whole and [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
1 + \frac{2}{3} \approx 1 + 0.6667 \approx 1.6667
\][/tex]
### Step 4: Draw the Number Line
Draw a horizontal number line and label some points to provide a reference:
[tex]\[
0 \quad \frac{1}{2} \quad 1 \quad 1 \frac{1}{2} \quad 2
\][/tex]
### Step 5: Plot the Points on the Number Line
- [tex]\(\frac{5}{6}\)[/tex] ([tex]\(0.8333\)[/tex]): This is a bit less than 1. You can mark this point slightly to the left of 1.
- [tex]\(1 \frac{2}{3}\)[/tex] ([tex]\(1.6667\)[/tex]): This is slightly more than [tex]\(1 \frac{1}{2}\)[/tex], and you can mark this point a bit to the right of [tex]\(1 \frac{1}{2}\)[/tex].
### Illustration:
[tex]\[
\begin{array}{c}
\overset{0.833}{|} \quad \quad \quad \overset{1.667}{|} \quad \quad \\
0 \quad \quad \frac{1}{2} \quad \quad 1 \quad \quad 1 \frac{1}{2} \quad \quad 2
\end{array}
\][/tex]
This way, [tex]\(\frac{5}{6}\)[/tex] and [tex]\(1 \frac{2}{3}\)[/tex] are accurately plotted on the number line.
