Certainly! Let's break down the calculation that is modeled on the number line step-by-step.
Step 1: Understanding the given numbers
We need to work with the numbers 5 and [tex]\(2 \frac{1}{3}\)[/tex].
Step 2: Understanding [tex]\(2 \frac{1}{3}\)[/tex]
Identify what [tex]\(2 \frac{1}{3}\)[/tex] represents. It is a mixed number that can be converted to an improper fraction for easier calculation, but for simplicity, we can also treat it as a mixed number directly.
Step 3: Subtract [tex]\(2 \frac{1}{3}\)[/tex] from 5
To perform the subtraction, you could first convert [tex]\(2 \frac{1}{3}\)[/tex] to an improper fraction, but it's not necessary here. Instead, you can think of it as subtracting two whole numbers and then taking care of the fractional part.
So think of subtracting 2 from 5 first:
[tex]\[5 - 2 = 3\][/tex]
Step 4: Handle the fractional part
Now subtract the fractional part:
[tex]\[3 - \frac{1}{3}\][/tex]
Converting 3 to a fraction with the same denominator as [tex]\(\frac{1}{3}\)[/tex], we get:
[tex]\[3 = \frac{9}{3}\][/tex]
So the subtraction becomes:
[tex]\[
\frac{9}{3} - \frac{1}{3} = \frac{8}{3}
\][/tex]
Step 5: Simplify the result
Convert [tex]\(\frac{8}{3}\)[/tex] back to a mixed number:
[tex]\[\frac{8}{3} = 2 \frac{2}{3}\][/tex]
So the final result of [tex]\(5 - 2 \frac{1}{3}\)[/tex] is:
[tex]\[5 - 2 \frac{1}{3} = 2 \frac{2}{3}\][/tex]
Therefore, the calculation modeled on the number line shows that subtracting [tex]\(2 \frac{1}{3}\)[/tex] from 5 results in [tex]\(2 \frac{2}{3}\)[/tex].
[tex]\[\boxed{2 \frac{2}{3}}\][/tex]
This explains the result.
