select the number line model that matches the expression $left|-\frac{2}{3}-\frac{5}{3}\right|$. choose 1…

Explanation:

Step1: Calculate the value inside the absolute - value

First, find the sum of $-\frac{2}{3}$ and $-\frac{5}{3}$. According to the rule of adding fractions with the same denominator, $-\frac{2}{3}-\frac{5}{3}=-\frac{2 + 5}{3}=-\frac{7}{3}$.

Step2: Calculate the absolute - value

The absolute - value of $-\frac{7}{3}$ is $\left|-\frac{7}{3}\right|=\frac{7}{3}$. This represents the distance from $-\frac{7}{3}$ to 0 on the number line. The distance from $-\frac{7}{3}$ to 0 on the number line is the same as the distance from 0 to $\frac{7}{3}$. The number line that shows the distance from 0 to $\frac{7}{3}$ (or from $-\frac{7}{3}$ to 0) is the one that has the correct length between the relevant points. If we consider the number line with intervals of $\frac{1}{3}$, the distance from 0 to $\frac{7}{3}$ is 7 intervals of $\frac{1}{3}$.

Answer:

We need to find the number - line model that shows a distance of $\frac{7}{3}$ from 0. Without seeing the full details of the number - line models in a more interactive way, we note that the expression simplifies to $\frac{7}{3}$. The correct number line should show the distance between 0 and $\frac{7}{3}$ (or 0 and $-\frac{7}{3}$) which is 7 intervals of $\frac{1}{3}$. If we assume the number lines are centered around 0 and show distances in terms of thirds, we look for a number line where the endpoints of the marked segment are 0 and $\frac{7}{3}$ or 0 and $-\frac{7}{3}$. Since we don't have the full visual details of each option's markings, we can't definitively pick an option letter from A, B, C. But the key is to find the number line where the distance between the two marked points (one of which should be 0) is $\frac{7}{3}$. If we had to guess based on the general understanding of number - line representation of absolute - value, we would look for a number line that has a segment starting at 0 and ending at $\frac{7}{3}$ or starting at $-\frac{7}{3}$ and ending at 0. If we assume the number lines are drawn with the left - hand side being negative and the right - hand side being positive, we want a number line that shows the distance from 0 to $\frac{7}{3}$ (7 intervals of $\frac{1}{3}$). If we assume the number lines are drawn in a standard way, we need to find the one that has the correct length of the segment representing the absolute - value result. If we had to choose based on the principle of absolute - value representing distance, we would look for a number line where the distance between the two key points (one being 0) is 7 intervals of $\frac{1}{3}$. If we assume the number lines are drawn with evenly spaced intervals of $\frac{1}{3}$, we want to find the number line where the segment representing the absolute - value has a length of 7 intervals of $\frac{1}{3}$. Without seeing the exact markings on A, B, C, we can't give a definite letter answer, but the correct number line should represent a distance of $\frac{7}{3}$ from 0.