Question

plotting mixed numbers on a number line
plot $2\frac{5}{6}$ and $1\frac{1}{3}$.

Explanation:

Step1: Analyze the number line

The number line has marks from 0 to 3, with 1 and 2 marked. Let's first determine the scale. Between 0 and 1, and between 1 and 2, and between 2 and 3, let's see how many segments. Let's assume each whole number is divided into 6 equal parts (since one of the fractions has denominator 6). So each small segment is $\frac{1}{6}$.

Step2: Plot $1\frac{1}{3}$

First, convert $1\frac{1}{3}$ to sixths. $1\frac{1}{3}=1\frac{2}{6}$. So starting at 1, we move 2 small segments (each $\frac{1}{6}$) to the right. So from 1, add $\frac{2}{6}$, so the position is $1 + \frac{2}{6}=1\frac{2}{6}=1\frac{1}{3}$.

Step3: Plot $2\frac{5}{6}$

$2\frac{5}{6}$ is 2 plus $\frac{5}{6}$. So starting at 2, we move 5 small segments (each $\frac{1}{6}$) to the right. So from 2, add $\frac{5}{6}$, so the position is $2+\frac{5}{6}=2\frac{5}{6}$.

Answer:

To plot $1\frac{1}{3}$ (which is $1\frac{2}{6}$) on the number line: Start at 1, move 2 small segments (each of length $\frac{1}{6}$) to the right. To plot $2\frac{5}{6}$: Start at 2, move 5 small segments (each of length $\frac{1}{6}$) to the right. (Note: The actual plotting would be marking these points on the number line as per the scale determined, with each small division being $\frac{1}{6}$.)