Question

consider the number line shown. what is the distance between point a and point b? units evaluate each expression. (answer each expression) 4 - 7\frac{1}{3} -2\frac{3}{8}-5\frac{1}{2}-(-9\frac{1}{4}) model each expression on the number line. 8 - 3 8 + (-3)

Explanation:

Step1: Find coordinates of points

From the number - line, point $A$ is at $- 2$ and point $B$ is at $1.5$.

Step2: Use distance formula on number - line

The distance $d$ between two points $x_1$ and $x_2$ on a number - line is $d=\vert x_2 - x_1\vert$. Here, $x_1=-2$ and $x_2 = 1.5$. So $d=\vert1.5-(-2)\vert=\vert1.5 + 2\vert=\vert3.5\vert = 3.5$.

Step3: Evaluate $4-7\frac{1}{3}$

Rewrite $4$ as $\frac{12}{3}$ and $7\frac{1}{3}$ as $\frac{22}{3}$. Then $4 - 7\frac{1}{3}=\frac{12}{3}-\frac{22}{3}=\frac{12 - 22}{3}=-\frac{10}{3}=-3\frac{1}{3}$.

Step4: Evaluate $-2\frac{3}{8}-5\frac{1}{2}-(-9\frac{1}{4})$

Rewrite the mixed numbers as improper fractions: $-2\frac{3}{8}=-\frac{19}{8}$, $5\frac{1}{2}=\frac{11}{2}=\frac{44}{8}$, and $9\frac{1}{4}=\frac{37}{4}=\frac{74}{8}$.
The expression becomes $-\frac{19}{8}-\frac{44}{8}+\frac{74}{8}=\frac{-19-44 + 74}{8}=\frac{-63 + 74}{8}=\frac{11}{8}=1\frac{3}{8}$.

Step5: Model $8 - 3$ on number - line

Start at $8$ on the number - line and move $3$ units to the left. You end up at $5$.

Step6: Model $8+(-3)$ on number - line

Adding a negative number is the same as subtracting the positive of that number. So $8+(-3)$ is equivalent to $8 - 3$. Start at $8$ on the number - line and move $3$ units to the left. You end up at $5$.

Answer:

• Distance between $A$ and $B$: $3.5$
• $4 - 7\frac{1}{3}$: $-3\frac{1}{3}$
• $-2\frac{3}{8}-5\frac{1}{2}-(-9\frac{1}{4})$: $1\frac{3}{8}$
• $8 - 3$ (model result): $5$
• $8+(-3)$ (model result): $5$