Question

consider the number line shown. what is the distance between point a and point b? 3.5 units evaluate each expression. (answer each express q5 4 - 7\frac{1}{3} q6 - 2 model each expression on the number line. 8 - 3

Explanation:

Q4

Step1: Identify coordinates

Point A is at - 2 and point B is at 1.5.

Step2: Use distance formula

The distance $d$ between two points $x_1$ and $x_2$ on a number - line is $d=\vert x_1 - x_2\vert$. Here, $x_1=-2$ and $x_2 = 1.5$, so $d=\vert-2 - 1.5\vert=\vert-3.5\vert = 3.5$.

Step1: Rewrite the mixed number as an improper fraction

$7\frac{1}{3}=\frac{7\times3 + 1}{3}=\frac{22}{3}$, and $4=\frac{12}{3}$.

Step2: Subtract the fractions

$4-7\frac{1}{3}=\frac{12}{3}-\frac{22}{3}=\frac{12 - 22}{3}=-\frac{10}{3}=-3\frac{1}{3}$.

Step1: Start at the first number

On the number - line, start at 8.

Step2: Move left for subtraction

Since we are subtracting 3, move 3 units to the left. We end up at 5.

Answer:

3.5 units

Q5