Question

this number line spans 0 to 5. find the sum of the values represented by the points. write the sum as a mixed number.

Explanation:

Determine the scale of the number line

Count the total number of equal intervals between 0 and 5.
There are 20 equal intervals spanning from 0 to 5.
Each major unit (1 whole) contains 4 intervals.
Thus, each tick mark represents \(\frac{1}{4}\).

Identify the value of each plotted point

Locate the position of each of the four points.
Point 1 is at the 3rd tick mark:

$$ P_1 = \frac{3}{4} $$

Point 2 is at the 7th tick mark:

$$ P_2 = \frac{7}{4} = 1\frac{3}{4} $$

Point 3 is at the 12th tick mark:

$$ P_3 = \frac{12}{4} = 3 $$

Point 4 is at the 16th tick mark:

$$ P_4 = \frac{16}{4} = 4 $$

Calculate the sum of the values

Add the four identified values together.

$$ \text{Sum} = \frac{3}{4} + \frac{7}{4} + \frac{12}{4} + \frac{16}{4} $$

Combine the numerators over the common denominator:

$$ \text{Sum} = \frac{3 + 7 + 12 + 16}{4} = \frac{38}{4} $$

Convert the sum to a mixed number

Simplify the improper fraction and convert it.

$$ \frac{38}{4} = \frac{19}{2} $$

Divide 19 by 2 to find the mixed number:

$$ 19 \div 2 = 9 \text{ with a remainder of } 1 $$

This gives:

$$ 9\frac{1}{2} $$

Answer:

\(9\frac{1}{2}\)