Question

consider the number line.
which equation does the number line represent?
a $\frac{10}{8} + \frac{1}{2} = \frac{14}{8}$
b $\frac{10}{2} + \frac{1}{2} = \frac{10}{2}$
c $\frac{10}{8} + \frac{4}{8} = \frac{14}{8}$
d $\frac{10}{8} + \frac{4}{8} = \frac{18}{8}$

Explanation:

Step1: Analyze the number line

The number line has segments. Let's assume each small tick represents a fraction with denominator 8 (since the options have denominators 8 or 2, and 8 is more likely for multiple ticks). The first jump is from $\frac{10}{8}$ (or $1\frac{2}{8}$) and the second jump is $\frac{4}{8}$.

Step2: Check the options

• Option A: $\frac{10}{8}+\frac{1}{2}=\frac{10}{8}+\frac{4}{8}=\frac{14}{8}$, but the second term in the option is $\frac{1}{2}$, but the number line's second segment should be $\frac{4}{8}$ (if ticks are $\frac{1}{8}$). Wait, no, let's recalculate. Wait, the first term is $\frac{10}{8}$, second term: if the second jump is 4 ticks (each $\frac{1}{8}$), then it's $\frac{4}{8}=\frac{1}{2}$? No, wait, maybe the number line's first part is from 0 to $\frac{10}{8}$? No, the labels are a, 1, 2. Wait, maybe the first arrow is from a (let's say 0) to 10/8 (which is 1 and 2/8), then the second arrow is 4/8 (since 10/8 + 4/8 = 14/8 = 1 and 6/8). Wait, option C is $\frac{10}{8}+\frac{4}{8}=\frac{14}{8}$, which matches the sum. Let's check the denominators: in the number line, if each tick is 1/8, then the first length is 10 ticks (10/8), the second is 4 ticks (4/8), so sum is 14/8. So option C is correct.

Answer:

C. $\frac{10}{8} + \frac{4}{8} = \frac{14}{8}$