Add `(5)/(3)` to `(-8)/(3)` on a number line.

Answer

To solve the problem of adding \(\frac{5}{3}\) to \(-\frac{8}{3}\) on a number line, we can follow these steps:

### Step 1: Understand the numbers
We have two rational numbers: \(\frac{5}{3}\) (which is positive) and \(-\frac{8}{3}\) (which is negative).

### Step 2: Find a common denominator
Since both numbers already have the same denominator (3), we can directly add the numerators.

### Step 3: Add the numerators
Now we will add the two fractions:
\[ -\frac{8}{3} + \frac{5}{3} = \frac{-8 + 5}{3} \]

### Step 4: Simplify the numerator
Calculating the numerator:
\[ -8 + 5 = -3 \]
So, we have:
\[ -\frac{8}{3} + \frac{5}{3} = \frac{-3}{3} \]

### Step 5: Simplify the fraction
Now, simplify \(\frac{-3}{3}\):
\[ \frac{-3}{3} = -1 \]

### Step 6: Conclusion
Thus, the result of adding \(\frac{5}{3}\) to \(-\frac{8}{3}\) is \(-1\).

### Summary of the solution:
\[ -\frac{8}{3} + \frac{5}{3} = -1 \]

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