Which of the following statements is incorrect ?

Options

A. `(-5)/(8)` lies to the left of 0 oon the number line.
B. On the number line, `(3)/(7)` lies to the right of 0.
C. The rational numbers `(1)/(2) and - (1)/(2)` are on opposite sides of 0 on the number line.
D. Sum of rational number `(5)/(3) and - (5)/(3)` is not zero.

Answer

To determine which of the statements is incorrect, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement 1:** Minus 5 by 8 lies to the left of 0 on the number line.

- **Solution:**
- On a number line, negative numbers are located to the left of 0. Since -5/8 is a negative number, it indeed lies to the left of 0.
- **Conclusion:** This statement is **correct**.

### Step 2: Analyze the second statement
**Statement 2:** 3 by 7 lies to the right of 0.

- **Solution:**
- The number 3/7 is positive. Positive numbers are located to the right of 0 on the number line.
- **Conclusion:** This statement is **correct**.

### Step 3: Analyze the third statement
**Statement 3:** The rational numbers 1/2 and -1/2 are on opposite sides of 0.

- **Solution:**
- The number 1/2 is positive and -1/2 is negative. Therefore, they are indeed on opposite sides of 0 on the number line.
- **Conclusion:** This statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement 4:** The sum of the rational numbers 5/3 and -5/3 is not zero.

- **Solution:**
- To find the sum, we calculate:
\[ \frac{5}{3} + \left(-\frac{5}{3}\right) = \frac{5}{3} - \frac{5}{3} = 0 \]
- The sum is indeed 0, which contradicts the statement that it is not zero.
- **Conclusion:** This statement is **incorrect**.

### Final Answer:
The incorrect statement is **Statement 4**: The sum of the rational numbers 5/3 and -5/3 is not zero.

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