Which of the following numbers is greater than 4: 5, −5, −1/2 or −25?

Introduction / Context:
This question checks very basic understanding of the number line and comparison of positive and negative numbers. You are asked to determine which given number is greater than 4. While simple, such questions ensure that fundamental concepts are solid.

Given Data / Assumptions:
The numbers to compare with 4 are 5, −5, −1/2 and −25.We must find which of these is strictly greater than 4.All numbers are real and can be compared on a standard number line.

Concept / Approach:
Positive numbers are greater than any negative numbers. Among positive numbers, those with larger magnitude are greater. Negative numbers lie to the left of zero on the number line and are always less than positive numbers. Fractions between −1 and 0 are still negative and less than any positive integer.

Step-by-Step Solution:
Step 1: Note that 5 is a positive integer greater than zero.Step 2: The numbers −5 and −25 are negative integers, both less than zero.Step 3: The number −1/2 is a negative fraction, also less than zero.Step 4: Because 4 is a positive integer, any negative number is automatically less than 4.Step 5: Therefore, −5, −1/2 and −25 are all less than 4.Step 6: Compare 5 and 4: 5 is one unit to the right of 4 on the number line, so 5 is greater than 4.

Verification / Alternative check:
Visualize or sketch a number line with points marked for −25, −5, −1/2, 0, 4 and 5. It is clear that −25, −5 and −1/2 lie to the left of 0, while 4 and 5 lie to the right. Since 5 is to the right of 4, it is greater. None of the negative numbers come close to 4 on the positive side of the line.

Why Other Options Are Wrong:
The number −5 is negative and therefore less than any positive number including 4. Similarly, −1/2 and −25 are negative and lie well to the left of 4 on the number line. None of these can be greater than 4. Only 5 is both positive and greater than 4.

Common Pitfalls:
Although rare at this level, some learners misinterpret the relative size of negative numbers, thinking that −25 is greater because its magnitude is larger. It is important to remember that on the number line, being further left means being smaller, so −25 is less than −5. Keeping a mental picture of the number line avoids such confusion.

Final Answer:
The only number greater than 4 among the options is 5.