Solve the Inequality: 4½ < -5 Using Number Line Visualization

Q: Why is a positive number always bigger than a negative number?

Think of it like temperature or money! Having $4.50 is always better than owing $5. On a number line, positive numbers are to the right of zero, negative numbers are to the left.

Q: How do I use the number line to compare these numbers?

Find both numbers on the number line. The number that appears further to the right is always the larger number. Since 4½ is far right of -5, we know $ 4\frac{1}{2} > -5 $.

Q: What if I mix up the inequality symbols?

Remember: the open mouth of the symbol always 'eats' the bigger number! So $ 4\frac{1}{2} > -5 $ means 4½ is greater than -5.

Q: Do I need to convert the mixed number to compare?

Not necessary for this comparison! Since 4½ is positive and -5 is negative, you can immediately tell that 4½ is larger without any calculations.

Q: How can I remember which numbers are bigger?

Use the number line rule: numbers get bigger as you move right. Also remember: Any positive number > any negative numberZero > any negative numberAny positive number > zero

Inequality Comparison with Mixed Numbers

$4\frac{1}{2} < -5$

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Understand the problem

$4\frac{1}{2} < -5$

Step-by-step solution

The answer is incorrect because a negative number cannot be greater than a positive number:

$4\frac{1}{2} > -5$

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic

Number Position: Positive numbers are always greater than negative numbers
Visual Method: Use number line position: 4½ is right of -5
Check: Compare signs first: positive 4½ > negative -5 ✓

Common Mistakes

Avoid these frequent errors

Comparing absolute values instead of actual values
Don't compare |4½| vs |-5| and say 4½ < 5 = wrong conclusion! This ignores the negative sign completely. Always compare the actual signed values: positive 4½ is always greater than negative -5.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

Why is a positive number always bigger than a negative number?

Think of it like temperature or money! Having $4.50 is always better than owing $5. On a number line, positive numbers are to the right of zero, negative numbers are to the left.

How do I use the number line to compare these numbers?

Find both numbers on the number line. The number that appears further to the right is always the larger number. Since 4½ is far right of -5, we know $4\frac{1}{2} > -5$ .

What if I mix up the inequality symbols?

Remember: the open mouth of the symbol always 'eats' the bigger number! So $4\frac{1}{2} > -5$ means 4½ is greater than -5.

Do I need to convert the mixed number to compare?

Not necessary for this comparison! Since 4½ is positive and -5 is negative, you can immediately tell that 4½ is larger without any calculations.

How can I remember which numbers are bigger?

Use the number line rule: numbers get bigger as you move right. Also remember:

Any positive number > any negative number
Zero > any negative number
Any positive number > zero

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