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

All negative numbers appear on the number line to the left of the number 0.

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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