Compare Points A and K: Finding the Correct Inequality Symbol on a Number Line

Q: Why is -5 less than 5 when 5 looks smaller than -5?

The negative sign is crucial! Think of it as debt vs. money: having -5 dollars (owing 5) is worse than having 5 dollars. On a number line, negative numbers are always to the left of positive numbers.

Q: How do I remember which way the inequality symbol goes?

The pointy end always points to the smaller number! Think of it like a hungry alligator that wants to eat the bigger number: \( -5 means the alligator eats 5.

Q: What if both numbers were negative?

With two negative numbers, the one closer to zero is greater. For example: $ -2 > -5 $ because -2 is further right on the number line.

Q: What's the difference between < and ≤?

(not equal), while ≤ means 'less than or equal to'. Since A = -5 and K = 5 are different numbers, we use

Number Line Comparison with Negative Values

Fill in the corresponding sign

$A?K$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the corresponding sign

$A?K$

Step-by-step solution

Let's locate the letters on the number line and see which numbers represent them:

$A=-5$

$K=5$

After locating the numbers, we can determine:

$-5<5$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Numbers increase from left to right on number lines
Technique: Locate positions: A is at -5, K is at 5
Check: Verify $-5 < 5$ by counting rightward movement ✓

Common Mistakes

Avoid these frequent errors

Thinking negative numbers are greater because they look bigger
Don't compare -5 and 5 by looking at the digit size = wrong comparison! The negative sign makes -5 smaller than any positive number. Always remember that negative numbers are always less than positive numbers.

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 -5 less than 5 when 5 looks smaller than -5?

The negative sign is crucial! Think of it as debt vs. money: having -5 dollars (owing 5) is worse than having 5 dollars. On a number line, negative numbers are always to the left of positive numbers.

How do I remember which way the inequality symbol goes?

The pointy end always points to the smaller number! Think of it like a hungry alligator that wants to eat the bigger number: $-5 < 5$ means the alligator eats 5.

What if both numbers were negative?

With two negative numbers, the one closer to zero is greater. For example: $-2 > -5$ because -2 is further right on the number line.

Do I always need to look at the number line?

Not always! Once you understand the pattern, you can compare mentally. But drawing a quick number line is always helpful when you're unsure about negative number comparisons.

What's the difference between < and ≤?

< means 'less than' (not equal), while ≤ means 'less than or equal to'. Since A = -5 and K = 5 are different numbers, we use < here.

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