Number Line Comparison: Finding the Relationship Between D(-2) and H(2)

Q: Why is -2 less than 2 when 2 is smaller than 2?

Think of it like temperature! -2°C is colder than 2°C, so -2 is actually smaller. The negative sign means the number is below zero on the number line, making it less than any positive number.

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

Use the number line trick: the inequality sign always "points" toward the smaller number. Since -2 is to the left of 2 on the number line, we write -2

Q: What if both numbers were negative?

With two negative numbers, the one closer to zero is actually larger. For example, -1 > -3 because -1 is further right on the number line than -3.

Q: Can I just ignore the negative signs?

Never ignore negative signs! They completely change the value. $ -2 \neq 2 $ - they're opposites! Always consider the sign when comparing numbers.

Q: How do I locate points on a number line quickly?

Start from zero and count: negative numbers go left, positive numbers go right. Each step represents one unit, so -2 is two steps left from zero.

Number Line Comparison with Negative Values

Fill in the missing sign (?):

$D?H$

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Understand the problem

Fill in the missing sign (?):

$D?H$

Step-by-step solution

First we will locate the letters on the number line to see which numbers they represent:

$D=-2$

$H=2$

Since the number 2 is positive and the number minus 2 is negative, we can write the following:

$-2<2$

Therefore, the answer is (b).

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Position Rule: Numbers further left on number line are smaller
Reading Technique: D is at -2, H is at 2, so -2 < 2
Check: Negative numbers are always less than positive numbers ✓

Common Mistakes

Avoid these frequent errors

Thinking negative numbers are greater because they have larger absolute values
Don't compare -2 and 2 by looking at just the digits = wrong conclusion that -2 > 2! This ignores the negative sign's meaning. Always remember that negative numbers are positioned left of zero and are smaller 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 -2 less than 2 when 2 is smaller than 2?

Think of it like temperature! -2°C is colder than 2°C, so -2 is actually smaller. The negative sign means the number is below zero on the number line, making it less than any positive number.

How do I remember which way the inequality sign goes?

Use the number line trick: the inequality sign always "points" toward the smaller number. Since -2 is to the left of 2 on the number line, we write -2 < 2.

What if both numbers were negative?

With two negative numbers, the one closer to zero is actually larger. For example, -1 > -3 because -1 is further right on the number line than -3.

Can I just ignore the negative signs?

Never ignore negative signs! They completely change the value. $-2 \neq 2$ - they're opposites! Always consider the sign when comparing numbers.

How do I locate points on a number line quickly?

Start from zero and count: negative numbers go left, positive numbers go right. Each step represents one unit, so -2 is two steps left from zero.

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