Solve: -3+(-3)+(-3)?3+3+3 - Negative and Positive Number Patterns

Q: Why does adding negative numbers make the result more negative?

Think of it like debt! If you owe $3 three times, you owe $9 total. Adding negative numbers means you're moving further left on the number line.

Q: How do I know which comparison symbol to use?

Calculate both sides completely first! Then ask: Is the left number bigger, smaller, or equal? Use $ if left is smaller, \( > $ if left is bigger, $ = $ if they're equal.

Q: What's the difference between +(-3) and -3?

They're exactly the same! The rule $ +(-x) = -x $ means adding a negative is the same as subtracting a positive.

Q: Can I just ignore the parentheses around negative numbers?

Yes, you can! Writing $ -3+(-3)+(-3) $ is the same as $ -3-3-3 $. The parentheses just help show the negative signs clearly.

Q: How do I remember that -9 is less than 9?

Use the number line! Negative numbers are always to the left of positive numbers. Since -9 is left of 9, we write \( -9 .

Integer Addition with Comparison Operations

$-3+(-3)+(-3)?3+3+3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 First, select the correct sign.

00:12 Locate negative three on the number line.

00:16 Remember, positive times negative is always negative.

00:20 Now, let's jump three steps left to the negative side.

00:25 Again, positive times negative remains negative.

00:30 Let's take another three steps left, again to the negative side.

00:35 That's it for the left side. Next, we'll work on the right.

00:40 Find positive three on the number line.

00:43 Take three jumps right, moving to the positive side.

00:47 And one more time, take another three jumps right.

00:52 We've solved the right side!

01:01 Great job, everyone! That's the complete solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-3+(-3)+(-3)?3+3+3$

Step-by-step solution

Let's remember the laws:

$-(-x)=+x$

$+(-x)=-x$

We'll solve the left side first.

Let's write the exercise in the appropriate form:

$-3-3-3=$

We'll solve the exercise from left to right:

$-3-3=-6$

$-6-3=-9$

Now let's solve the right side:

$3+3+3=$

$3+3=6$

$6+3=9$

Since the right side is larger, the appropriate sign will be:

$-9 < 9$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Sign Rules: Adding negatives means subtracting their absolute values
Technique: Calculate each side separately: -3-3-3 = -9 and 3+3+3 = 9
Check: Compare final values: -9 < 9 means left side is smaller ✓

Common Mistakes

Avoid these frequent errors

Confusing addition of negatives with subtraction
Don't treat -3+(-3)+(-3) as -3-(-3)-(-3) = -3+3+3 = 3! This changes negatives to positives incorrectly. Always remember that +(-x) means -x, so you're adding negative values together.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why does adding negative numbers make the result more negative?

Think of it like debt! If you owe $3 three times, you owe$ 9 total. Adding negative numbers means you're moving further left on the number line.

How do I know which comparison symbol to use?

Calculate both sides completely first! Then ask: Is the left number bigger, smaller, or equal? Use $<$ if left is smaller, $>$ if left is bigger, $=$ if they're equal.

What's the difference between +(-3) and -3?

They're exactly the same! The rule $+(-x) = -x$ means adding a negative is the same as subtracting a positive.

Can I just ignore the parentheses around negative numbers?

Yes, you can! Writing $-3+(-3)+(-3)$ is the same as $-3-3-3$ . The parentheses just help show the negative signs clearly.

How do I remember that -9 is less than 9?

Use the number line! Negative numbers are always to the left of positive numbers. Since -9 is left of 9, we write $-9 < 9$ .

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Solve: -3+(-3)+(-3)?3+3+3 - Negative and Positive Number Patterns

Integer Addition with Comparison Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does adding negative numbers make the result more negative?

How do I know which comparison symbol to use?

What's the difference between +(-3) and -3?

Can I just ignore the parentheses around negative numbers?

How do I remember that -9 is less than 9?

🌟 Unlock Your Math Potential

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