Find the Missing Operator in -5-5-5-5?5-15: Mathematical Expression Challenge

Q: Why is -20 less than -10 when 20 is bigger than 10?

With negative numbers, the rules flip! Think of a number line: -20 is further to the left than -10, making it smaller. The more negative a number, the smaller its value.

Q: Do I need to follow order of operations here?

Yes! Even though these are just addition and subtraction, work from left to right: -5-5 = -10, then -10-5 = -15, then -15-5 = -20.

Q: What if I get confused about negative number comparisons?

Use the number line trick: whatever number is further to the left is smaller. You can also think about temperature: -20°F is colder (smaller) than -10°F!

Q: Should I change subtraction to addition when working with negatives?

You can, but it's not necessary here. $ -5-5 $ is the same as $ -5+(-5) $, both equal -10. Use whichever method feels more comfortable!

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

Remember: the symbol opens toward the larger number. Since -10 is larger than -20, we write -20

Negative Integer Comparison with Multiple Operations

Insert the compatible sign:

$-5-5-5-5?5-15$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 First, pick the correct mathematical sign. Ready?

00:14 Next, find the point, negative five, on the number line.

00:19 Now, take three jumps to the left, toward the negative side.

00:24 Remember, each jump here equals five units.

00:28 Great! We've solved the left side. Let's tackle the right side.

00:33 Locate the point fifteen on the number line.

00:36 Take one jump to the left. That's moving toward the negative.

00:42 Fantastic! We've completed the right side.

00:47 As you move right on the number line, numbers increase.

00:51 And there you have it! That's how you solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Insert the compatible sign:

$-5-5-5-5?5-15$

Step-by-step solution

Let's recall the laws:

$-(-x)=+x$

$+(-x)=-x$

We'll solve the left side first:

$-5-5=-10$

$-10-5=-15$

$-15-5=-20$

Now let's solve the right side:

$5-15=-10$

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

$-20 < -10$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Evaluate both sides completely before comparing values
Technique: Left side: -5-5-5-5 = -20, Right side: 5-15 = -10
Check: Compare final results: -20 < -10 since -20 is further left on number line ✓

Common Mistakes

Avoid these frequent errors

Comparing before completing all operations
Don't insert comparison operator before calculating both sides completely = wrong comparison! You might think -5 > 5 and choose wrong symbol. Always evaluate left side (-5-5-5-5 = -20) and right side (5-15 = -10) first, then compare final results.

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 is -20 less than -10 when 20 is bigger than 10?

With negative numbers, the rules flip! Think of a number line: -20 is further to the left than -10, making it smaller. The more negative a number, the smaller its value.

Do I need to follow order of operations here?

Yes! Even though these are just addition and subtraction, work from left to right: -5-5 = -10, then -10-5 = -15, then -15-5 = -20.

What if I get confused about negative number comparisons?

Use the number line trick: whatever number is further to the left is smaller. You can also think about temperature: -20°F is colder (smaller) than -10°F!

Should I change subtraction to addition when working with negatives?

You can, but it's not necessary here. $-5-5$ is the same as $-5+(-5)$ , both equal -10. Use whichever method feels more comfortable!

How do I remember which comparison symbol to use?

Remember: the symbol opens toward the larger number. Since -10 is larger than -20, we write -20 < -10. The 'mouth' of the < symbol opens toward -10!

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Find the Missing Operator in -5-5-5-5?5-15: Mathematical Expression Challenge

Negative Integer Comparison with Multiple 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 is -20 less than -10 when 20 is bigger than 10?

Do I need to follow order of operations here?

What if I get confused about negative number comparisons?

Should I change subtraction to addition when working with negatives?

How do I remember which comparison symbol to use?

🌟 Unlock Your Math Potential

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