Compare Expressions: 24:6:2 vs 24:(6:2) - Which Sign Fits?

Q: Why do parentheses change the answer so much?

Parentheses force you to calculate in a different order! In $ 24:(6:2) $, you must solve 6÷2=3 first, then 24÷3=8. Without parentheses, you work left-to-right: 24÷6=4, then 4÷2=2.

Q: What if I forget about the parentheses?

You'll get the wrong answer! Always look for parentheses first before starting any calculation. They're like mathematical traffic signals - they control which operation goes first.

Q: How do I remember the order of operations?

Use PEMDAS: Parentheses first, then Exponents, then Multiplication/Division from left-to-right, then Addition/Subtraction from left-to-right.

Q: Are there other symbols that work like parentheses?

Yes! Brackets [ ] and braces { } also group operations. Always solve the innermost grouping symbols first, then work outward.

Q: What does the colon symbol mean in this problem?

The colon (:) means division, just like ÷. So $ 24:6:2 $ is the same as 24÷6÷2. Both symbols represent the same operation!

Order of Operations with Parentheses Priority

What is the correct sign?
$24:6:2$ _____ $24:(6:2)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 First, find the correct sign to use.

00:16 Now, let's calculate each side separately.

00:20 Solve the problem from left to right using the order of operations.

00:24 We've found the solution for the left side. Now, let's focus on the right side.

00:30 Always start by solving what's inside the parentheses first.

00:35 Then, solve the remaining parts of the expression.

00:39 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the correct sign?
$24:6:2$ _____ $24:(6:2)$

Step-by-step solution

We solve the exercise:

$24:6:2=$

According to the rules, we solve the exercise from left to right:

$24:6=4$

$4:2=2$

Now we solve the exercise:

$24:(6:2)=$

According to the rules, first we solve the exercise inside the parentheses and then we divide:

$6:2=3$

$24:3=8$

Therefore:

$3 < 8$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Operations in parentheses are always calculated first
Technique: Left-to-right division: 24÷6÷2 becomes 4÷2 = 2
Check: Compare final results: 2 < 8 confirms correct comparison ✓

Common Mistakes

Avoid these frequent errors

Treating all division operations equally without considering parentheses
Don't calculate 24÷6÷2 = 24÷(6÷2) = 24÷3 = 8! This ignores parentheses priority and gives the wrong result. Always solve parentheses first, then work left-to-right for operations of equal precedence.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why do parentheses change the answer so much?

Parentheses force you to calculate in a different order! In $24:(6:2)$ , you must solve 6÷2=3 first, then 24÷3=8. Without parentheses, you work left-to-right: 24÷6=4, then 4÷2=2.

What if I forget about the parentheses?

You'll get the wrong answer! Always look for parentheses first before starting any calculation. They're like mathematical traffic signals - they control which operation goes first.

How do I remember the order of operations?

Use PEMDAS: Parentheses first, then Exponents, then Multiplication/Division from left-to-right, then Addition/Subtraction from left-to-right.

Are there other symbols that work like parentheses?

Yes! Brackets [ ] and braces { } also group operations. Always solve the innermost grouping symbols first, then work outward.

What does the colon symbol mean in this problem?

The colon (:) means division, just like ÷. So $24:6:2$ is the same as 24÷6÷2. Both symbols represent the same operation!

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Compare Expressions: 24:6:2 vs 24:(6:2) - Which Sign Fits?

Order of Operations with Parentheses Priority

❤️ 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 do parentheses change the answer so much?

What if I forget about the parentheses?

How do I remember the order of operations?

Are there other symbols that work like parentheses?

What does the colon symbol mean in this problem?

🌟 Unlock Your Math Potential

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