Solve Division Expression: 66÷(360÷60) Step by Step

Q: Why do I have to do the division in parentheses first?

The parentheses tell you the exact order to follow! In math, parentheses have the highest priority - they're like saying 'do this calculation first, then use that result.'

Q: What if I forget about the parentheses and just work left to right?

You'll get a completely wrong answer! $ 66÷360÷60 $ would give you about 0.003, but $ 66÷(360÷60) $ gives you 11 - that's a huge difference!

Q: How can I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Parentheses always come first!

Q: Is there a way to check my answer besides working backwards?

Yes! You can also think about it logically: since $ 360÷60 = 6 $, we're really asking 'how many 6's fit into 66?' That's 11, which matches our answer.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:07 Therefore when opening the parentheses, it will end up multiplied by C

00:11 We will use this formula in our exercise

00:18 We will solve one operation at a time

00:23 We will write division as a fraction

00:27 We will divide by 6, and substitute in our exercise

00:33 We will reduce what we can

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$66:(360:60)=$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate the inner division $360 : 60$ .
Step 2: Use the result from Step 1 to evaluate the outer division $66 : \text{(result from Step 1)}$ .

Now, let's work through each step:

Step 1: Evaluate $360 : 60$ . This means $\frac{360}{60}$ . Dividing, we have:

$\frac{360}{60} = 6$ .

Step 2: Use the result from Step 1 to evaluate $66 : 6$ . This means $\frac{66}{6}$ . Dividing, we get:

$\frac{66}{6} = 11$ .

Therefore, the solution to the problem is $11$ .

3

Final Answer

11

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve expressions inside parentheses first
Technique: Calculate 360÷60 = 6, then solve 66÷6 = 11
Check: Work backwards: 11×6 = 66 and 6×60 = 360 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without respecting parentheses
Don't calculate 66÷360 first = 0.18, then divide by 60 = 0.003! This ignores the parentheses which change the order completely. Always evaluate expressions inside parentheses before anything else.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I have to do the division in parentheses first?

+

The parentheses tell you the exact order to follow! In math, parentheses have the highest priority - they're like saying 'do this calculation first, then use that result.'

What if I forget about the parentheses and just work left to right?

+

You'll get a completely wrong answer! $66÷360÷60$ would give you about 0.003, but $66÷(360÷60)$ gives you 11 - that's a huge difference!

How can I remember the order of operations?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Parentheses always come first!

Is there a way to check my answer besides working backwards?

+

Yes! You can also think about it logically: since $360÷60 = 6$ , we're really asking 'how many 6's fit into 66?' That's 11, which matches our answer.

What if the numbers inside the parentheses don't divide evenly?

+

No problem! Just calculate the decimal or fraction result from the parentheses first, then use that exact value for the outer division. Always be precise with your intermediate steps.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve Division Expression: 66÷(360÷60) Step by Step

Order of Operations with Nested Division

❤️ Continue Your Math Journey!