Solve 18-((560÷(70/3)-14)-9): Order of Operations Challenge

Q: Why do I divide by a fraction using multiplication?

Dividing by a fraction is the same as multiplying by its reciprocal! So $ 560 ÷ \frac{70}{3} $ becomes $ 560 × \frac{3}{70} $. This makes the calculation much easier.

Q: How do I keep track of all these parentheses?

Work from the inside out, one layer at a time. Start with the innermost parentheses first: $ 560 ÷ \frac{70}{3} $, then move to the next layer. Cross out each step as you complete it!

Q: What if I get confused with the order of operations?

Remember PEMDAS: Parentheses first (innermost), then Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Take your time with each step!

Q: Can I use a calculator for the fraction division?

Yes! But convert to decimals carefully. $ \frac{70}{3} = 23.333... $, so $ 560 ÷ 23.333... = 24 $. The reciprocal method is often more accurate for exact answers.

Q: How do I check if 17 is really the right answer?

Substitute back into the original: $ 18-((560÷\frac{70}{3}-14)-9) $. Work through: $ 560÷\frac{70}{3} = 24 $, $ 24-14 = 10 $, $ 10-9 = 1 $, $ 18-1 = 17 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem together.

00:14 Remember, dividing is like multiplying by the reciprocal.

00:26 Break 560 into factors of 8 and 70. Great job so far!

00:42 Next, let's simplify whatever we can. You're doing great!

00:52 Always start by solving inside the parentheses first.

00:56 And that's how we find the solution to the question. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$18-((560:\frac{70}{3}-14)-9)=\text{?}$

2

Step-by-step solution

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

Step 1: Calculate the division inside the innermost parentheses: $560 : \frac{70}{3}$ .
Step 2: Use the reciprocal to perform division: Rewrite as $560 \times \frac{3}{70}$ .
Step 3: Continue simplifying the expression from inside to outside.

Now, let's work through each step:
Step 1: Evaluate $560 : \frac{70}{3}$ . This is equivalent to $560 \times \frac{3}{70}$ .
Step 2: Perform the multiplication: $(560 \times 3) / 70 = 1680 / 70 = 24$ .
Step 3: Simplify $24 - 14$ . This results in $10$ .
Step 4: Calculate $10 - 9$ . This equals $1$ .
Step 5: Subtract this from 18: $18 - 1 = 17$ .

Therefore, the answer to the problem is $17$ .

3

Final Answer

$17$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always work from innermost parentheses outward
Division Technique: Convert $560 ÷ \frac{70}{3}$ to $560 × \frac{3}{70} = 24$
Check Work: Substitute back step by step: 18-((24-14)-9) = 18-1 = 17 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following parentheses order
Don't calculate 18-560 first = massive negative number! This ignores the nested parentheses structure and creates impossible calculations. Always start with the innermost parentheses and work outward following PEMDAS.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I divide by a fraction using multiplication?

+

Dividing by a fraction is the same as multiplying by its reciprocal! So $560 ÷ \frac{70}{3}$ becomes $560 × \frac{3}{70}$ . This makes the calculation much easier.

How do I keep track of all these parentheses?

+

Work from the inside out, one layer at a time. Start with the innermost parentheses first: $560 ÷ \frac{70}{3}$ , then move to the next layer. Cross out each step as you complete it!

What if I get confused with the order of operations?

+

Remember PEMDAS: Parentheses first (innermost), then Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Take your time with each step!

Can I use a calculator for the fraction division?

+

Yes! But convert to decimals carefully. $\frac{70}{3} = 23.333...$ , so $560 ÷ 23.333... = 24$ . The reciprocal method is often more accurate for exact answers.

How do I check if 17 is really the right answer?

+

Substitute back into the original: $18-((560÷\frac{70}{3}-14)-9)$ . Work through: $560÷\frac{70}{3} = 24$ , $24-14 = 10$ , $10-9 = 1$ , $18-1 = 17$ ✓

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Solve 18-((560÷(70/3)-14)-9): Order of Operations Challenge

Complex Division with Nested Parentheses

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