Solve Complex Order of Operations: -9-(15-3-[17-14]+4)+12÷3×7

Q: Why do we solve the brackets [17-14] before anything else?

Brackets have the highest priority in PEMDAS! We must solve the innermost brackets first: $ [17-14]=3 $, then work our way outward to the parentheses.

Q: Is 12÷3×7 the same as 12÷(3×7)?

No! Without parentheses, we solve from left to right: $ 12\div3\times7 = 4\times7 = 28 $. But $ 12\div(3\times7) = 12\div21 = \frac{4}{7} $ is completely different!

Q: What if I get confused with all the brackets and parentheses?

Work from the inside out! First solve square brackets $ [17-14] $, then regular parentheses, then division/multiplication from left to right, and finally addition/subtraction from left to right.

Order of Operations with Nested Brackets

Solve the following equation:

$-9-(15-3-\lbrack17-14\rbrack+4)+12\colon3\times7=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:14 Let's solve this problem together.

00:19 First, tackle everything inside the parentheses. If you see nested ones, start with the innermost.

00:42 Next, handle each operation step by step.

01:07 Remember, multiplication and division come before addition and subtraction.

01:26 Keep solving from left to right, following the order of operations.

01:32 And there's your solution! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$-9-(15-3-\lbrack17-14\rbrack+4)+12\colon3\times7=$

Step-by-step solution

According to the order of arithmetic operations, we begin by solving the innermost parenthesis and the division exercise first:

$-9-(15-3-3+4)+4\times7=$

We then solve the parenthesis exercise from left to right:

$15-3-3+4=12-3+4=9+4=13$

We obtain the following exercise:

$-9-13+(4\times7)=$

We then solve the multiplication exercise and obtain:

$-9-13+28=$

Lastly we solve the exercise from left to right:

$-9-13=-22$

$-22+28=6$

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Solve innermost brackets first, then work outward systematically
Technique: Replace $12\div3\times7$ with $4\times7=28$ from left to right
Check: Final calculation $-22+28=6$ matches the correct answer ✓

Common Mistakes

Avoid these frequent errors

Solving operations out of order
Don't solve $12\div3\times7$ as $12\div(3\times7)=12\div21$ = wrong answer! Multiplication and division have equal priority and must be solved left to right. Always follow PEMDAS strictly: brackets first, then multiplication/division from left to right.

Practice Quiz

Test your knowledge with interactive questions

Solve the following problem:

$187\times(8-5)=$

FAQ

Everything you need to know about this question

Why do we solve the brackets [17-14] before anything else?

Brackets have the highest priority in PEMDAS! We must solve the innermost brackets first: $[17-14]=3$ , then work our way outward to the parentheses.

Is 12÷3×7 the same as 12÷(3×7)?

No! Without parentheses, we solve from left to right: $12\div3\times7 = 4\times7 = 28$ . But $12\div(3\times7) = 12\div21 = \frac{4}{7}$ is completely different!

How do I keep track of all the negative signs?

Be extra careful with negatives! The expression starts with $-9-$ , so you're subtracting the entire parentheses result. Write it as negative 9 minus positive 13 to get $-22$ .

What if I get confused with all the brackets and parentheses?

Work from the inside out! First solve square brackets $[17-14]$ , then regular parentheses, then division/multiplication from left to right, and finally addition/subtraction from left to right.

Can I use a calculator for this problem?

Yes, but be careful with order of operations! Many calculators follow PEMDAS automatically, but it's better to solve step by step to avoid input errors with all those brackets and negative signs.

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Solve Complex Order of Operations: -9-(15-3-[17-14]+4)+12÷3×7

Order of Operations with Nested Brackets

❤️ 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 we solve the brackets [17-14] before anything else?

Is 12÷3×7 the same as 12÷(3×7)?

How do I keep track of all the negative signs?

What if I get confused with all the brackets and parentheses?

Can I use a calculator for this problem?

🌟 Unlock Your Math Potential

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