Solve (12-6+9)×(7+3): Order of Operations Practice

Order of Operations with Nested Parentheses

(12−6+9)×(7+3)= (12-6+9)\times(7+3)= ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Parentheses precede all other operations, so we'll start with them
00:06 Solve the operations within the parentheses according to order of operations
00:16 We're left with a simple multiplication problem
00:19 That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(12−6+9)×(7+3)= (12-6+9)\times(7+3)= ?

2

Step-by-step solution

According to the order of operations, we will first solve the expressions in parentheses and then multiply:

(12−6+9)=(6+9)=15 (12-6+9)=(6+9)=15

(7+3)=10 (7+3)=10

Then solve the multiplication exercise:

15×10=150 15\times10=150

3

Final Answer

150 150

Key Points to Remember

Essential concepts to master this topic
  • Rule: Solve expressions inside parentheses before multiplying between them
  • Technique: Calculate (12-6+9)=15 and (7+3)=10, then multiply 15×10=150
  • Check: Work left to right inside parentheses: 12-6=6, then 6+9=15 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying before solving parentheses completely
    Don't multiply 12×7 first or mix operations between parentheses = wrong answer like 84! This ignores the order of operations. Always complete each set of parentheses fully before multiplying the results together.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why can't I just multiply the first numbers in each parentheses?

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Because parentheses mean "do this entire calculation first"! You must finish all operations inside each set of parentheses before moving to multiplication.

Do I solve both parentheses at the same time?

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You can solve them in any order since they're separate! Many students find it easier to work left to right: solve (12-6+9) first, then (7+3).

What if I get different numbers inside the parentheses?

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Double-check your arithmetic! For (12-6+9): first 12−6=6 12-6=6 , then 6+9=15 6+9=15 . Work step by step and don't rush.

How do I remember the order of operations?

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Use PEMDAS (Please Excuse My Dear Aunt Sally): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Always do parentheses first!

What if there were no parentheses in this problem?

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Without parentheses, you'd follow left-to-right order: 12−6+9×7+3 12-6+9×7+3 would give a completely different answer because multiplication happens before addition/subtraction!

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