Evaluate (7+2+3)(7+6)(12-3-4): Multi-Parentheses Multiplication

Order of Operations with Multiple Parentheses

(7+2+3)(7+6)(1234)=? (7+2+3)(7+6)(12-3-4)=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:03 Always solve the parentheses first, starting with the leftmost operation
00:13 Continue to solve all the parentheses using the same method
00:16 There's multiplication between parentheses
00:23 We'll continue to solve all parentheses
00:38 Arrange the equation into a more manageable format
00:47 Solve each multiplication separately and then continue to solve
00:51 Solve the expression using long multiplication
01:42 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(7+2+3)(7+6)(1234)=? (7+2+3)(7+6)(12-3-4)=\text{?}

2

Step-by-step solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all else.

Therefore we'll start by simplifying the expressions in parentheses first:
(7+2+3)(7+6)(1234)=12135 (7+2+3)(7+6)(12-3-4)=\\ 12\cdot13\cdot5

Now we'll calculate the multiplication result step by step from left to right:

12135=1565=780 12\cdot13\cdot5 =\\ 156\cdot5 =\\ 780

Note that since the commutative property of multiplication applies to the expression we simplified above between all terms, the order of operations in this calculation doesn't matter (it's not necessary to perform the left multiplication first etc. as we did). However it is recommended to practice performing operations from left to right since this is the natural order of arithmetic operations (in the absence of parentheses, or other preceding arithmetic operations according to the order of operations mentioned at the beginning of this solution).

Therefore the correct answer is answer C.

3

Final Answer

780

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always simplify expressions inside parentheses first
  • Technique: Calculate left to right: 1213=156 12 \cdot 13 = 156 , then 1565=780 156 \cdot 5 = 780
  • Check: Verify each parentheses: (7+2+3)=12, (7+6)=13, (12-3-4)=5 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying before simplifying parentheses
    Don't multiply 7×7×12 = 588 then add/subtract other numbers! This ignores order of operations and gives wrong results. Always simplify each set of parentheses completely before multiplying the results together.

Practice Quiz

Test your knowledge with interactive questions

Solve the following problem:

\( 15\times2\times8= \)

FAQ

Everything you need to know about this question

Why can't I just multiply all the first numbers together?

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Because the order of operations requires you to complete everything inside parentheses first! You must calculate (7+2+3), (7+6), and (12-3-4) separately before multiplying.

Does it matter which parentheses I solve first?

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No! You can solve the parentheses in any order you want. Just make sure to complete each one fully before moving to multiplication.

Can I multiply the results in a different order?

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Yes! Due to the commutative property, 12×13×5 12 \times 13 \times 5 gives the same result as 5×12×13 5 \times 12 \times 13 . However, calculating left to right is good practice.

What if I get different numbers in the parentheses?

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Double-check your arithmetic! For this problem: 7+2+3=12 7+2+3=12 , 7+6=13 7+6=13 , and 1234=5 12-3-4=5 . Getting different results means there's an addition or subtraction error.

How do I remember the order of operations?

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Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In this problem, parentheses come first, then multiplication!

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