Solve (32-15-12)×34×12: Order of Operations Challenge

Q: Why do I solve the parentheses from left to right?

When you have only addition and subtraction inside parentheses, work from left to right. So $ 32-15-12 $ becomes $ 17-12 = 5 $. This follows the same left-to-right rule as regular order of operations.

Q: Can I multiply 34×12 first instead of doing parentheses?

No! Parentheses always come first in PEMDAS. You must solve $ (32-15-12) $ to get 5 before doing any multiplication. Skipping this step gives completely wrong answers.

Q: Why did you rearrange 5×34×12 to 5×12×34?

Since multiplication is commutative, you can multiply in any order! Calculating $ 5\times12 = 60 $ first makes $ 60\times34 $ easier than $ 5\times34 = 170 $ then $ 170\times12 $.

Q: What if I get a different answer when checking my work?

Go back and check each step! Most errors happen when skipping parentheses or making arithmetic mistakes. Recalculate $ 32-15-12 $ carefully, then multiply step by step.

Q: Do I always need to use PEMDAS for every math problem?

Yes! PEMDAS (order of operations) is a universal rule in mathematics. Even simple problems benefit from following this order to avoid mistakes and ensure consistent, correct results.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's solve this problem together.

00:14 First, we follow the order of operations, starting with parentheses. Let's find that part first.

00:21 Next, solve from left to right, just like reading a book.

00:25 Take each step at a time, starting with the leftmost operation.

00:36 Let's rearrange everything to make solving easier for us.

00:41 Solve each multiplication separately. Then keep going until we're done.

00:47 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$(32-15-12)\cdot34\cdot12=\text{?}$

2

Step-by-step solution

According to the rules of the order of operations, we first solve the exercise within parentheses from left to right:

$32-15=17$

$17-12=5$

Now, we obtain the exercise:

$5\times34\times12=$

According to the rules of the order of operations, since this is an exercise with only a multiplication operation, we rearrange the numbers to make the solution easier for us:

$5\times12\times34=$

We solve the exercise from left to right:

$5\times12=60$

$60\times34=2040$

3

Final Answer

2040

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication from left to right
Strategic Calculation: Rearrange $5\times34\times12$ to $5\times12\times34$ for easier computation
Final Check: Verify $(32-15-12)\times34\times12 = 5\times408 = 2040$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring parentheses and calculating left to right
Don't solve 32-15-12×34×12 without parentheses first = 32-15-4080 = -4063! This completely ignores order of operations rules. Always solve what's inside parentheses before any other operations, then multiply the result.

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 do I solve the parentheses from left to right?

+

When you have only addition and subtraction inside parentheses, work from left to right. So $32-15-12$ becomes $17-12 = 5$ . This follows the same left-to-right rule as regular order of operations.

Can I multiply 34×12 first instead of doing parentheses?

+

No! Parentheses always come first in PEMDAS. You must solve $(32-15-12)$ to get 5 before doing any multiplication. Skipping this step gives completely wrong answers.

Why did you rearrange 5×34×12 to 5×12×34?

+

Since multiplication is commutative, you can multiply in any order! Calculating $5\times12 = 60$ first makes $60\times34$ easier than $5\times34 = 170$ then $170\times12$ .

What if I get a different answer when checking my work?

+

Go back and check each step! Most errors happen when skipping parentheses or making arithmetic mistakes. Recalculate $32-15-12$ carefully, then multiply step by step.

Do I always need to use PEMDAS for every math problem?

+

Yes! PEMDAS (order of operations) is a universal rule in mathematics. Even simple problems benefit from following this order to avoid mistakes and ensure consistent, correct results.

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Solve (32-15-12)×34×12: Order of Operations Challenge

Order of Operations with Parentheses Priority

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