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

$74+32+6+4+4=\text{?}$

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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