Solve (16-6)×9+(7-3): Order of Operations Challenge

Order of Operations with Mixed Parentheses

Solve the following problem using the order of operations:

(166)×9+(73)= (16-6)\times9+(7-3)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's start with the parentheses, they always come first.
00:19 Next, we handle multiplication and division before any addition or subtraction.
00:25 Now, we're left with an easy addition problem.
00:28 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem using the order of operations:

(166)×9+(73)= (16-6)\times9+(7-3)=

2

Step-by-step solution

According to the order of operations, we'll first solve the exercises in parentheses:

(166)=10 (16-6)=10

(73)=4 (7-3)=4

We should obtain the following exercise:

10×9+4 10\times9+4

We'll place the multiplication exercise in parentheses to avoid confusion in the rest of the solution:

(10×9)+4= (10\times9)+4=

According to the order of operations, we'll solve the multiplication exercise and then add:

90+4=94 90+4=94

3

Final Answer

94 94

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve parentheses first, then multiplication and addition
  • Technique: Calculate (166)=10 (16-6) = 10 and (73)=4 (7-3) = 4 before other operations
  • Check: Final calculation 10×9+4=90+4=94 10 \times 9 + 4 = 90 + 4 = 94

Common Mistakes

Avoid these frequent errors
  • Solving operations left to right without following PEMDAS
    Don't calculate 16-6×9 first = 16-54 = wrong negative result! This ignores the parentheses and multiplication priority rules. Always solve parentheses first, then follow PEMDAS order completely.

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 can't I just solve from left to right?

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Mathematics has a specific order called PEMDAS to avoid confusion! Without it, the same expression could have different answers. Parentheses always come first, no matter where they appear.

Do I need to write out every step like in the solution?

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Yes! Writing each step helps you avoid mistakes and makes it easier to check your work. Show the parentheses calculations first: (166)=10 (16-6) = 10 and (73)=4 (7-3) = 4 .

What if I forget to do the parentheses first?

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You'll get the wrong answer! For example, doing 166×9 16-6 \times 9 first gives you 1654=38 16-54 = -38 , which is completely different from the correct answer of 94.

Is there a way to double-check my PEMDAS work?

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Absolutely! After solving, try working backwards from your answer. Does 944=90 94 - 4 = 90 and 90÷9=10 90 ÷ 9 = 10 ? This matches our parentheses results!

Why do we solve multiplication before addition in this problem?

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Even though addition appears last in the expression, multiplication always comes before addition in PEMDAS. So 10×9 10 \times 9 must be calculated before adding 4.

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