Solve the Expression: [(27÷3)-9×2]+(5+3) Using Order of Operations

Q: Why can't I just work from left to right?

Mathematics has a specific order of operations (PEMDAS) that everyone follows. Without it, the same expression could have different answers! Always do multiplication and division before addition and subtraction.

Q: What's the difference between ÷ and : symbols?

Both $ ÷ $ and $ : $ mean division - they're just different ways to write the same operation. So $ 27:3 $ is exactly the same as $ 27÷3 = 9 $.

Q: Do I solve what's in brackets first or follow PEMDAS inside?

Great question! You solve brackets first, but inside the brackets you still follow PEMDAS. So in $ [(27:3)-9×2] $, do division first: $ 27:3 = 9 $, then multiplication: $ 9×2 = 18 $.

Q: How do I handle negative numbers in my final calculation?

When you get to $ 9-18+5+3 $, work left to right: $ 9-18 = -9 $, then $ -9+5 = -4 $, finally $ -4+3 = -1 $. Don't be afraid of negative answers!

Q: What if I get a different answer than the choices given?

Double-check your work! Go through each step again carefully. Most mistakes happen when rushing through multiplication/division or when adding/subtracting negative numbers.

Order of Operations with Mixed Arithmetic

$[(27:3)-9\cdot2]+(5+3)=$

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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

00:07 Multiplication and division precede addition and subtraction

00:13 Calculate the parentheses

00:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$[(27:3)-9\cdot2]+(5+3)=$

Step-by-step solution

We begin by simplifying the given expression paying attention to the order of arithmetic operations which states that powers precede multiplication, division precedes addition and subtraction and that parentheses precede all of the above.

Let's keep in mind that in the given expression there are no parentheses or powers. However there are multiplication and division operations, so we will use them as our starting point. After which we will perform the addition and subtraction operations:

$27:3-9\cdot2+5+3= \\ 9-18+5+3=\\ -1$ Therefore, the correct answer is option B.

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication/division left to right
Technique: Work inside brackets: 27÷3 = 9, then 9×2 = 18
Check: Final calculation: 9-18+5+3 = -1 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following PEMDAS
Don't just calculate 27÷3-9×2 as (27÷3-9)×2 = wrong answer! This ignores order of operations and gives incorrect results. Always complete all multiplication and division first, then add and subtract from left to right.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why can't I just work from left to right?

Mathematics has a specific order of operations (PEMDAS) that everyone follows. Without it, the same expression could have different answers! Always do multiplication and division before addition and subtraction.

What's the difference between ÷ and : symbols?

Both $÷$ and $:$ mean division - they're just different ways to write the same operation. So $27:3$ is exactly the same as $27÷3 = 9$ .

Do I solve what's in brackets first or follow PEMDAS inside?

Great question! You solve brackets first, but inside the brackets you still follow PEMDAS. So in $[(27:3)-9×2]$ , do division first: $27:3 = 9$ , then multiplication: $9×2 = 18$ .

How do I handle negative numbers in my final calculation?

When you get to $9-18+5+3$ , work left to right: $9-18 = -9$ , then $-9+5 = -4$ , finally $-4+3 = -1$ . Don't be afraid of negative answers!

What if I get a different answer than the choices given?

Double-check your work! Go through each step again carefully. Most mistakes happen when rushing through multiplication/division or when adding/subtracting negative numbers.

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