Solve 8-3²÷3: Order of Operations Practice Problem

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

Mathematics has a special order that's different from reading! Without PEMDAS, the same expression could have multiple answers, which would make math confusing and unreliable.

Q: What does the colon (:) symbol mean in this problem?

The colon (:) is another way to write division, just like ÷. So $ 9:3 $ means $ 9 \div 3 $ or $ \frac{9}{3} $.

Q: How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember it as "Please Excuse My Dear Aunt Sally."

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

If your check doesn't work out, go back and double-check each step. Make sure you calculated $ 3^2 = 9 $ correctly and followed the proper order!

Q: Are there any shortcuts for this type of problem?

No real shortcuts here! The key is to be systematic and follow PEMDAS carefully. Write out each step clearly to avoid mistakes.

Order of Operations with Exponents and Division

$8-3^2:3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:02 Calculate the exponent

00:05 Always solve multiplication and division before addition and subtraction

00:08 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$8-3^2:3=$

Step-by-step solution

Let's solve the expression step by step using the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The given expression is: $8-3^2:3=$

Step 1: Evaluate Exponents
The expression has an exponent, which we need to evaluate first. The exponent is $3^2$ .
Calculate $3^2$ which equals $9$ .
Now the expression becomes: $8 - 9 : 3$

Step 2: Division
Next, perform the division operation. Here we divide $9$ by $3$ .
Calculate $9 : 3$ which equals $3$ .
Now the expression becomes: $8 - 3$

Step 3: Subtraction
Finally, perform the subtraction.
Calculate $8 - 3$ which equals $5$ .

Therefore, the solution to the expression $8-3^2:3$ is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always evaluate exponents before division and subtraction operations
Technique: Calculate $3^2 = 9$ , then $9 \div 3 = 3$ , finally $8 - 3 = 5$
Check: Work backwards: $5 + 3 = 8$ and $3 \times 3 = 9 = 3^2$ ✓

Common Mistakes

Avoid these frequent errors

Performing operations from left to right without following PEMDAS
Don't calculate 8 - 3 = 5 first, then 5² ÷ 3 = 25/3! This ignores the order of operations and gives a completely wrong answer. Always follow PEMDAS: exponents first, then division, then subtraction.

Practice Quiz

Test your knowledge with interactive questions

$5+\sqrt{36}-1=$

FAQ

Everything you need to know about this question

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

Mathematics has a special order that's different from reading! Without PEMDAS, the same expression could have multiple answers, which would make math confusing and unreliable.

What does the colon (:) symbol mean in this problem?

The colon (:) is another way to write division, just like ÷. So $9:3$ means $9 \div 3$ or $\frac{9}{3}$ .

How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember it as "Please Excuse My Dear Aunt Sally."

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

If your check doesn't work out, go back and double-check each step. Make sure you calculated $3^2 = 9$ correctly and followed the proper order!

Are there any shortcuts for this type of problem?

No real shortcuts here! The key is to be systematic and follow PEMDAS carefully. Write out each step clearly to avoid mistakes.

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