Solve 4² ÷ 2 + 5²: Order of Operations Practice

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

Mathematics has a specific order that must be followed to get the correct answer! Working left to right would give you different results depending on how you group operations. PEMDAS ensures everyone gets the same answer.

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

The colon (:) is another way to write division, just like ÷. So $ 4^2:2 $ means $ 4^2 ÷ 2 $ or "16 divided by 2."

Q: Do I really need to calculate both exponents first?

Yes! Even though they're in different parts of the expression, all exponents must be calculated before any division or addition. This is what the 'E' in PEMDAS means.

Q: How can I remember the order of operations?

Use the acronym PEMDAS: Please Excuse My Dear Aunt Sally. This helps you remember: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Q: What if I got 13 as my answer?

You likely added $ 4^2 ÷ 2 = 8 $ and $ 5 = 5 $ instead of $ 5^2 = 25 $. Double-check that you calculated both exponents: $ 4^2 = 16 $ and $ 5^2 = 25 $.

Order of Operations with Mixed Exponents

Solve the following exercise:

$4^2:2+5^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following expression

00:05 Break down the exponents

00:17 Always solve multiplication and division before addition and subtraction

00:38 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$4^2:2+5^2=$

Step-by-step solution

To solve the expression $4^2:2+5^2$ , we need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This guide will help us apply the correct sequence to solve the problem.

Step 1: Exponents
First, we solve the exponents in the expression. In this case, we have $4^2$ and $5^2$ .
Calculate each:
$4^2 = 4 \times 4 = 16$
$5^2 = 5 \times 5 = 25$
Step 2: Division
Next, we perform the division operation. In the expression $16 : 2$ , divide 16 by 2:
$16 : 2 = 8$
Step 3: Addition
Finally, we add the results from the previous steps together:
$8 + 25 = 33$

Thus, the value of the expression $4^2:2+5^2$ is $33$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always solve exponents first, then division, finally addition
Technique: Calculate $4^2 = 16$ and $5^2 = 25$ before other operations
Check: Final answer should be 33: $16 ÷ 2 + 25 = 8 + 25 = 33$ ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following PEMDAS
Don't solve $4^2 ÷ 2 + 5^2$ as (4² ÷ 2 + 5)² = 13² = 169! This ignores order of operations and gives a completely wrong result. Always calculate all exponents first, then division, then addition following PEMDAS.

Practice Quiz

Test your knowledge with interactive questions

$$ 6^2= $$

FAQ

Everything you need to know about this question

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

Mathematics has a specific order that must be followed to get the correct answer! Working left to right would give you different results depending on how you group operations. PEMDAS ensures everyone gets the same answer.

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

The colon (:) is another way to write division, just like ÷. So $4^2:2$ means $4^2 ÷ 2$ or "16 divided by 2."

Do I really need to calculate both exponents first?

Yes! Even though they're in different parts of the expression, all exponents must be calculated before any division or addition. This is what the 'E' in PEMDAS means.

How can I remember the order of operations?

Use the acronym PEMDAS: Please Excuse My Dear Aunt Sally. This helps you remember: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

What if I got 13 as my answer?

You likely added $4^2 ÷ 2 = 8$ and $5 = 5$ instead of $5^2 = 25$ . Double-check that you calculated both exponents: $4^2 = 16$ and $5^2 = 25$ .

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Solve 4² ÷ 2 + 5²: Order of Operations Practice

Order of Operations with Mixed Exponents

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

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

Do I really need to calculate both exponents first?

How can I remember the order of operations?

What if I got 13 as my answer?

🌟 Unlock Your Math Potential

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