Solve: 2×(3+½×8) Using Order of Operations

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

Mathematics has a special order that's different from reading! PEMDAS ensures everyone gets the same answer. Without it, $ 2 \times (3 + \frac{1}{2} \times 8) $ could have multiple interpretations.

Q: How do I handle fractions mixed with whole numbers?

Treat fractions like any other number! In this problem, $ \frac{1}{2} \times 8 = 4 $, then add: $ 3 + 4 = 7 $. The fraction multiplication happens before the addition.

Q: What if I get confused about which operation to do first?

Write down PEMDAS and check each step! For this problem: Parentheses contain multiplication and addition, so do $ \frac{1}{2} \times 8 $ first, then $ 3 + 4 $, finally $ 2 \times 7 $.

Q: Can I convert everything to decimals instead?

Yes! $ \frac{1}{2} = 0.5 $, so $ 2 \times (3 + 0.5 \times 8) = 2 \times (3 + 4) = 14 $. Both methods work, but fractions are often more precise for exact calculations.

Q: How do I check my work step by step?

Follow PEMDAS and verify each step: $ \frac{1}{2} \times 8 = 4 $ ✓, then $ 3 + 4 = 7 $ ✓, finally $ 2 \times 7 = 14 $ ✓. Each step should make sense!

Order of Operations with Mixed Fractions

$2\times(3+\frac{1}{2}\times8)=\text{ ?}$

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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

00:06 Multiplication and division precede addition and subtraction

00:10 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2\times(3+\frac{1}{2}\times8)=\text{ ?}$

Step-by-step solution

According to the order of operations, parentheses take precedence over everything else.

Therefore, we will first solve the multiplication and then addition within parenthesis.

To make solving the multiplication exercise easier, we will convert 8 into a simple fraction:

$2\times(3+\frac{1}{2}\times\frac{8}{1})=2\times(3+\frac{8}{2})=2\times(3+4)$

Now we will solve the addition exercise inside the parentheses and finally multiply to get our answer:

$2\times7=14$

Final Answer

$14$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication and division left to right
Technique: Convert $\frac{1}{2} \times 8 = \frac{8}{2} = 4$ before adding
Check: Substitute: $2 \times (3 + 4) = 2 \times 7 = 14$ ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following PEMDAS
Don't calculate $2 \times 3 = 6$ first = wrong answer of 10! This ignores parentheses which have highest priority. Always solve everything inside parentheses completely before multiplying by the outside number.

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 like reading?

Mathematics has a special order that's different from reading! PEMDAS ensures everyone gets the same answer. Without it, $2 \times (3 + \frac{1}{2} \times 8)$ could have multiple interpretations.

How do I handle fractions mixed with whole numbers?

Treat fractions like any other number! In this problem, $\frac{1}{2} \times 8 = 4$ , then add: $3 + 4 = 7$ . The fraction multiplication happens before the addition.

What if I get confused about which operation to do first?

Write down PEMDAS and check each step! For this problem: Parentheses contain multiplication and addition, so do $\frac{1}{2} \times 8$ first, then $3 + 4$ , finally $2 \times 7$ .

Can I convert everything to decimals instead?

Yes! $\frac{1}{2} = 0.5$ , so $2 \times (3 + 0.5 \times 8) = 2 \times (3 + 4) = 14$ . Both methods work, but fractions are often more precise for exact calculations.

How do I check my work step by step?

Follow PEMDAS and verify each step: $\frac{1}{2} \times 8 = 4$ ✓, then $3 + 4 = 7$ ✓, finally $2 \times 7 = 14$ ✓. Each step should make sense!

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