Solve: 30.63 - (14.68 - 5½) Using Order of Operations

Q: Why do I need to convert the mixed number to decimal first?

Converting mixed numbers to decimals makes subtraction much easier! $ 5\frac{1}{2} $ becomes 5.5, so you can directly calculate 14.68 - 5.5 without dealing with fraction arithmetic.

Q: What if I forget to work inside the parentheses first?

You'll get the wrong answer! The order of operations (PEMDAS) requires parentheses first. If you calculate left to right instead, you get 10.45 instead of the correct answer 21.45.

Q: How do I convert mixed numbers to decimals quickly?

For $ 5\frac{1}{2} $: Keep the whole number (5) and convert the fraction. Since $ \frac{1}{2} = 0.5 $, you get 5.5. Practice common fractions like $ \frac{1}{4} = 0.25 $ and $ \frac{3}{4} = 0.75 $!

Q: Can I work with fractions instead of converting to decimals?

Yes, but it's harder! You'd need to convert 14.68 to a fraction first: $ \frac{1468}{100} $. Converting mixed numbers to decimals is usually much simpler for these problems.

Q: How can I check if my final answer is correct?

Use reverse operations! Add 9.18 to your answer: 21.45 + 9.18 = 30.63 ✓. This confirms you solved the parentheses correctly and applied the final subtraction properly.

Step-by-step video solution

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Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$30.63-(14.68-5\frac{1}{2})=$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Simplify inside the parentheses $14.68 - 5\frac{1}{2}$
Step 2: Convert the mixed number $5\frac{1}{2}$ to decimal form
Step 3: Perform the subtraction from Step 1
Step 4: Complete the outer subtraction $30.63 - \text{(result from Step 3)}$

Now, let's work through each step:

Step 1: Inside the parentheses, simplify $14.68 - 5\frac{1}{2}$ .
Step 2: Convert $5\frac{1}{2}$ to a decimal which is $5.5$ .
Step 3: Calculate $14.68 - 5.5$ , which equals $9.18$ .
Step 4: Final calculation: $30.63 - 9.18 = 21.45$ .

Therefore, the solution to the problem is $21.45$ .

3

Final Answer

21.45

Key Points to Remember

Essential concepts to master this topic

Rule: Work inside parentheses first before outer operations
Technique: Convert $5\frac{1}{2}$ to 5.5 before calculating 14.68 - 5.5 = 9.18
Check: Verify 30.63 - 9.18 = 21.45 by adding: 21.45 + 9.18 = 30.63 ✓

Common Mistakes

Avoid these frequent errors

Working left to right instead of parentheses first
Don't calculate 30.63 - 14.68 first = 15.95! This ignores parentheses and gives 10.45 as wrong final answer. Always solve inside parentheses completely before moving to outer operations.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to decimal first?

+

Converting mixed numbers to decimals makes subtraction much easier! $5\frac{1}{2}$ becomes 5.5, so you can directly calculate 14.68 - 5.5 without dealing with fraction arithmetic.

What if I forget to work inside the parentheses first?

+

You'll get the wrong answer! The order of operations (PEMDAS) requires parentheses first. If you calculate left to right instead, you get 10.45 instead of the correct answer 21.45.

How do I convert mixed numbers to decimals quickly?

+

For $5\frac{1}{2}$ : Keep the whole number (5) and convert the fraction. Since $\frac{1}{2} = 0.5$ , you get 5.5. Practice common fractions like $\frac{1}{4} = 0.25$ and $\frac{3}{4} = 0.75$ !

Can I work with fractions instead of converting to decimals?

+

Yes, but it's harder! You'd need to convert 14.68 to a fraction first: $\frac{1468}{100}$ . Converting mixed numbers to decimals is usually much simpler for these problems.

How can I check if my final answer is correct?

+

Use reverse operations! Add 9.18 to your answer: 21.45 + 9.18 = 30.63 ✓. This confirms you solved the parentheses correctly and applied the final subtraction properly.

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Solve: 30.63 - (14.68 - 5½) Using Order of Operations

Order of Operations with Mixed Numbers

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