Solve Mixed Number Equation: 3¼ - (½ - ½) with Order of Operations

Q: Why do I need to simplify the fractions first?

Simplifying makes the arithmetic easier! When you see $ \frac{3}{6} $ and $ \frac{5}{10} $, converting them to $ \frac{1}{2} $ shows they're equal, so their difference is 0.

Q: Do I always convert mixed numbers to improper fractions?

Not always! In this problem, since we're subtracting 0, the mixed number stays the same. Only convert when you need to perform actual addition or subtraction with fractions.

Q: How do I know if I followed order of operations correctly?

Check that you solved parentheses first, then any other operations. Write each step clearly: parentheses → simplify → final calculation.

Q: What's the difference between 3²/₄ and 3½?

They're the same value! $ 3\frac{2}{4} = 3\frac{1}{2} $ because $ \frac{2}{4} $ simplifies to $ \frac{1}{2} $. Always simplify fractions to their lowest terms.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve a problem together!

00:08 Remember, when you see a minus times a minus, it turns into a plus.

00:15 We'll use this idea in our exercise.

00:24 Now, solve step by step. Follow the order of operations, working left to right.

00:35 Reduce the fractions and solve them carefully.

00:45 Great job! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$3\frac{2}{4}-(\frac{3}{6}-\frac{5}{10})=$

2

Step-by-step solution

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

Step 1: Simplify the fractions inside the parentheses.
Step 2: Perform the arithmetic operation inside the parentheses.
Step 3: Subtract this result from the mixed number.

Now, let's work through each step:
Step 1: Simplify the fractions: $\frac{3}{6} = \frac{1}{2}$ and $\frac{5}{10} = \frac{1}{2}$ .
Step 2: Perform arithmetic inside the parentheses: $\frac{1}{2} - \frac{1}{2} = 0$ .
Step 3: Subtract $0$ from $3\frac{2}{4}$ . First, convert $3\frac{2}{4}$ to a simpler form: $3\frac{2}{4} = 3\frac{1}{2}$ . Therefore, $3\frac{1}{2} - 0 = 3\frac{1}{2}$ .

Therefore, the solution to the problem is $3\frac{1}{2}$ .

3

Final Answer

$3\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Always solve inside parentheses first before other operations
Simplification: Convert $\frac{3}{6} = \frac{1}{2}$ and $\frac{5}{10} = \frac{1}{2}$ before subtracting
Verification: $\frac{1}{2} - \frac{1}{2} = 0$ , so $3\frac{1}{2} - 0 = 3\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and working left to right
Don't subtract $3\frac{2}{4} - \frac{3}{6}$ first = wrong setup! This skips the parentheses and breaks the order of operations. Always solve what's inside parentheses before doing any other operations.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do I need to simplify the fractions first?

+

Simplifying makes the arithmetic easier! When you see $\frac{3}{6}$ and $\frac{5}{10}$ , converting them to $\frac{1}{2}$ shows they're equal, so their difference is 0.

What if the parentheses don't equal zero?

+

Then you'd subtract that result from the mixed number! For example, if the parentheses equaled $\frac{1}{4}$ , you'd calculate $3\frac{1}{2} - \frac{1}{4}$ by finding a common denominator.

Do I always convert mixed numbers to improper fractions?

+

Not always! In this problem, since we're subtracting 0, the mixed number stays the same. Only convert when you need to perform actual addition or subtraction with fractions.

How do I know if I followed order of operations correctly?

+

Check that you solved parentheses first, then any other operations. Write each step clearly: parentheses → simplify → final calculation.

What's the difference between 3²/₄ and 3½?

+

They're the same value! $3\frac{2}{4} = 3\frac{1}{2}$ because $\frac{2}{4}$ simplifies to $\frac{1}{2}$ . Always simplify fractions to their lowest terms.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve Mixed Number Equation: 3¼ - (½ - ½) with Order of Operations

Mixed Number Subtraction with Parentheses

❤️ Continue Your Math Journey!