Solve Mixed Number Subtraction: 13⅔ minus 3⅓

Q: Why don't I subtract the denominators too?

The denominator tells you the size of each piece - it stays the same! You're just taking away fewer pieces. Think of it like having 2 pizza slices out of 3, then eating 1 slice - you still have thirds, just fewer of them.

Q: What if the denominators were different?

If denominators don't match, you'd need to find a common denominator first. Convert both fractions to equivalent fractions with the same bottom number, then subtract normally.

Q: Can I convert to improper fractions instead?

Absolutely! Converting $ 13\frac{2}{3} $ to $ \frac{41}{3} $ and $ 3\frac{1}{3} $ to $ \frac{10}{3} $, then subtracting gives the same result. Use whichever method feels easier!

Q: How do I know if my final answer is simplified?

Check if the numerator and denominator share any common factors. In $ 10\frac{1}{3} $, the fraction $ \frac{1}{3} $ is already simplified since 1 and 3 have no common factors except 1.

Mixed Number Subtraction with Common Denominators

$13\frac{2}{3}-3\frac{1}{3}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 First, we'll break each mixed fraction into its whole number and fraction part.

00:19 Next, we'll subtract the fractions step by step.

00:29 Let's rearrange the numbers for easier subtraction, using the commutative property.

00:36 Now, calculate the difference between the whole numbers.

00:43 Subtract the fractions using a common denominator.

00:53 Combine the fractions and whole numbers to find the total.

00:58 And that's the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$13\frac{2}{3}-3\frac{1}{3}=$

Step-by-step solution

To solve $13\frac{2}{3} - 3\frac{1}{3}$ , we'll follow these steps:

Step 1: Subtract the whole numbers: $13 - 3 = 10$ .
Step 2: Subtract the fractions: $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$ .
Step 3: Combine the results: Combine the whole number and the fraction to get $10\frac{1}{3}$ .

Therefore, the solution to the problem is $10\frac{1}{3}$ .

Final Answer

$10\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtract whole numbers first, then subtract fractions separately
Technique: Since denominators match, subtract numerators: $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$
Check: Verify by converting to improper fractions: $\frac{41}{3} - \frac{10}{3} = \frac{31}{3} = 10\frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract $\frac{2}{3} - \frac{1}{3}$ as $\frac{1}{2}$ by subtracting both tops and bottoms! This gives the wrong denominator and incorrect answer. Always keep the common denominator the same and only subtract the numerators.

Practice Quiz

Test your knowledge with interactive questions

$2\frac{2}{5}+2\frac{2}{5}=$

FAQ

Everything you need to know about this question

Why don't I subtract the denominators too?

The denominator tells you the size of each piece - it stays the same! You're just taking away fewer pieces. Think of it like having 2 pizza slices out of 3, then eating 1 slice - you still have thirds, just fewer of them.

What if the denominators were different?

If denominators don't match, you'd need to find a common denominator first. Convert both fractions to equivalent fractions with the same bottom number, then subtract normally.

Can I convert to improper fractions instead?

Absolutely! Converting $13\frac{2}{3}$ to $\frac{41}{3}$ and $3\frac{1}{3}$ to $\frac{10}{3}$ , then subtracting gives the same result. Use whichever method feels easier!

How do I know if my final answer is simplified?

Check if the numerator and denominator share any common factors. In $10\frac{1}{3}$ , the fraction $\frac{1}{3}$ is already simplified since 1 and 3 have no common factors except 1.

What if I need to borrow from the whole number?

This happens when the first fraction is smaller than the second! You'd borrow 1 from the whole number and add it to the fraction as an improper fraction, then subtract normally.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Mixed Fractions 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