Solve Fraction Addition: 1/5 + 2/5 Step-by-Step

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

The denominator tells us the size of each piece. Since both fractions have pieces of the same size (fifths), we keep that size. We only count how many pieces we have total by adding the numerators!

Q: What if the denominators were different?

Then you'd need to find a common denominator first! Convert both fractions so they have the same denominator, then add the numerators like normal.

Q: How can I picture this problem?

Imagine a pizza cut into 5 equal slices. You have 1 slice, then someone gives you 2 more slices. Now you have 3 slices total out of 5, which is $ \frac{3}{5} $!

Q: Do I need to simplify my answer?

Always check if you can simplify! In this case, $ \frac{3}{5} $ is already in lowest terms because 3 and 5 share no common factors other than 1.

Q: What's the fastest way to check my work?

Convert to decimals: $ \frac{1}{5} = 0.2 $ and $ \frac{2}{5} = 0.4 $, so 0.2 + 0.4 = 0.6, which equals $ \frac{3}{5} $!

Fraction Addition with Like Denominators

$\frac{1}{5}+\frac{2}{5}=$

❤️ 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

00:00 Solve

00:04 Add under common denominator

00:08 Calculate the numerator

00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{1}{5}+\frac{2}{5}=$

Step-by-step solution

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

Step 1: Identify the numbers to add: $\frac{1}{5}$ and $\frac{2}{5}$ .
Step 2: Confirm they have a common denominator.
Step 3: Add their numerators.
Step 4: Keep the common denominator.

Let's execute these steps:

Step 1: We have the fractions $\frac{1}{5}$ and $\frac{2}{5}$ .

Step 2: Confirmed, both fractions have a common denominator, which is 5.

Step 3: Add the numerators: $1 + 2 = 3$ .

Step 4: The denominator remains the same: 5.

Therefore, the sum of the fractions is $\frac{3}{5}$ .

Final Answer

$\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators when denominators are the same
Technique: Keep denominator 5, add 1 + 2 = 3
Check: Verify $\frac{3}{5}$ makes sense: 3 parts out of 5 ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 1+2 and 5+5 to get $\frac{3}{10}$ = wrong answer! This creates a completely different fraction that doesn't represent the actual sum. Always keep the denominator the same and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why don't I add the denominators too?

The denominator tells us the size of each piece. Since both fractions have pieces of the same size (fifths), we keep that size. We only count how many pieces we have total by adding the numerators!

What if the denominators were different?

Then you'd need to find a common denominator first! Convert both fractions so they have the same denominator, then add the numerators like normal.

How can I picture this problem?

Imagine a pizza cut into 5 equal slices. You have 1 slice, then someone gives you 2 more slices. Now you have 3 slices total out of 5, which is $\frac{3}{5}$ !

Do I need to simplify my answer?

Always check if you can simplify! In this case, $\frac{3}{5}$ is already in lowest terms because 3 and 5 share no common factors other than 1.

What's the fastest way to check my work?

Convert to decimals: $\frac{1}{5} = 0.2$ and $\frac{2}{5} = 0.4$ , so 0.2 + 0.4 = 0.6, which equals $\frac{3}{5}$ !

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with 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