Solve the Fraction Addition: 2/3 + 1/3 Step by Step

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

The denominator tells us what size pieces we're working with. Since both fractions have thirds, we're still working with thirds after adding - just more of them!

Q: What if my answer is an improper fraction?

That's perfectly normal! $ \frac{3}{3} $ is an improper fraction that equals the whole number 1. Always simplify your final answer when possible.

Q: Do I always get a whole number when adding fractions?

No! For example, $ \frac{1}{3} + \frac{1}{3} = \frac{2}{3} $, which stays as a fraction. It depends on whether your numerators add up to a multiple of the denominator.

Q: How can I check if my answer is right?

Think about it logically: $ \frac{2}{3} $ plus $ \frac{1}{3} $ gives you all 3 thirds, which makes 1 whole. You can also convert to decimals: 0.67 + 0.33 ≈ 1 ✓

Q: What if the denominators were different?

Then you'd need to find a common denominator first! But since both fractions here have denominator 3, you can add directly. Lucky you!

Fraction Addition with Like Denominators

$\frac{2}{3}+\frac{1}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this problem together!

00:06 First, we need a common denominator to add the fractions.

00:10 Next, calculate the numerator carefully.

00:14 Remember, any number divided by itself equals one.

00:18 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{3}+\frac{1}{3}=$

Step-by-step solution

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

Step 1: Identify the common denominator.
Step 2: Add the numerators.
Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions, $\frac{2}{3}$ and $\frac{1}{3}$ , have the same denominator of 3.

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

Step 3: Place the sum over the common denominator to get $\frac{3}{3}$ .

The fraction $\frac{3}{3}$ simplifies to 1.

Therefore, the solution to the problem is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are the same, add only the numerators
Technique: Keep denominator 3, add numerators: 2 + 1 = 3
Check: Simplify the result: $\frac{3}{3} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 2 + 1 = 3 AND 3 + 3 = 6 to get $\frac{3}{6}$ ! This creates a completely wrong fraction that doesn't represent the actual sum. Always keep the denominator the same when adding fractions with like denominators.

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 what size pieces we're working with. Since both fractions have thirds, we're still working with thirds after adding - just more of them!

What if my answer is an improper fraction?

That's perfectly normal! $\frac{3}{3}$ is an improper fraction that equals the whole number 1. Always simplify your final answer when possible.

Do I always get a whole number when adding fractions?

No! For example, $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ , which stays as a fraction. It depends on whether your numerators add up to a multiple of the denominator.

How can I check if my answer is right?

Think about it logically: $\frac{2}{3}$ plus $\frac{1}{3}$ gives you all 3 thirds, which makes 1 whole. You can also convert to decimals: 0.67 + 0.33 ≈ 1 ✓

What if the denominators were different?

Then you'd need to find a common denominator first! But since both fractions here have denominator 3, you can add directly. Lucky you!

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