Solve the Addition: 1/3 + 1/3 Step-by-Step

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

The denominator tells you what size pieces you're working with. When adding $ \frac{1}{3} + \frac{1}{3} $, you're adding thirds + thirds = more thirds, not sixths!

Q: What if the denominators were different?

You'd need to find a common denominator first! Convert both fractions so they have the same bottom number, then add the numerators.

Q: How do I know if my answer needs to be simplified?

$ \frac{2}{3} $ is already in lowest terms because 2 and 3 share no common factors other than 1. Always check if you can divide both top and bottom by the same number.

Q: Can I convert this to a decimal instead?

Yes! $ \frac{2}{3} = 0.666... $ or 0.67 rounded. But keeping it as a fraction is usually more exact.

Q: What does it mean to have 'like denominators'?

Like denominators means the bottom numbers are the same. This makes addition easy because you're adding the same type of pieces (thirds, fourths, etc.).

Fraction Addition with Common Denominators

Solve the following exercise:

$\frac{1}{3}+\frac{1}{3}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's add the fractions under a common denominator

00:09 Let's 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

Solve the following exercise:

$\frac{1}{3}+\frac{1}{3}=\text{?}$

Step-by-step solution

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

Step 1: Acknowledge that the fractions have a common denominator of 3.
Step 2: Add the numerators of the two fractions.
Step 3: Maintain the common denominator and simplify if necessary.

Now, let's work through each step:

Step 1: The fractions given are $\frac{1}{3}$ and $\frac{1}{3}$ , both having the denominator 3.

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

Step 3: The resulting fraction is $\frac{2}{3}$ , with the denominator remaining unchanged. Simplification is not required.

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

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators when denominators are the same
Technique: $\frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \frac{2}{3}$
Check: Verify denominator stays 3 and numerators were added correctly ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators: $\frac{1}{3} + \frac{1}{3} ≠ \frac{2}{6}$ ! This creates a completely different fraction value. Always keep the common denominator unchanged 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 together?

The denominator tells you what size pieces you're working with. When adding $\frac{1}{3} + \frac{1}{3}$ , you're adding thirds + thirds = more thirds, not sixths!

What if the denominators were different?

You'd need to find a common denominator first! Convert both fractions so they have the same bottom number, then add the numerators.

How do I know if my answer needs to be simplified?

$\frac{2}{3}$ is already in lowest terms because 2 and 3 share no common factors other than 1. Always check if you can divide both top and bottom by the same number.

Can I convert this to a decimal instead?

Yes! $\frac{2}{3} = 0.666...$ or 0.67 rounded. But keeping it as a fraction is usually more exact.

What does it mean to have 'like denominators'?

Like denominators means the bottom numbers are the same. This makes addition easy because you're adding the same type of pieces (thirds, fourths, etc.).

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