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

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

The denominator tells you the size of each piece. When adding $ \frac{1}{3} + \frac{1}{3} $, you're adding two pieces that are each one-third in size. The piece size stays the same!

Q: What if the denominators were different?

Then you'd need to find a common denominator first! But in this problem, both fractions already have the same denominator (3), so you can add directly.

Q: How can I visualize this problem?

Think of a pizza cut into 3 equal slices. You eat 1 slice, then eat 1 more slice. You've eaten $ \frac{2}{3} $ of the pizza total!

Q: Is my answer in simplest form?

Yes! $ \frac{2}{3} $ cannot be simplified further because 2 and 3 share no common factors other than 1.

Q: What's the difference between this and regular addition?

With whole numbers like 1 + 1 = 2, you're counting complete units. With fractions, you're adding parts of units while keeping track of what size those parts are.

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

00:07 Let's solve this problem together.

00:10 First, divide the rectangle into three equal parts.

00:14 Now, let's color each third with a different color.

00:18 Next, connect the colored sections and place them in the numerator.

00:23 And that gives us the solution. Great job!

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: Recognize that both fractions share the same denominator, which is 3.
Step 2: Add the numerators: $1 + 1 = 2$ .
Step 3: Keep the common denominator of 3, resulting in the fraction $\frac{2}{3}$ .

Now, let's work through each step:
Step 1: We observe that the denominators of both fractions are 3, so we do not need to change them.
Step 2: We add the numerators. Each fraction has a numerator of 1, so adding them gives us 2.
Step 3: We write the sum of the numerators over the common denominator, giving us $\frac{2}{3}$ .

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: When denominators are the same, add only the numerators
Technique: Add numerators: 1 + 1 = 2, keep denominator 3
Check: Verify $\frac{2}{3}$ by counting: two one-thirds = two-thirds ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators: 1/3 + 1/3 ≠ 2/6! Adding denominators creates a completely different fraction size. Always keep the common denominator unchanged and add only 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 you the size of each piece. When adding $\frac{1}{3} + \frac{1}{3}$ , you're adding two pieces that are each one-third in size. The piece size stays the same!

What if the denominators were different?

Then you'd need to find a common denominator first! But in this problem, both fractions already have the same denominator (3), so you can add directly.

How can I visualize this problem?

Think of a pizza cut into 3 equal slices. You eat 1 slice, then eat 1 more slice. You've eaten $\frac{2}{3}$ of the pizza total!

Is my answer in simplest form?

Yes! $\frac{2}{3}$ cannot be simplified further because 2 and 3 share no common factors other than 1.

What's the difference between this and regular addition?

With whole numbers like 1 + 1 = 2, you're counting complete units. With fractions, you're adding parts of units while keeping track of what size those parts are.

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