Solve the Fraction Addition: 2/7 + 1/7 Step by Step

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

The denominator tells us what size pieces we're working with. Since $ \frac{2}{7} $ and $ \frac{1}{7} $ are both sevenths, we're adding pieces of the same size, so the denominator stays 7.

Q: How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 2 slices plus 1 more slice. That gives you 3 slices total, which is $ \frac{3}{7} $ of the whole pizza!

Q: What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But since both fractions have 7 as the denominator, you can add them directly!

Fraction Addition with Same Denominators

$\frac{2}{7}+\frac{1}{7}=$

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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 color the appropriate number of squares, according to the given data

00:12 Now let's count and add to the numerator in the new fraction

00:16 The denominator equals the number of cells we divided

00:21 Any number divided by itself always equals 1

00:25 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

$\frac{2}{7}+\frac{1}{7}=$

Step-by-step solution

To solve the problem of adding $\frac{2}{7}$ and $\frac{1}{7}$ , we will follow these steps:

Step 1: Identify the common denominator. Since both fractions have the same denominator, 7, we can proceed to add the numerators directly.
Step 2: Add the numerators: $2 + 1$ .
Step 3: Keep the common denominator in the result.

Now, let's work through each step:
Step 1: Both fractions, $\frac{2}{7}$ and $\frac{1}{7}$ , have the denominator 7.
Step 2: Add the numerators: $2 + 1 = 3$ .
Step 3: The fraction becomes $\frac{3}{7}$ by keeping the common denominator.

Thus, the sum of $\frac{2}{7}$ and $\frac{1}{7}$ is $\frac{3}{7}$ .

Final Answer

$\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Same Denominator Rule: Add numerators only, keep the denominator unchanged
Addition Technique: $2 + 1 = 3$ , so $\frac{2}{7} + \frac{1}{7} = \frac{3}{7}$
Check Method: Count visual parts: 2 sevenths plus 1 seventh equals 3 sevenths total ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add $\frac{2}{7} + \frac{1}{7}$ as $\frac{3}{14}$ ! This creates smaller pieces than you started with and gives the wrong answer. Always keep the same denominator and add only the numerators when denominators are identical.

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 us what size pieces we're working with. Since $\frac{2}{7}$ and $\frac{1}{7}$ are both sevenths, we're adding pieces of the same size, so the denominator stays 7.

How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 2 slices plus 1 more slice. That gives you 3 slices total, which is $\frac{3}{7}$ of the whole pizza!

What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But since both fractions have 7 as the denominator, you can add them directly!

Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $\frac{3}{7}$ cannot be reduced further since 3 and 7 share no common factors.

How do I know my answer is correct?

Look at the visual diagram! Count the shaded sections: 2 sections plus 1 section equals 3 sections out of 7 total, confirming $\frac{3}{7}$ is correct.

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