Solve the Fraction Addition: 3/7 + 1/7 Step-by-Step

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

The denominator tells you how many equal parts the whole is divided into. Since both fractions are parts of the same whole (divided into 7), you're just combining pieces - not changing the size of the pieces!

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. But here, they're already the same.

Q: How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 3 slices, then get 1 more slice. You now have $ \frac{4}{7} $ of the pizza - 4 slices out of 7 total!

Q: Do I need to simplify my answer?

Always check if you can simplify! For $ \frac{4}{7} $, since 4 and 7 share no common factors except 1, this fraction is already in lowest terms.

Q: What does the rectangle diagram show?

The rectangle is divided into 7 equal parts (vertical lines create sections). The shaded portion represents the sum - you can count the parts to verify your answer matches the visual!

Fraction Addition with Like Denominators

Solve the following exercise:

$\frac{3}{7}+\frac{1}{7}=\text{?}$

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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 divide our complete rectangle into 7 parts

00:09 Let's color the parts corresponding to each fraction

00:16 Let's combine all the colored parts and place in the numerator

00:21 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:

$\frac{3}{7}+\frac{1}{7}=\text{?}$

Step-by-step solution

To solve this problem of adding fractions with like denominators, we will follow these steps:

Step 1: Identify and confirm that the denominators of both fractions are the same. Here, both fractions have the denominator $7$ .
Step 2: Add the numerators of both fractions: $3 + 1 = 4$ .
Step 3: Keep the common denominator, which is $7$ .
Step 4: Write the resultant fraction as $\frac{4}{7}$ .

Therefore, the sum of $\frac{3}{7}$ and $\frac{1}{7}$ is $\frac{4}{7}$ .

Final Answer

$\frac{4}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, add numerators and keep denominator
Technique: Add numerators: 3 + 1 = 4, keep 7
Check: Count visual parts: 3 shaded + 1 shaded = 4 out of 7 total ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 3/7 + 1/7 = 4/14! This creates a completely different fraction with wrong value. Always keep the same denominator when fractions have like denominators - 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 you how many equal parts the whole is divided into. Since both fractions are parts of the same whole (divided into 7), you're just combining pieces - not changing the size of the pieces!

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. But here, they're already the same.

How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 3 slices, then get 1 more slice. You now have $\frac{4}{7}$ of the pizza - 4 slices out of 7 total!

Do I need to simplify my answer?

Always check if you can simplify! For $\frac{4}{7}$ , since 4 and 7 share no common factors except 1, this fraction is already in lowest terms.

What does the rectangle diagram show?

The rectangle is divided into 7 equal parts (vertical lines create sections). The shaded portion represents the sum - you can count the parts to verify your answer matches the visual!

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