Solve the Fraction Addition: 1/7 + 3/7 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 are sevenths, we keep sevenths! Adding denominators would change the piece size completely.

Q: What if the denominators were different?

If denominators are different, you need to find a common denominator first. But here both are already sevenths, so we can add directly!

Q: How can I visualize this problem?

Think of a pizza cut into 7 slices. You have 1 slice plus 3 more slices = 4 slices total out of 7. That's $ \frac{4}{7} $!

Q: Do I need to simplify my answer?

$ \frac{4}{7} $ is already in lowest terms since 4 and 7 share no common factors other than 1. Always check if your answer can be simplified!

Q: What's the easiest way to remember this rule?

Think: Same bottom, add the top! When denominators match, just add the numerators and keep the same denominator.

Fraction Addition with Same Denominators

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Add under common denominator

00:06 Calculate the numerator

00:10 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

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

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the fractions to be added: $\frac{1}{7}$ and $\frac{3}{7}$ .
Step 2: Recognize that both fractions have the same denominator, which is 7.
Step 3: Add the numerators: $1 + 3 = 4$ .
Step 4: Use the same denominator for the result: 7.

Therefore, the solution is that the sum of the two fractions is $\frac{4}{7}$ .

The correct multiple-choice answer is : $\frac{4}{7}$

Final Answer

$\frac{4}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators when denominators are the same
Technique: $1 + 3 = 4$ , keep denominator 7
Check: Count unit fractions: $\frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = \frac{4}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add $\frac{1}{7} + \frac{3}{7}$ as $\frac{4}{14}$ ! This creates a completely different fraction value. Always keep the same denominator and only add the numerators when denominators match.

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 are sevenths, we keep sevenths! Adding denominators would change the piece size completely.

What if the denominators were different?

If denominators are different, you need to find a common denominator first. But here both are already sevenths, so we can add directly!

How can I visualize this problem?

Think of a pizza cut into 7 slices. You have 1 slice plus 3 more slices = 4 slices total out of 7. That's $\frac{4}{7}$ !

Do I need to simplify my answer?

$\frac{4}{7}$ is already in lowest terms since 4 and 7 share no common factors other than 1. Always check if your answer can be simplified!

What's the easiest way to remember this rule?

Think: Same bottom, add the top! When denominators match, just add the numerators and keep the same denominator.

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