Adding Fractions with Like Denominators: Sevenths Example

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

The denominator tells us what size pieces we're working with. Since both fractions are sevenths, we're adding pieces of the same size. Adding denominators would change the piece size, which doesn't make mathematical sense!

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

Check if the numerator and denominator share any common factors. In $ \frac{4}{7} $, since 4 and 7 don't share any factors except 1, it's already in simplest form.

Q: Can I use this method for any fractions?

Only when denominators are the same! If denominators are different (like $ \frac{1}{3} + \frac{1}{4} $), you need to find equivalent fractions with common denominators first.

Q: What does it mean to have like denominators?

Like denominators means the bottom numbers are exactly the sameExamples: $ \frac{2}{5} + \frac{3}{5} $ or $ \frac{1}{8} + \frac{7}{8} $This makes addition much easier!

Fraction Addition with Like Denominators

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

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Step-by-step video solution

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00:00 Solve

00:03 Add under the 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

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

Step-by-step solution

To solve this problem, we follow these steps:

Step 1: Confirm the fractions have the same denominator.
Step 2: Add the numerators of the fractions.
Step 3: Keep the common denominator the same.

Let's work through these steps:
Step 1: The two fractions are $\frac{3}{7}$ and $\frac{1}{7}$ . Both have the same denominator of 7.
Step 2: Add the numerators, $3$ and $1$ . This results in $3 + 1 = 4$ .
Step 3: The denominator remains 7.
Thus, when we add the fractions, we get $\frac{4}{7}$ .

Therefore, the solution to the problem 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 unchanged
Technique: Add numerators: $3 + 1 = 4$ , keep denominator 7
Check: Verify $\frac{4}{7}$ is in simplest form and makes sense ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add numerators AND denominators like $\frac{3+1}{7+7} = \frac{4}{14}$ ! This changes the value completely and gives the wrong answer. Always keep the common denominator the same 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 we add the denominators too?

The denominator tells us what size pieces we're working with. Since both fractions are sevenths, we're adding pieces of the same size. Adding denominators would change the piece size, which doesn't make mathematical sense!

What if I get a fraction bigger than 1?

That's totally normal! If your numerator becomes larger than the denominator, you can convert it to a mixed number. For example, $\frac{9}{7} = 1\frac{2}{7}$ .

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

Check if the numerator and denominator share any common factors. In $\frac{4}{7}$ , since 4 and 7 don't share any factors except 1, it's already in simplest form.

Can I use this method for any fractions?

Only when denominators are the same! If denominators are different (like $\frac{1}{3} + \frac{1}{4}$ ), you need to find equivalent fractions with common denominators first.

What does it mean to have like denominators?

Like denominators means the bottom numbers are exactly the same
Examples: $\frac{2}{5} + \frac{3}{5}$ or $\frac{1}{8} + \frac{7}{8}$
This makes addition much easier!

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