Adding Fractions with Same Denominator: 3/13 + 7/13

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

The denominator tells you what size pieces you're working with. Since both fractions have pieces of size $ \frac{1}{13} $, you're just counting how many pieces total - that's why you only add numerators!

Q: What if the denominators were different?

When denominators are different, you must find a common denominator first by finding the LCD, then convert both fractions before adding. Same denominators make it much easier!

Q: Can this fraction be simplified?

$ \frac{10}{13} $ is already in lowest terms because 10 and 13 share no common factors other than 1. Always check if your final answer can be simplified!

Q: How do I know if my addition is correct?

Double-check your arithmetic: 3 + 7 = 10. You can also convert to decimals: $ \frac{3}{13} ≈ 0.23 $ and $ \frac{7}{13} ≈ 0.54 $, so the sum should be about 0.77!

Fraction Addition with Identical Denominators

Solve the following exercise:

$\frac{3}{13}+\frac{7}{13}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Let's add the fractions under a common denominator

00:09 Let's calculate the numerator

00:12 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:

$\frac{3}{13}+\frac{7}{13}=\text{?}$

Step-by-step solution

To solve this problem, we add the fractions $\frac{3}{13}$ and $\frac{7}{13}$ which have the same denominator.

When fractions have the same denominator, we simply add the numerators and place the sum over the common denominator.

$\frac{3}{13} + \frac{7}{13} = \frac{3 + 7}{13} = \frac{10}{13}$

The sum of the numerators is $10$ and the denominator remains $13$ .

Therefore, the solution to the problem is $\frac{10}{13}$ .

Final Answer

$\frac{10}{13}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators, keep the common denominator unchanged
Technique: $\frac{3}{13} + \frac{7}{13} = \frac{3+7}{13} = \frac{10}{13}$
Check: Verify numerators add correctly: 3 + 7 = 10 ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators together like $\frac{3}{13} + \frac{7}{13} = \frac{10}{26}$ ! This creates a completely different fraction with wrong value. Always keep the common denominator unchanged when adding fractions.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

FAQ

Everything you need to know about this question

Why don't I add the denominators together?

The denominator tells you what size pieces you're working with. Since both fractions have pieces of size $\frac{1}{13}$ , you're just counting how many pieces total - that's why you only add numerators!

What if the denominators were different?

When denominators are different, you must find a common denominator first by finding the LCD, then convert both fractions before adding. Same denominators make it much easier!

Can this fraction be simplified?

$\frac{10}{13}$ is already in lowest terms because 10 and 13 share no common factors other than 1. Always check if your final answer can be simplified!

How do I know if my addition is correct?

Double-check your arithmetic: 3 + 7 = 10. You can also convert to decimals: $\frac{3}{13} ≈ 0.23$ and $\frac{7}{13} ≈ 0.54$ , so the sum should be about 0.77!

What's the easiest way to remember this rule?

Think of it like pizza slices: if you have 3 slices of a 13-slice pizza and get 7 more slices from the same pizza, you now have 10 slices total - still from that same 13-slice pizza!

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