Calculate the Sum: Solving 3/11 + 7/11 Step by Step

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

The denominator tells us what type of pieces we're working with. Since both fractions have elevenths ($ \frac{1}{11} $), we're adding the same type of pieces. Only the number of pieces (numerators) changes!

Q: What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But here, both fractions already have the same denominator (11), so you can add directly!

Q: How do I know if I need to simplify my answer?

Always check if your numerator and denominator share any common factors. Since 10 and 11 don't share any factors except 1, $ \frac{10}{11} $ is already in simplest form.

Q: Can this fraction be converted to a mixed number?

No, because the numerator (10) is smaller than the denominator (11). Mixed numbers only work when the numerator is larger than the denominator.

Q: What's the fastest way to check my work?

Ask yourself: "Does my numerator equal the sum of the original numerators?" Here, 10 = 3 + 7, so $ \frac{10}{11} $ is correct!

Adding Fractions with Same Denominators

$\frac{3}{11}+\frac{7}{11}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together!

00:07 First, we add the fractions using a common denominator.

00:12 Now, let's calculate the numerator step by step.

00:16 And there you have it, the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{3}{11}+\frac{7}{11}=$

Step-by-step solution

To solve this problem, we'll follow a simple approach:

Step 1: Identify the numerators and denominator. The fractions given are $\frac{3}{11}$ and $\frac{7}{11}$ . The numerator of the first fraction is $3$ , and the second is $7$ . The shared denominator is $11$ .
Step 2: Add the numerators together. Calculate $3 + 7 = 10$ .
Step 3: Keep the common denominator $11$ unchanged.

Thus, the sum of the fractions is $\frac{10}{11}$ .

We compare this to the given choices:

Choice 1: $1$
Choice 2: $\frac{10}{11}$
Choice 3: $\frac{8}{11}$
Choice 4: $\frac{1}{11}$

The correct solution matches Choice 2: $\frac{10}{11}$ .

Final Answer

$\frac{10}{11}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators when denominators are the same
Technique: Keep denominator 11, add numerators: 3 + 7 = 10
Check: Verify $\frac{10}{11}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 3+7 AND 11+11 to get $\frac{10}{22}$ ! This creates a completely different fraction. Always keep the common denominator unchanged 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 I add the denominators too?

The denominator tells us what type of pieces we're working with. Since both fractions have elevenths ( $\frac{1}{11}$ ), we're adding the same type of pieces. Only the number of pieces (numerators) changes!

What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But here, both fractions already have the same denominator (11), so you can add directly!

How do I know if I need to simplify my answer?

Always check if your numerator and denominator share any common factors. Since 10 and 11 don't share any factors except 1, $\frac{10}{11}$ is already in simplest form.

Can this fraction be converted to a mixed number?

No, because the numerator (10) is smaller than the denominator (11). Mixed numbers only work when the numerator is larger than the denominator.

What's the fastest way to check my work?

Ask yourself: "Does my numerator equal the sum of the original numerators?" Here, 10 = 3 + 7, so $\frac{10}{11}$ is correct!

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