Solve 1/8 + 6/8: Adding Fractions with Common Denominators

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

The denominator tells us what size pieces we're working with. Since both fractions are eighths, we're adding pieces of the same size, so the piece size (denominator) stays the same!

Q: How can I visualize this problem?

Think of a pizza cut into 8 slices. You have 1 slice plus 6 slices, which gives you 7 slices total. The pizza is still cut into 8 pieces!

Q: What if my numerator becomes bigger than the denominator?

That's fine! You'd get an improper fraction like $ \frac{9}{8} $. You can leave it as is or convert to a mixed number like $ 1\frac{1}{8} $.

Q: Can I use this method for any fractions?

This method only works when denominators are the same. If denominators are different, you must first find a common denominator before adding.

Fraction Addition with Same Denominators

$\frac{1}{8}+\frac{6}{8}=$

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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 Color the right number of squares based on the data we have.

00:18 Now, count them and add to our new fraction's top number, or numerator.

00:23 The bottom number, or denominator, is how many cells we divided.

00:28 And that's how we find our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{1}{8}+\frac{6}{8}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify that both fractions have the same denominator.
Step 2: Add the numerators of the two fractions.
Step 3: Keep the common denominator unchanged.
Step 4: Express the result as a simplified fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions are $\frac{1}{8}$ and $\frac{6}{8}$ , with a common denominator of 8.
Step 2: Add the numerators: $1 + 6 = 7$ .
Step 3: Use the common denominator to create the sum: $\frac{7}{8}$ .
Step 4: The fraction $\frac{7}{8}$ is already in its simplest form, as 7 and 8 have no common factors other than 1.

Therefore, the solution to the problem is $\frac{7}{8}$ .

Final Answer

$\frac{7}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, add numerators and keep denominator unchanged
Technique: Add numerators: 1 + 6 = 7, keep denominator 8
Check: Verify $\frac{7}{8}$ cannot simplify further since 7 and 8 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 1+6=7 AND 8+8=16 to get $\frac{7}{16}$ ! This creates a completely wrong fraction that's much smaller than either original fraction. Always keep the common denominator unchanged when adding fractions.

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 eighths, we're adding pieces of the same size, so the piece size (denominator) stays the same!

How can I visualize this problem?

Think of a pizza cut into 8 slices. You have 1 slice plus 6 slices, which gives you 7 slices total. The pizza is still cut into 8 pieces!

Do I need to simplify my answer?

Always check if you can simplify! Since 7 and 8 don't share any common factors (7 is prime), $\frac{7}{8}$ is already in simplest form.

What if my numerator becomes bigger than the denominator?

That's fine! You'd get an improper fraction like $\frac{9}{8}$ . You can leave it as is or convert to a mixed number like $1\frac{1}{8}$ .

Can I use this method for any fractions?

This method only works when denominators are the same. If denominators are different, you must first find a common denominator before adding.

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