Solve 1/9 + 2/9: Adding Fractions with Same Denominator

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

The denominator tells you what type of pieces you have (ninths). When you add $ \frac{1}{9} + \frac{2}{9} $, you're adding 1 ninth plus 2 ninths, which gives you 3 ninths total!

Q: How do I know when to simplify my answer?

Always check if the numerator and denominator have common factors. Since 3 and 9 are both divisible by 3, you can simplify $ \frac{3}{9} $ to $ \frac{1}{3} $.

Q: What if the fractions had different denominators?

Then you'd need to find a common denominator first! But since $ \frac{1}{9} $ and $ \frac{2}{9} $ already have the same denominator (9), you can add directly.

Q: Can I use the visual rectangle to help me?

Absolutely! The rectangle is divided into 9 equal parts. Color 1 part for $ \frac{1}{9} $ and 2 more parts for $ \frac{2}{9} $. You'll see 3 parts colored out of 9 total!

Q: Is 1/3 really the same as 3/9?

Yes! They're equivalent fractions. You can verify this: $ \frac{1}{3} = \frac{1×3}{3×3} = \frac{3}{9} $. Both represent the same amount, but $ \frac{1}{3} $ is in simplest form.

Fraction Addition with Simplification Required

$\frac{1}{9}+\frac{2}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem together.

00:08 First, add with a common denominator.

00:16 Next, calculate the numerator carefully.

00:22 Now, let's reduce the fraction as much as possible.

00:27 We can simplify it by dividing by three.

00:30 Remember to divide both the top and bottom numbers.

00:35 And that's the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{1}{9}+\frac{2}{9}=$

Step-by-step solution

To solve the problem of adding the fractions $\frac{1}{9}$ and $\frac{2}{9}$ , we proceed with the following steps:

Step 1: Verify that the fractions have the same denominator.
Both fractions, $\frac{1}{9}$ and $\frac{2}{9}$ , have a common denominator of 9.
Step 2: Add the numerators.
The numerators are 1 and 2, respectively. So, $1 + 2 = 3$ .
Step 3: Write the result over the common denominator.
This gives us the fraction $\frac{3}{9}$ .
Step 4: Simplify the fraction if possible.
The fraction $\frac{3}{9}$ can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 3: $\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}$

Therefore, the solution to the problem is $\frac{1}{3}$ .

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators only when denominators are the same
Technique: Add 1 + 2 = 3, keep denominator 9: $\frac{3}{9}$
Check: Simplify by dividing both parts by GCD: $\frac{3÷3}{9÷3} = \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add 1+2 AND 9+9 to get $\frac{3}{18}$ ! This creates a completely wrong fraction that doesn't represent the actual sum. 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 together?

The denominator tells you what type of pieces you have (ninths). When you add $\frac{1}{9} + \frac{2}{9}$ , you're adding 1 ninth plus 2 ninths, which gives you 3 ninths total!

How do I know when to simplify my answer?

Always check if the numerator and denominator have common factors. Since 3 and 9 are both divisible by 3, you can simplify $\frac{3}{9}$ to $\frac{1}{3}$ .

What if the fractions had different denominators?

Then you'd need to find a common denominator first! But since $\frac{1}{9}$ and $\frac{2}{9}$ already have the same denominator (9), you can add directly.

Can I use the visual rectangle to help me?

Absolutely! The rectangle is divided into 9 equal parts. Color 1 part for $\frac{1}{9}$ and 2 more parts for $\frac{2}{9}$ . You'll see 3 parts colored out of 9 total!

Is 1/3 really the same as 3/9?

Yes! They're equivalent fractions. You can verify this: $\frac{1}{3} = \frac{1×3}{3×3} = \frac{3}{9}$ . Both represent the same amount, but $\frac{1}{3}$ is in simplest form.

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