Solve the Fraction Addition: 1/9 + 2/9 Step-by-Step

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

The denominator tells you the size of each piece. When fractions have the same denominator, you're adding pieces of the same size! Think of it like pizza slices - if you have 1 slice of 9 plus 2 slices of 9, you get 3 slices of 9, not 3 slices of 18.

Q: Do I need to simplify my answer?

It's always good practice to simplify when possible! For $ \frac{3}{9} $, you can divide both top and bottom by 3 to get $ \frac{1}{3} $. Both answers are correct, but simplified is preferred.

Q: What if the fractions had different denominators?

Then you'd need to find a common denominator first! But in this problem, both fractions already have 9 as the denominator, so you can add directly.

Q: How can I check if my answer is right?

Convert to decimals and check: $ \frac{1}{9} ≈ 0.111 $ and $ \frac{2}{9} ≈ 0.222 $, so $ \frac{3}{9} ≈ 0.333 $. Also, 0.111 + 0.222 = 0.333 ✓

Q: Why is this easier than other fraction problems?

Same denominators make addition simple! You don't need to find common denominators or do complex calculations. Just add the numerators and you're done!

Fraction Addition with Same Denominators

Solve the following exercise:

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

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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

00:11 Let's calculate the numerator

00:14 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:

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

Step-by-step solution

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

Step 1: Identify the common denominator for the fractions $\frac{1}{9}$ and $\frac{2}{9}$ .
Step 2: Add the numerators since the denominators are the same.
Step 3: Write the sum over the common denominator.

Let's work through each step:

Step 1: Both fractions have a denominator of 9.

Step 2: Add the numerators: $1 + 2 = 3$ .

Step 3: Write the result over the common denominator: $\frac{3}{9}$ .

Therefore, the solution to the problem is $\frac{3}{9}$ , which is choice 1.

Final Answer

$\frac{3}{9}$

Key Points to Remember

Essential concepts to master this topic

Same Denominator Rule: Add numerators and keep the common denominator
Technique: $\frac{1}{9} + \frac{2}{9} = \frac{1+2}{9} = \frac{3}{9}$
Check: Verify numerators sum correctly: 1 + 2 = 3 ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators like 1/9 + 2/9 = 3/18! This gives a completely wrong answer because you're changing the size of the pieces. Always keep the same denominator when adding fractions with identical denominators.

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 the size of each piece. When fractions have the same denominator, you're adding pieces of the same size! Think of it like pizza slices - if you have 1 slice of 9 plus 2 slices of 9, you get 3 slices of 9, not 3 slices of 18.

Do I need to simplify my answer?

It's always good practice to simplify when possible! For $\frac{3}{9}$ , you can divide both top and bottom by 3 to get $\frac{1}{3}$ . Both answers are correct, but simplified is preferred.

What if the fractions had different denominators?

Then you'd need to find a common denominator first! But in this problem, both fractions already have 9 as the denominator, so you can add directly.

How can I check if my answer is right?

Convert to decimals and check: $\frac{1}{9} ≈ 0.111$ and $\frac{2}{9} ≈ 0.222$ , so $\frac{3}{9} ≈ 0.333$ . Also, 0.111 + 0.222 = 0.333 ✓

Why is this easier than other fraction problems?

Same denominators make addition simple! You don't need to find common denominators or do complex calculations. Just add the numerators and you're done!

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