Solve the Fraction Addition: 1/3 + 2/9 Step by Step

Q: Why can't I just add 1+2 and 3+9 separately?

Because fractions represent parts of a whole! You can't add $ \frac{1}{3} $ (1 piece of 3) and $ \frac{2}{9} $ (2 pieces of 9) without making the pieces the same size first.

Q: How do I know 9 is the right common denominator?

Since 9 is a multiple of 3 (3 × 3 = 9), it's already the least common denominator. You could use 18 or 27, but 9 is the smallest number that both 3 and 9 divide into evenly.

Q: What if the fractions don't have such obvious denominators?

List the multiples of each denominator until you find the smallest common one. For example: multiples of 4 (4, 8, 12...) and multiples of 6 (6, 12, 18...) share 12 as their LCD.

Q: Do I need to simplify my final answer?

$ \frac{5}{9} $ is already in simplest form because 5 and 9 share no common factors other than 1. Always check if you can reduce your final fraction!

Q: Can I convert both fractions to decimals instead?

You could, but working with fractions keeps your answer exact. Converting to decimals might introduce rounding errors, especially with repeating decimals.

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{1}{3}+\frac{2}{9}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem step by step.

00:08 First, we need to multiply the fraction by 3 to get a common denominator, which will help us add the fractions.

00:15 Remember an important rule: when we multiply a fraction, we must multiply both the top number (numerator) and bottom number (denominator).

00:24 Now, let's work out these multiplications carefully.

00:28 Great! Now we can add the fractions since they have the same denominator.

00:34 Let's add the numbers in the numerator while keeping the same denominator.

00:38 And there we have it! This is our final answer. Well done following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{3}+\frac{2}{9}=\text{?}$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the common denominator.
Since 9 is a multiple of 3, our least common denominator will be 9.
Step 2: Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 9.
To do this, multiply both the numerator and the denominator by 3: $\frac{1 \times 3}{3 \times 3} = \frac{3}{9}$ .
Step 3: The other fraction, $\frac{2}{9}$ , already has the denominator 9, so we don't need to change it.
Step 4: Add the fractions $\frac{3}{9} + \frac{2}{9}$ .
Step 5: Add the numerators: $3 + 2 = 5$ .
Step 6: Combine over the common denominator: $\frac{5}{9}$ .

Therefore, the solution to the problem is $\frac{5}{9}$ .

Final Answer

$\frac{5}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions together
Technique: Convert $\frac{1}{3}$ to $\frac{3}{9}$ by multiplying by 3/3
Check: Verify $\frac{3}{9} + \frac{2}{9} = \frac{5}{9}$ by adding numerators only ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1+2=3 and 3+9=12 to get $\frac{3}{12}$ = wrong answer! This ignores the need for common denominators and creates meaningless fractions. Always find the LCD first, then add only the numerators while keeping the same denominator.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why can't I just add 1+2 and 3+9 separately?

Because fractions represent parts of a whole! You can't add $\frac{1}{3}$ (1 piece of 3) and $\frac{2}{9}$ (2 pieces of 9) without making the pieces the same size first.

How do I know 9 is the right common denominator?

Since 9 is a multiple of 3 (3 × 3 = 9), it's already the least common denominator. You could use 18 or 27, but 9 is the smallest number that both 3 and 9 divide into evenly.

What if the fractions don't have such obvious denominators?

List the multiples of each denominator until you find the smallest common one. For example: multiples of 4 (4, 8, 12...) and multiples of 6 (6, 12, 18...) share 12 as their LCD.

Do I need to simplify my final answer?

$\frac{5}{9}$ is already in simplest form because 5 and 9 share no common factors other than 1. Always check if you can reduce your final fraction!

Can I convert both fractions to decimals instead?

You could, but working with fractions keeps your answer exact. Converting to decimals might introduce rounding errors, especially with repeating decimals.

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