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

Q: Why can't I just add the numerators and denominators?

Because fractions represent parts of different wholes! Adding $ \frac{2}{3} $ and $ \frac{2}{9} $ means combining 2 thirds with 2 ninths. You need the same-sized pieces (common denominator) first.

Q: How do I find the least common denominator quickly?

Look for the largest denominator first. Check if the smaller denominator divides into it evenly. Here, 9 ÷ 3 = 3, so 9 is our LCD! If not, multiply the denominators together.

Q: What if both fractions need to be converted?

Convert both fractions to have the LCD as denominator. For example, if adding $ \frac{1}{4} + \frac{1}{6} $, convert both to twelfths: $ \frac{3}{12} + \frac{2}{12} $.

Q: Do I need to simplify my final answer?

Always check if you can simplify! Look for common factors in the numerator and denominator. In this case, $ \frac{8}{9} $ is already in lowest terms since 8 and 9 share no common factors.

Fraction Addition with Different Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem.

00:09 First, we need to find the least common denominator.

00:13 So, we'll multiply by 3 to get a common denominator of 9.

00:18 Remember, we must multiply both the numerator and the denominator.

00:23 Now, let's calculate these multiplications.

00:29 Next, add them under the common denominator.

00:33 Then, calculate the numerator.

00:36 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

To solve this problem, we need to add the fractions $\frac{2}{3}$ and $\frac{2}{9}$ .

Step 1: Find a common denominator.

Given fractions have denominators 3 and 9. The least common multiple of 3 and 9 is 9. Therefore, we use 9 as the common denominator.

Step 2: Convert fractions to have the same denominator.

The second fraction, $\frac{2}{9}$ , already has 9 as its denominator. We need to convert $\frac{2}{3}$ to have a denominator of 9.

To convert $\frac{2}{3}$ :
Multiply both the numerator and the denominator by 3:
$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$ .

Step 3: Add the fractions $\frac{6}{9}$ and $\frac{2}{9}$ .

Since the denominators are the same, add the numerators:
$\frac{6}{9} + \frac{2}{9} = \frac{6+2}{9} = \frac{8}{9}$ .

Therefore, the sum of $\frac{2}{3}$ and $\frac{2}{9}$ is $\frac{8}{9}$ , which corresponds to choice number 3.

Final Answer

$\frac{8}{9}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCD to add fractions with different denominators
Technique: Convert $\frac{2}{3}$ to $\frac{6}{9}$ by multiplying by $\frac{3}{3}$
Check: Verify $\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{2}{3} + \frac{2}{9}$ as $\frac{4}{12}$ ! This ignores the fundamental rule that fractions must have the same denominator before adding. Always find the common denominator first, then add only 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 can't I just add the numerators and denominators?

Because fractions represent parts of different wholes! Adding $\frac{2}{3}$ and $\frac{2}{9}$ means combining 2 thirds with 2 ninths. You need the same-sized pieces (common denominator) first.

How do I find the least common denominator quickly?

Look for the largest denominator first. Check if the smaller denominator divides into it evenly. Here, 9 ÷ 3 = 3, so 9 is our LCD! If not, multiply the denominators together.

What if both fractions need to be converted?

Convert both fractions to have the LCD as denominator. For example, if adding $\frac{1}{4} + \frac{1}{6}$ , convert both to twelfths: $\frac{3}{12} + \frac{2}{12}$ .

Do I need to simplify my final answer?

Always check if you can simplify! Look for common factors in the numerator and denominator. In this case, $\frac{8}{9}$ is already in lowest terms since 8 and 9 share no common factors.

Can I use a different common denominator instead of the LCD?

Yes, but it makes more work! You could use 18 or 27, but you'd get larger numbers like $\frac{16}{18}$ that need simplifying. The LCD saves time and keeps numbers smaller.

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