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

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

Because fractions represent parts of a whole, and you can only add parts that are the same size! $ \frac{1}{9} $ represents ninths while $ \frac{2}{3} $ represents thirds - different sized pieces.

Q: How do I find the common denominator?

Look for the Least Common Multiple (LCM) of the denominators. Since 9 is already a multiple of 3 (9 = 3 × 3), the LCD is 9. Convert $ \frac{2}{3} $ to ninths!

Q: Do I always multiply by 3 to get ninths?

Not always! You multiply by whatever makes the denominators match. Here, $ \frac{2}{3} \times \frac{3}{3} = \frac{6}{9} $ because we need ninths to match $ \frac{1}{9} $.

Q: Can I convert both fractions instead of just one?

Absolutely! You could convert both to a larger common denominator like 18ths, but it's easier to use the smallest common denominator (9) to keep numbers simple.

Fraction Addition with Unlike Denominators

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Find the point on the axis

00:07 To connect, we'll go right (positive) on the axis

00:17 Multiply the fraction by 3 to get a common denominator

00:22 Make sure to multiply both numerator and denominator

00:30 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

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

Step-by-step solution

Let's multiply the numerator and denominator of the fraction $\frac{2}{3}$ by 3 and the numerator and denominator of the fraction $\frac{1}{9}$ by 1 in order to find a common denominator:

$\frac{2\times3}{3\times3}=\frac{6}{9}$

$\frac{1\times1}{9\times1}=\frac{1}{9}$

Finally let's perform the addition operation to find our answer:

$\frac{1}{9}+\frac{6}{9}=\frac{7}{9}$

Final Answer

$\frac{7}{9}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCD before adding fractions with different denominators
Convert: Change $\frac{2}{3}$ to $\frac{6}{9}$ by multiplying by $\frac{3}{3}$
Verify: Check that $\frac{1}{9} + \frac{6}{9} = \frac{7}{9}$ makes sense ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{9} + \frac{2}{3}$ as $\frac{1+2}{9+3} = \frac{3}{12}$ ! This completely ignores how fractions work and gives a wrong answer. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

$(+8)+(+12)=\text{ ?}$

FAQ

Everything you need to know about this question

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

Because fractions represent parts of a whole, and you can only add parts that are the same size! $\frac{1}{9}$ represents ninths while $\frac{2}{3}$ represents thirds - different sized pieces.

How do I find the common denominator?

Look for the Least Common Multiple (LCM) of the denominators. Since 9 is already a multiple of 3 (9 = 3 × 3), the LCD is 9. Convert $\frac{2}{3}$ to ninths!

Do I always multiply by 3 to get ninths?

Not always! You multiply by whatever makes the denominators match. Here, $\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$ because we need ninths to match $\frac{1}{9}$ .

What if my answer doesn't match the choices?

Double-check your work! Make sure you found the correct LCD and converted fractions properly. In this problem, $\frac{1}{9} + \frac{6}{9} = \frac{7}{9}$ should be your final answer.

Can I convert both fractions instead of just one?

Absolutely! You could convert both to a larger common denominator like 18ths, but it's easier to use the smallest common denominator (9) to keep numbers simple.

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