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

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

Because fractions show parts of a whole! $ \frac{2}{3} $ means 2 parts out of 3, while $ \frac{1}{9} $ means 1 part out of 9. You can't add different-sized parts directly - you need the same size pieces first!

Q: How do I find the LCD of 3 and 9?

Look for the smallest number both denominators divide into evenly. Since 9 ÷ 3 = 3 (no remainder), 9 is already a multiple of 3. So the LCD is 9!

Q: What if both fractions need to be converted?

Convert both fractions to have the LCD as their denominator. For example, with $ \frac{1}{2} + \frac{1}{3} $, the LCD is 6, so you'd get $ \frac{3}{6} + \frac{2}{6} $.

Q: Why multiply by 3/3 instead of just 3?

Multiplying by $ \frac{3}{3} $ is the same as multiplying by 1, which keeps the fraction's value unchanged. This is the fundamental principle of creating equivalent fractions!

Fraction Addition with Unlike Denominators

Solve the following exercise:

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

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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'll multiply the fraction by 3 to get a common denominator between the fractions.

00:14 Remember an important rule: when we multiply a fraction, we need to multiply both the top number (numerator) and bottom number (denominator).

00:23 Now, let's work out all the multiplications we've set up.

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

00:33 Let's add the numbers in the numerator while keeping the same denominator.

00:38 And there we have it! We've successfully solved the problem. Well done for following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

To solve this problem, we need to add the fractions $\frac{2}{3}$ and $\frac{1}{9}$ by finding a common denominator.

First, we identify the least common denominator (LCD). The LCD of 3 and 9 is 9. We must convert $\frac{2}{3}$ to an equivalent fraction with a denominator of 9.

To convert $\frac{2}{3}$ , we multiply both the numerator and the denominator by 3 (since $3 \times 3 = 9$ ), giving us:

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

Now, we can add the fractions:

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

Therefore, the solution to the problem is $\frac{7}{9}$ .

Final Answer

$\frac{7}{9}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator Rule: 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 LCD is correct: 9 ÷ 3 = 3 and 9 ÷ 9 = 1 ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{2}{3} + \frac{1}{9} = \frac{3}{12}$ ! This ignores that fractions represent parts of different wholes. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

FAQ

Everything you need to know about this question

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

Because fractions show parts of a whole! $\frac{2}{3}$ means 2 parts out of 3, while $\frac{1}{9}$ means 1 part out of 9. You can't add different-sized parts directly - you need the same size pieces first!

How do I find the LCD of 3 and 9?

Look for the smallest number both denominators divide into evenly. Since 9 ÷ 3 = 3 (no remainder), 9 is already a multiple of 3. So the LCD is 9!

What if both fractions need to be converted?

Convert both fractions to have the LCD as their denominator. For example, with $\frac{1}{2} + \frac{1}{3}$ , the LCD is 6, so you'd get $\frac{3}{6} + \frac{2}{6}$ .

Can I simplify the answer further?

Always check! If the numerator and denominator share a common factor, divide both by it. In this case, $\frac{7}{9}$ cannot be simplified since 7 and 9 share no common factors.

Why multiply by 3/3 instead of just 3?

Multiplying by $\frac{3}{3}$ is the same as multiplying by 1, which keeps the fraction's value unchanged. This is the fundamental principle of creating equivalent fractions!

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