Solve: 1/2 + 1/6 + 3/12 Fraction Addition Problem

Q: How do I find the least common denominator (LCD)?

Find the smallest number that all denominators divide into evenly. For 2, 6, and 12: List multiples of the largest (12): 12, 24, 36... Since 2 and 6 both divide into 12, the LCD is 12!

Q: What if one fraction already has the common denominator?

Lucky you! Like $ \frac{3}{12} $ in this problem - it stays exactly the same. You only need to convert the other fractions to have denominator 12.

Q: Why can't I just add the numerators: 1 + 1 + 3 = 5?

Because fractions represent different-sized pieces! $ \frac{1}{2} $ is a bigger piece than $ \frac{1}{6} $. You need equal-sized pieces (same denominator) before adding.

Q: Do I need to simplify my final answer?

Always check if you can simplify! Look for common factors in numerator and denominator. Since 11 and 12 share no common factors, $ \frac{11}{12} $ is already in simplest form.

Q: What if my answer is greater than 1?

That's fine! You can leave it as an improper fraction like $ \frac{13}{12} $, or convert to a mixed number like $ 1\frac{1}{12} $ - both are correct!

Fraction Addition with Mixed Denominators

Solve the following exercise:

$\frac{1}{2}+\frac{1}{6}+\frac{3}{12}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's start solving the problem.

00:10 First, we need to find the least common denominator.

00:14 So, we'll multiply by 6 and by 2, to get a common denominator of 12.

00:20 Make sure you multiply both the numerator and the denominator for each fraction.

00:29 Now, let's do the multiplication together.

00:36 Add the fractions using the common denominator you found.

00:44 Finally, calculate the numerator to reach the answer.

00:49 And there you have it! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{2}+\frac{1}{6}+\frac{3}{12}=\text{?}$

Step-by-step solution

To solve the given problem, let's follow these steps:

Step 1: Find the Least Common Denominator (LCD)
The denominators are 2, 6, and 12. The least common multiple (LCM) of these numbers is 12.
Step 2: Convert each fraction to have the common denominator of 12
Here is how to convert each fraction:
- $\frac{1}{2}$ becomes $\frac{1 \times 6}{2 \times 6} = \frac{6}{12}$
- $\frac{1}{6}$ becomes $\frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
- $\frac{3}{12}$ is already with denominator 12, so it remains $\frac{3}{12}$ .
Step 3: Add the fractions
Now add the equivalent fractions: $\frac{6}{12} + \frac{2}{12} + \frac{3}{12} = \frac{6 + 2 + 3}{12} = \frac{11}{12}$ .

Therefore, the solution to the problem is $\frac{11}{12}$ .

Final Answer

$\frac{11}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before adding fractions with different denominators
Technique: Convert $\frac{1}{2}$ to $\frac{6}{12}$ using LCD 12
Check: Final answer should be in simplest form: $\frac{11}{12}$ is already simplified ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{2} + \frac{1}{6}$ as $\frac{2}{8}$ ! This gives completely wrong results because you can't add fractions without a common denominator. Always find the LCD first and convert all fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I find the least common denominator (LCD)?

Find the smallest number that all denominators divide into evenly. For 2, 6, and 12: List multiples of the largest (12): 12, 24, 36... Since 2 and 6 both divide into 12, the LCD is 12!

What if one fraction already has the common denominator?

Lucky you! Like $\frac{3}{12}$ in this problem - it stays exactly the same. You only need to convert the other fractions to have denominator 12.

Why can't I just add the numerators: 1 + 1 + 3 = 5?

Because fractions represent different-sized pieces! $\frac{1}{2}$ is a bigger piece than $\frac{1}{6}$ . You need equal-sized pieces (same denominator) before adding.

How do I convert a fraction to have the LCD?

Multiply both numerator and denominator by the same number. For $\frac{1}{2}$ to get denominator 12: multiply by 6/6 to get $\frac{6}{12}$ .

Do I need to simplify my final answer?

Always check if you can simplify! Look for common factors in numerator and denominator. Since 11 and 12 share no common factors, $\frac{11}{12}$ is already in simplest form.

What if my answer is greater than 1?

That's fine! You can leave it as an improper fraction like $\frac{13}{12}$ , or convert to a mixed number like $1\frac{1}{12}$ - both are correct!

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