Solve the Fraction Addition: 1/2 + 1/6 Step by Step

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

Because fractions represent parts of a whole, and you can only add parts that are the same size! $ \frac{1}{2} $ means 1 piece out of 2, while $ \frac{1}{6} $ means 1 piece out of 6. These pieces are different sizes!

Q: What if the LCD is bigger than both denominators?

That's totally normal! For example, adding $ \frac{1}{3} + \frac{1}{4} $ requires LCD = 12. You'll convert both fractions: $ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} $.

Q: Should I simplify my final answer?

It depends on what the problem asks! $ \frac{4}{6} $ can be simplified to $ \frac{2}{3} $, but if the answer choices show $ \frac{4}{6} $, that's what they want. Always match the format requested.

Fraction Addition with Common Denominators

Solve the following exercise:

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

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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 together.

00:08 First, we need to find the smallest common denominator.

00:12 So, let's multiply by two to get the common denominator of six.

00:17 Remember to multiply both the numerator and the denominator. Great job so far!

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

00:27 Go ahead and add them under the common denominator.

00:31 Calculate the numerator to find the final answer.

00:35 And that's how we solve this problem! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the common denominator of the fractions.
Step 2: Convert each fraction to an equivalent fraction with this common denominator.
Step 3: Add the fractions.

Now, let's work through each step:

Step 1: The denominators of our fractions are 2 and 6. The least common denominator (LCD) between 2 and 6 is 6.

Step 2: Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 6. To do this, multiply both the numerator and the denominator by 3:

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

Since $\frac{1}{6}$ already has the common denominator of 6, it remains unchanged, $\frac{1}{6}$ .

Step 3: Add the fractions:

$\frac{3}{6} + \frac{1}{6} = \frac{3+1}{6} = \frac{4}{6}$

Therefore, the correct answer is $\frac{4}{6}$ .

Verify this matches choice 4. Thus, the correct choice is : $\frac{4}{6}$

Final Answer

$\frac{4}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator to add fractions with different denominators
Technique: Convert $\frac{1}{2}$ to $\frac{3}{6}$ by multiplying by 3
Check: Verify $\frac{3}{6} + \frac{1}{6} = \frac{4}{6}$ equals original problem ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1+1=2 for numerators and 2+6=8 for denominators = $\frac{2}{8}$ ! This completely ignores fraction rules and gives meaningless results. 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 the numerators and denominators directly?

Because fractions represent parts of a whole, and you can only add parts that are the same size! $\frac{1}{2}$ means 1 piece out of 2, while $\frac{1}{6}$ means 1 piece out of 6. These pieces are different sizes!

How do I find the least common denominator?

Look for the smallest number that both denominators divide into evenly. For 2 and 6: 6 ÷ 2 = 3 and 6 ÷ 6 = 1, so 6 is our LCD. You can also list multiples: 2, 4, 6, 8... and 6, 12, 18...

What if the LCD is bigger than both denominators?

That's totally normal! For example, adding $\frac{1}{3} + \frac{1}{4}$ requires LCD = 12. You'll convert both fractions: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

Should I simplify my final answer?

It depends on what the problem asks! $\frac{4}{6}$ can be simplified to $\frac{2}{3}$ , but if the answer choices show $\frac{4}{6}$ , that's what they want. Always match the format requested.

Why is my answer different from the choices given?

Double-check your LCD and conversion steps! The most common error is forgetting to convert one fraction or making arithmetic mistakes. Work slowly: $\frac{1}{2} = \frac{3}{6}$ , then $\frac{3}{6} + \frac{1}{6} = \frac{4}{6}$ .

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