Solve: Adding Fractions 1/6 + 4/12 Step by Step

Q: Why can't I just add the fractions as they are?

You can only add fractions when they have the same denominator. Think of it like adding different sized pieces - you need equal-sized pieces first! Convert to common denominators, then add.

Q: How do I find the LCD of 6 and 12?

The LCD is the smallest number that both denominators divide into evenly. Since 12 ÷ 6 = 2, the number 12 is already a multiple of 6, so 12 is the LCD!

Q: Should I simplify my final answer?

It depends on what the question asks for! $ \frac{6}{12} $ simplifies to $ \frac{1}{2} $, but if the answer choices show $ \frac{6}{12} $, keep it that way.

Q: What if the denominators don't divide evenly?

Then find the LCD using prime factorization or by listing multiples. For example, with denominators 4 and 6, the LCD would be 12 (the first number that appears in both multiplication tables).

Q: Can I convert the second fraction instead?

Absolutely! You could convert $ \frac{4}{12} $ to $ \frac{2}{6} $, but it's usually easier to convert to the larger denominator to avoid working with bigger numbers.

Fraction Addition with Common Denominators

Solve the following exercise:

$\frac{1}{6}+\frac{4}{12}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this step by step.

00:06 First, we need to multiply the fraction by 2 to get a common denominator. This will help us add the fractions together.

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

00:23 Now, let's do the multiplication in each part.

00:27 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.

00:37 And there we have it! We've found our solution. Great job following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{6}+\frac{4}{12}=\text{?}$

Step-by-step solution

To solve the problem of adding $\frac{1}{6} + \frac{4}{12}$ , follow these steps:

Step 1: Find the least common denominator (LCD) for the fractions. The denominators are 6 and 12, and the LCD is 12.
Step 2: Convert $\frac{1}{6}$ to an equivalent fraction with a denominator of 12. To do this, multiply both the numerator and the denominator by 2: $\frac{1}{6} \times \frac{2}{2} = \frac{2}{12}$ .
Step 3: The fraction $\frac{4}{12}$ already has the denominator of 12, so no conversion is needed.
Step 4: Add the fractions with the common denominator: $\frac{2}{12} + \frac{4}{12} = \frac{6}{12}$ .
Step 5: Simplify the resulting fraction if possible. In this case, $\frac{6}{12}$ simplifies to $\frac{1}{2}$ , but we will leave it as $\frac{6}{12}$ as it appears in the options.

Therefore, the solution to the problem is $\frac{6}{12}$ , which matches option 3 from the provided answers.

Final Answer

$\frac{6}{12}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find the least common denominator before adding fractions
Technique: Convert $\frac{1}{6}$ to $\frac{2}{12}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{2}{12} + \frac{4}{12} = \frac{6}{12}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add $\frac{1}{6} + \frac{4}{12}$ as $\frac{5}{18}$ ! Adding denominators creates a completely wrong fraction. Always find the LCD first, then add only the numerators while keeping the common denominator.

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 fractions as they are?

You can only add fractions when they have the same denominator. Think of it like adding different sized pieces - you need equal-sized pieces first! Convert to common denominators, then add.

How do I find the LCD of 6 and 12?

The LCD is the smallest number that both denominators divide into evenly. Since 12 ÷ 6 = 2, the number 12 is already a multiple of 6, so 12 is the LCD!

Should I simplify my final answer?

It depends on what the question asks for! $\frac{6}{12}$ simplifies to $\frac{1}{2}$ , but if the answer choices show $\frac{6}{12}$ , keep it that way.

What if the denominators don't divide evenly?

Then find the LCD using prime factorization or by listing multiples. For example, with denominators 4 and 6, the LCD would be 12 (the first number that appears in both multiplication tables).

Can I convert the second fraction instead?

Absolutely! You could convert $\frac{4}{12}$ to $\frac{2}{6}$ , but it's usually easier to convert to the larger denominator to avoid working with bigger numbers.

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