Solve the Fraction Addition: 2/6 + 4/12 Step by Step

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

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

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 to cut them into the same size first! $ \frac{2}{6} $ and $ \frac{4}{12} $ are different sized pieces.

Q: Do I need to simplify my final answer?

It's always good practice to simplify! $ \frac{8}{12} $ can be simplified to $ \frac{2}{3} $ by dividing both numerator and denominator by their greatest common factor of 4.

Q: Can I convert both fractions to have denominator 24 instead?

Yes, but that makes more work! While 24 is a common denominator, the least common denominator (12) keeps numbers smaller and easier to work with.

Fraction Addition with Different Denominators

Solve the following equation:

$\frac{2}{6}+\frac{4}{12}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem together.

00:09 First, multiply the fraction by 2 to find a common denominator.

00:14 Remember, multiply both the numerator and the denominator by 2.

00:20 Now, calculate the products of your multiplication.

00:24 Next, add them using the common denominator.

00:28 Calculate your new numerator now.

00:32 Great job! And that's how you solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{2}{6}+\frac{4}{12}=$

Step-by-step solution

We must first identify the lowest common denominator between 6 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 6 and 12.

In this case, the common denominator is 12.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{6\times2}+\frac{4\times1}{12\times1}=\frac{4}{12}+\frac{4}{12}$

Finally we'll combine and obtain the following:

$\frac{4+4}{12}=\frac{8}{12}$

Final Answer

$\frac{8}{12}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCD to add fractions with different denominators
Technique: Convert $\frac{2}{6}$ to $\frac{4}{12}$ by multiplying by 2
Check: Verify $\frac{4}{12} + \frac{4}{12} = \frac{8}{12}$ using addition ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{2}{6} + \frac{4}{12}$ as $\frac{2+4}{6+12} = \frac{6}{18}$ ! This ignores the fundamental rule that fractions need common denominators to be added. Always find the LCD first, then convert both fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the LCD of 6 and 12?

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

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 to cut them into the same size first! $\frac{2}{6}$ and $\frac{4}{12}$ are different sized pieces.

Do I need to simplify my final answer?

It's always good practice to simplify! $\frac{8}{12}$ can be simplified to $\frac{2}{3}$ by dividing both numerator and denominator by their greatest common factor of 4.

What if the LCD isn't obvious like in this problem?

When denominators don't divide evenly, list multiples of each number until you find a match. For example: multiples of 6 are 6, 12, 18, 24... and multiples of 12 are 12, 24, 36... So the LCD is 12!

Can I convert both fractions to have denominator 24 instead?

Yes, but that makes more work! While 24 is a common denominator, the least common denominator (12) keeps numbers smaller and easier to work with.

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