Solve the Fraction Addition: 2/4 + 1/6

Q: How do I find the least common denominator between 4 and 6?

List the multiples of each number: 4: 4, 8, 12, 16... and 6: 6, 12, 18... The smallest number that appears in both lists is 12, so that's your LCD!

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 apples and oranges - you need to convert them to the same "unit" first!

Q: Do I need to simplify my final answer?

Yes! Always check if your answer can be simplified. $ \frac{8}{12} $ can be simplified to $ \frac{2}{3} $ by dividing both numerator and denominator by 4.

Q: What if the denominators are really big numbers?

The same process works! Find the LCD using prime factorization or listing multiples. Even with big numbers, the steps remain: find LCD, convert fractions, add numerators.

Q: Can I use cross-multiplication for this problem?

No, cross-multiplication is for equations like $ \frac{a}{b} = \frac{c}{d} $. For addition of fractions, you must use the LCD method.

Fraction Addition with Different Denominators

Solve the following equation:

$\frac{2}{4}+\frac{1}{6}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each fraction by 3 and 2 respectively to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:15 Calculate the multiplications

00:22 Add with the common denominator

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{2}{4}+\frac{1}{6}=$

Step-by-step solution

Let's begin by identifying the lowest common denominator between 4 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 6.

In this case, the common denominator is 12.

We'll proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 2

$\frac{2\times3}{4\times3}+\frac{1\times2}{6\times2}=\frac{6}{12}+\frac{2}{12}$

Finally let's combine to obtain the following.

$\frac{6+2}{12}=\frac{8}{12}$

Final Answer

$\frac{8}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator (LCD) before adding fractions
Technique: Convert $\frac{2}{4}$ to $\frac{6}{12}$ and $\frac{1}{6}$ to $\frac{2}{12}$
Check: Add numerators over common denominator: $\frac{6+2}{12} = \frac{8}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{2}{4}+\frac{1}{6}$ as $\frac{2+1}{4+6} = \frac{3}{10}$ ! This treats fractions like whole numbers and gives completely wrong results. Always find the LCD first, convert both fractions, then add only the 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 least common denominator between 4 and 6?

List the multiples of each number: 4: 4, 8, 12, 16... and 6: 6, 12, 18... The smallest number that appears in both lists is 12, so that's your LCD!

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 apples and oranges - you need to convert them to the same "unit" first!

Do I need to simplify my final answer?

Yes! Always check if your answer can be simplified. $\frac{8}{12}$ can be simplified to $\frac{2}{3}$ by dividing both numerator and denominator by 4.

What if the denominators are really big numbers?

The same process works! Find the LCD using prime factorization or listing multiples. Even with big numbers, the steps remain: find LCD, convert fractions, add numerators.

Can I use cross-multiplication for this problem?

No, cross-multiplication is for equations like $\frac{a}{b} = \frac{c}{d}$ . For addition of fractions, you must use the LCD method.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime