Solve the Fraction Addition: 3/4 + 1/6 Step-by-Step

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

Fractions represent parts of a whole. You can only add parts when they're the same size! $ \frac{3}{4} $ means 3 pieces of size 1/4, while $ \frac{1}{6} $ means 1 piece of size 1/6 - different sized pieces!

Q: What if my LCD is wrong?

If your LCD doesn't work, check that it's divisible by both denominators. For 4 and 6: 12 ÷ 4 = 3 ✓ and 12 ÷ 6 = 2 ✓. Both give whole numbers, so 12 is correct!

Q: Do I need to simplify my final answer?

$ \frac{11}{12} $ is already in simplest form because 11 and 12 don't share any common factors except 1. Always check if you can reduce your answer further!

Fraction Addition with Different Denominators

Solve the following exercise:

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

❤️ 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

00:06 Alright, let's solve this problem together!

00:09 First, we need to find the least common denominator.

00:13 So, we multiply by three and by two, for a common denominator of twelve.

00:19 Don't forget to multiply both the numerator and the denominator by these numbers.

00:27 Let's do the multiplication now, step by step.

00:37 Great job! Now, add your fractions under the common denominator.

00:43 Calculate the numerator, and we're almost there!

00:47 And that's the solution to our question! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

To solve the addition of these two fractions, we'll proceed as follows:

Step 1: Determine the least common denominator (LCD) of the fractions.
The denominators are 4 and 6, and the smallest number that is a multiple of both is 12. Thus, the LCD is 12.
Step 2: Convert each fraction to an equivalent fraction with the denominator 12.
- For $\frac{3}{4}$ , multiply both numerator and denominator by 3: $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$ .
- For $\frac{1}{6}$ , multiply both numerator and denominator by 2: $\frac{1 \times 2}{6 \times 2} = \frac{2}{12}$ .
Step 3: Add the converted fractions.
$\frac{9}{12} + \frac{2}{12} = \frac{9 + 2}{12} = \frac{11}{12}$ .

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

LCD Rule: Find least common denominator before adding fractions
Technique: Convert $\frac{3}{4}$ to $\frac{9}{12}$ and $\frac{1}{6}$ to $\frac{2}{12}$
Check: Verify LCD is correct: 12 ÷ 4 = 3 and 12 ÷ 6 = 2 ✓

Common Mistakes

Avoid these frequent errors

Adding denominators together instead of finding LCD
Don't add 4 + 6 = 10 to get $\frac{4}{10}$ ! This creates a meaningless fraction that doesn't represent the actual sum. Always find the LCD (12 for denominators 4 and 6) and convert both fractions first.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

FAQ

Everything you need to know about this question

How do I find the LCD of 4 and 6?

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

Why can't I just add the numerators and denominators separately?

Fractions represent parts of a whole. You can only add parts when they're the same size! $\frac{3}{4}$ means 3 pieces of size 1/4, while $\frac{1}{6}$ means 1 piece of size 1/6 - different sized pieces!

What if my LCD is wrong?

If your LCD doesn't work, check that it's divisible by both denominators. For 4 and 6: 12 ÷ 4 = 3 ✓ and 12 ÷ 6 = 2 ✓. Both give whole numbers, so 12 is correct!

Do I need to simplify my final answer?

$\frac{11}{12}$ is already in simplest form because 11 and 12 don't share any common factors except 1. Always check if you can reduce your answer further!

Can I use a different common denominator instead of the LCD?

Yes, but it makes the problem harder! You could use 24 instead of 12, but then you'd work with $\frac{18}{24} + \frac{4}{24} = \frac{22}{24}$ , which simplifies back to $\frac{11}{12}$ anyway.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with 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

Solve the Fraction Addition: 3/4 + 1/6 Step-by-Step

Fraction Addition with Different Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I find the LCD of 4 and 6?

Why can't I just add the numerators and denominators separately?

What if my LCD is wrong?

Do I need to simplify my final answer?

Can I use a different common denominator instead of the LCD?

🌟 Unlock Your Math Potential

More Questions

All Operations in Fractions

Solve: Adding Fractions 5/10 + 1/4 Step by Step

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

Solve the Fraction Addition: 4/10 + 2/6 Step by Step

Adding Fractions with Unlike Denominators: 4/10 + 5/12

Addition of Fractions

Solve the Fraction Addition: 5/10 + 1/6 Step by Step

Solve the Fraction Addition: 1/5 + 3/10 + 2/5 Step-by-Step

Solve the Fraction Addition: 2/5 + 3/10 Step by Step

Solve the Fraction Addition: 1/4 + 4/6 Step by Step