Solve Fraction Addition: 3/12 + 1/4 Step-by-Step

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

Because fractions represent parts of a whole! Adding $ \frac{3}{12} + \frac{1}{4} $ as $ \frac{4}{16} $ is like adding 3 twelfths to 1 fourth - they're different sized pieces! You need the same denominator to add properly.

Q: How do I know which denominator to use as the common denominator?

Look for the Least Common Multiple (LCM) of the denominators. Here, 12 and 4: since 12 is already a multiple of 4, use 12 as your common denominator. This keeps the math simple!

Q: Do I always need to simplify my final answer?

Yes! Always simplify to the lowest terms. $ \frac{6}{12} $ and $ \frac{1}{2} $ are equal, but $ \frac{1}{2} $ is the simplified form that's easier to understand and use.

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

Find the LCM of both denominators. For example, with $ \frac{1}{3} + \frac{1}{5} $, the LCM of 3 and 5 is 15, so convert both fractions to fifteenths first.

Q: Can I use a calculator to check my work?

Absolutely! Convert to decimals: $ \frac{3}{12} = 0.25 $ and $ \frac{1}{4} = 0.25 $, so 0.25 + 0.25 = 0.5 = $ \frac{1}{2} $ ✓

Fraction Addition with Common Denominators

$\frac{3}{12}+\frac{1}{4}=$

❤️ 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 We want to find the least common denominator

00:06 Therefore multiply by 3 to get the common denominator 12

00:09 Remember to multiply both numerator and denominator

00:19 Calculate the multiplications

00:27 Add under the common denominator

00:30 Calculate the numerator

00:33 Reduce the fraction as much as possible

00:37 Remember to divide both numerator and denominator

00:43 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{3}{12}+\frac{1}{4}=$

Step-by-step solution

To solve this problem, we'll take the following steps:

Step 1: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 12.
Since $4 \times 3 = 12$ , multiply both the numerator and the denominator of $\frac{1}{4}$ by 3 to get $\frac{3}{12}$ .
Step 2: Add $\frac{3}{12} + \frac{3}{12}$ .
The numerators will add to $3 + 3$ , giving $\frac{6}{12}$ .
Step 3: Simplify the fraction $\frac{6}{12}$ .
The greatest common divisor of 6 and 12 is 6, so divide both the numerator and the denominator by 6 to get $\frac{1}{2}$ .

Therefore, the solution to the problem is $\frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to have the same denominator before adding
Technique: Multiply $\frac{1}{4}$ by 3 to get $\frac{3}{12}$
Check: Verify $\frac{1}{2} = 0.5$ matches $\frac{6}{12} = 0.5$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{3}{12} + \frac{1}{4}$ as $\frac{3+1}{12+4} = \frac{4}{16}$ ! This gives completely wrong results because you're not following fraction addition rules. Always find a common denominator first, then add only the numerators.

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 numerators and denominators separately?

Because fractions represent parts of a whole! Adding $\frac{3}{12} + \frac{1}{4}$ as $\frac{4}{16}$ is like adding 3 twelfths to 1 fourth - they're different sized pieces! You need the same denominator to add properly.

How do I know which denominator to use as the common denominator?

Look for the Least Common Multiple (LCM) of the denominators. Here, 12 and 4: since 12 is already a multiple of 4, use 12 as your common denominator. This keeps the math simple!

Do I always need to simplify my final answer?

Yes! Always simplify to the lowest terms. $\frac{6}{12}$ and $\frac{1}{2}$ are equal, but $\frac{1}{2}$ is the simplified form that's easier to understand and use.

What if the denominators don't divide evenly into each other?

Find the LCM of both denominators. For example, with $\frac{1}{3} + \frac{1}{5}$ , the LCM of 3 and 5 is 15, so convert both fractions to fifteenths first.

Can I use a calculator to check my work?

Absolutely! Convert to decimals: $\frac{3}{12} = 0.25$ and $\frac{1}{4} = 0.25$ , so 0.25 + 0.25 = 0.5 = $\frac{1}{2}$ ✓

🌟 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