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

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

Because fractions represent parts of different wholes! $ \frac{1}{4} $ means 1 piece of something cut into 4 parts, while $ \frac{1}{2} $ means 1 piece of something cut into 2 parts. You need the same-sized pieces (common denominator) to add them.

Q: Do I need to simplify my final answer?

Always check if you can simplify! In this problem, $ \frac{3}{4} $ is already in lowest terms because 3 and 4 share no common factors other than 1. If your answer was $ \frac{6}{8} $, you'd simplify to $ \frac{3}{4} $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:07 Multiply the fraction by 2 to get a common denominator

00:11 Remember to multiply both numerator and denominator

00:17 Calculate the multiplications

00:23 Add under common denominator

00:27 Calculate the numerator

00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following exercise:

$\frac{1}{4}+\frac{1}{2}=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the least common denominator (LCD) of the fractions $\frac{1}{4}$ and $\frac{1}{2}$ .
Step 2: Convert each fraction to have the common denominator.
Step 3: Add the fractions together.

Now, let's work through each step:

Step 1: Identify the Least Common Denominator (LCD).

The denominators are 4 and 2. The smallest number that both 4 and 2 can divide into without a remainder is 4. Thus, the LCD is 4.

Step 2: Convert each fraction to have the common denominator.

The fraction $\frac{1}{4}$ already has the denominator 4, so it remains the same: $\frac{1}{4}$ .

The fraction $\frac{1}{2}$ needs to be converted. We multiply both the numerator and denominator by 2 to get the equivalent fraction $\frac{2}{4}$ .

Step 3: Add the fractions.

The fractions $\frac{1}{4}$ and $\frac{2}{4}$ share a common denominator, so we can add the numerators:

$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$ .

Therefore, the solution to the problem is $\frac{3}{4}$ .

3

Final Answer

$\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before adding fractions with different denominators
Technique: Convert $\frac{1}{2}$ to $\frac{2}{4}$ when LCD is 4
Check: Verify $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1 + 1 = 2 and 4 + 2 = 6 to get $\frac{2}{6}$ ! This ignores the need for common denominators and gives completely wrong results. Always find the LCD first, then convert fractions before adding numerators only.

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 directly?

+

Because fractions represent parts of different wholes! $\frac{1}{4}$ means 1 piece of something cut into 4 parts, while $\frac{1}{2}$ means 1 piece of something cut into 2 parts. You need the same-sized pieces (common denominator) to add them.

How do I find the LCD of 4 and 2?

+

List the multiples: 4: 4, 8, 12... and 2: 2, 4, 6, 8... The smallest number that appears in both lists is 4, so LCD = 4. Since 4 is already a multiple of 2, the LCD is simply 4!

What if my LCD is wrong?

+

You'll still get the right answer, but it might be harder! If you use 8 instead of 4, you get $\frac{2}{8} + \frac{4}{8} = \frac{6}{8}$ , which simplifies to $\frac{3}{4}$ . Using the smallest common denominator just makes the math easier.

Do I need to simplify my final answer?

+

Always check if you can simplify! In this problem, $\frac{3}{4}$ is already in lowest terms because 3 and 4 share no common factors other than 1. If your answer was $\frac{6}{8}$ , you'd simplify to $\frac{3}{4}$ .

What if I get an improper fraction?

+

That's fine! Some fraction additions result in improper fractions like $\frac{5}{4}$ . You can leave it as is or convert to a mixed number: $\frac{5}{4} = 1\frac{1}{4}$ . Both forms are correct!

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

Fraction Addition with Common Denominators

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