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

Q: Why can't I just add the tops and bottoms separately?

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

Q: How do I find the least common denominator?

Look for the smallest number both denominators divide into evenly. For 2 and 4, ask: what's the smallest number that 2 and 4 both go into? Since 4 ÷ 2 = 2 and 4 ÷ 4 = 1, the LCD is 4.

Q: What if both fractions need to be converted?

Convert both fractions to have the LCD as denominator. For example, $ \frac{1}{3} + \frac{1}{6} $ becomes $ \frac{2}{6} + \frac{1}{6} $ since LCD = 6.

Q: Can I simplify the answer?

Always check if your answer can be simplified! If the numerator and denominator share common factors, divide both by the greatest common factor. $ \frac{3}{4} $ is already in simplest form.

Q: What's a quick way to check my answer?

Convert your fractions to decimals and add: $ \frac{1}{2} = 0.5 $ and $ \frac{1}{4} = 0.25 $, so 0.5 + 0.25 = 0.75 = $ \frac{3}{4} $ ✓

Fraction Addition with Different Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this math problem together.

00:08 First, we need to find the least common denominator.

00:12 We'll multiply by two to get the common denominator of four.

00:17 Remember, multiply both the numerator and the denominator.

00:21 Now, let's do the multiplications step by step.

00:30 Add the fractions under the common denominator.

00:34 Next, calculate the numerator carefully.

00:38 And that's the solution to our question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

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

Step 1: Identify the least common denominator (LCD)

The denominators given are 2 and 4. The least common multiple of these numbers is 4. Thus, the least common denominator is 4.

Step 2: Convert each fraction to have the common denominator

We need to convert $\frac{1}{2}$ to a fraction with a denominator of 4. To do this, we multiply both the numerator and the denominator of $\frac{1}{2}$ by 2:

$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$

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

Step 3: Add the converted fractions

Now add $\frac{2}{4}$ and $\frac{1}{4}$ :

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

Therefore, the sum of $\frac{1}{2} + \frac{1}{4}$ is $\frac{3}{4}$ .

Final Answer

$\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find least common denominator before adding fractions
Technique: Convert $\frac{1}{2}$ to $\frac{2}{4}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{3}{4}$ equals 0.75 when converted to decimal ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{2} + \frac{1}{4}$ as $\frac{2}{6}$ ! This ignores that fractions represent parts of different-sized wholes. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just add the tops and bottoms separately?

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

How do I find the least common denominator?

Look for the smallest number both denominators divide into evenly. For 2 and 4, ask: what's the smallest number that 2 and 4 both go into? Since 4 ÷ 2 = 2 and 4 ÷ 4 = 1, the LCD is 4.

What if both fractions need to be converted?

Convert both fractions to have the LCD as denominator. For example, $\frac{1}{3} + \frac{1}{6}$ becomes $\frac{2}{6} + \frac{1}{6}$ since LCD = 6.

Can I simplify the answer?

Always check if your answer can be simplified! If the numerator and denominator share common factors, divide both by the greatest common factor. $\frac{3}{4}$ is already in simplest form.

What's a quick way to check my answer?

Convert your fractions to decimals and add: $\frac{1}{2} = 0.5$ and $\frac{1}{4} = 0.25$ , so 0.5 + 0.25 = 0.75 = $\frac{3}{4}$ ✓

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