Solve the Fraction Addition: 1/2 + 1/8 + 1/4 Step by Step

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

You can only add fractions when they have the same denominator. Think of it like this: you can't add 2 apples + 3 oranges and get 5 apples! Each denominator represents a different "size" of piece.

Q: What if my LCD is really big? Is there an easier way?

Sometimes! If one denominator is already a multiple of the others (like 8 is a multiple of both 2 and 4), then that largest denominator is your LCD. No complex calculations needed!

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

Yes! Always check if your answer can be simplified. In this case, $ \frac{7}{8} $ is already in lowest terms because 7 and 8 share no common factors except 1.

Q: What if I get an improper fraction as my answer?

That's fine! You can leave it as an improper fraction like $ \frac{9}{8} $ or convert it to a mixed number like $ 1\frac{1}{8} $. Both forms are correct.

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{1}{2}+\frac{1}{8}+\frac{1}{4}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 We want to find the smallest common denominator

00:06 Therefore we'll multiply 4, 2 respectively for the common denominator 8

00:09 Remember to multiply both numerator and denominator

00:21 Let's calculate the multiplications

00:30 Add under common denominator

00:40 Calculate the numerator

00:43 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 exercise:

$\frac{1}{2}+\frac{1}{8}+\frac{1}{4}=\text{?}$

Step-by-step solution

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

Step 1: Find the least common denominator of 2, 8, and 4.
Step 2: Convert each fraction to have the common denominator.
Step 3: Perform the addition of the adjusted fractions.
Step 4: Simplify the result if needed.

Now, let's work through each step:
Step 1: The denominators are 2, 8, and 4. The least common denominator (LCD) of these numbers is 8.
Step 2: Convert each fraction:
$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$
$\frac{1}{8} = \frac{1}{8}$ (already in the desired form)
$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$
Step 3: Add the fractions:
$\frac{4}{8} + \frac{1}{8} + \frac{2}{8} = \frac{4 + 1 + 2}{8} = \frac{7}{8}$
Step 4: The fraction $\frac{7}{8}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{7}{8}$ .

Final Answer

$\frac{7}{8}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find the least common denominator of all fractions first
Technique: Convert $\frac{1}{2}$ to $\frac{4}{8}$ and $\frac{1}{4}$ to $\frac{2}{8}$
Check: Verify $\frac{4}{8} + \frac{1}{8} + \frac{2}{8} = \frac{7}{8}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{2} + \frac{1}{8} + \frac{1}{4}$ as $\frac{3}{14}$ by adding 1+1+1=3 and 2+8+4=14! This creates a meaningless result because you can't add fractions with different denominators directly. Always find the LCD first and convert all fractions to equivalent fractions with the same denominator.

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?

You can only add fractions when they have the same denominator. Think of it like this: you can't add 2 apples + 3 oranges and get 5 apples! Each denominator represents a different "size" of piece.

How do I find the LCD of 2, 8, and 4?

List the multiples: 2 (2,4,6,8...), 4 (4,8,12...), 8 (8,16...). The smallest number that appears in all lists is 8, so LCD = 8.

What if my LCD is really big? Is there an easier way?

Sometimes! If one denominator is already a multiple of the others (like 8 is a multiple of both 2 and 4), then that largest denominator is your LCD. No complex calculations needed!

Do I always need to simplify my final answer?

Yes! Always check if your answer can be simplified. In this case, $\frac{7}{8}$ is already in lowest terms because 7 and 8 share no common factors except 1.

What if I get an improper fraction as my answer?

That's fine! You can leave it as an improper fraction like $\frac{9}{8}$ or convert it to a mixed number like $1\frac{1}{8}$ . Both forms are correct.

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