Adding Unlike Fractions: Finding the Sum of 1/4 and 4/8

Q: Why can't I just add the top and bottom numbers separately?

Fractions represent parts of a whole, not separate numbers! Adding $ \frac{1}{4} + \frac{4}{8} $ as $ \frac{5}{12} $ would be like adding 1 quarter plus 4 eighths and getting 5 twelfths - that doesn't make sense!

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

Use the Least Common Multiple (LCM) of the denominators. For 4 and 8, since 8 is already a multiple of 4, we use 8 as our common denominator.

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

It depends on what the question asks for! In this problem, $ \frac{6}{8} $ is the correct answer choice, even though it simplifies to $ \frac{3}{4} $. Always read carefully to see which form is expected.

Q: What if the fractions have completely different denominators?

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

Q: How can I check if I converted the fraction correctly?

Make sure the new fraction equals the original! $ \frac{1}{4} $ should equal $ \frac{2}{8} $. You can verify: 1÷4 = 0.25 and 2÷8 = 0.25 ✓

Q: Why did we choose 8 instead of finding a different common denominator?

Since 8 is already a multiple of 4, it's the easiest choice! We could use 12, 16, or 20, but that would create larger numbers and make the problem unnecessarily complicated.

Fraction Addition with Common Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's multiply the fraction by 2 to get a common denominator

00:11 Remember to multiply both numerator and denominator

00:19 Let's calculate the multiplications

00:26 Let's add under the common denominator

00:29 Let's calculate the numerator

00:33 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:

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

Step-by-step solution

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

Step 1: Convert $\frac{1}{4}$ to a fraction with a denominator of 8.
Step 2: Add the fractions.
Step 3: Simplify the result.

Now, let's work through each step:

Step 1: Convert $\frac{1}{4}$ to have a denominator of 8. Since $8 \div 4 = 2$ , multiply both the numerator and denominator of $\frac{1}{4}$ by 2:

$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$

Step 2: Now add $\frac{2}{8}$ and $\frac{4}{8}$ :

$\frac{2}{8} + \frac{4}{8} = \frac{2 + 4}{8} = \frac{6}{8}$

Step 3: Simplify $\frac{6}{8}$ if possible. The greatest common divisor of 6 and 8 is 2. So, $\frac{6}{8}$ simplifies to:

$\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Therefore, the solution to the problem is $\frac{6}{8}$ .

Final Answer

$\frac{6}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to same denominator before adding numerators
Technique: Convert $\frac{1}{4}$ to $\frac{2}{8}$ by multiplying by 2
Check: Verify $\frac{2}{8} + \frac{4}{8} = \frac{6}{8}$ equals $\frac{3}{4}$ simplified ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{4} + \frac{4}{8}$ as $\frac{1+4}{4+8} = \frac{5}{12}$ ! This creates a completely wrong fraction that doesn't represent the actual sum. Always convert to common denominators 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 top and bottom numbers separately?

Fractions represent parts of a whole, not separate numbers! Adding $\frac{1}{4} + \frac{4}{8}$ as $\frac{5}{12}$ would be like adding 1 quarter plus 4 eighths and getting 5 twelfths - that doesn't make sense!

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

Use the Least Common Multiple (LCM) of the denominators. For 4 and 8, since 8 is already a multiple of 4, we use 8 as our common denominator.

Do I always need to simplify my final answer?

It depends on what the question asks for! In this problem, $\frac{6}{8}$ is the correct answer choice, even though it simplifies to $\frac{3}{4}$ . Always read carefully to see which form is expected.

What if the fractions have completely different denominators?

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

How can I check if I converted the fraction correctly?

Make sure the new fraction equals the original! $\frac{1}{4}$ should equal $\frac{2}{8}$ . You can verify: 1÷4 = 0.25 and 2÷8 = 0.25 ✓

Why did we choose 8 instead of finding a different common denominator?

Since 8 is already a multiple of 4, it's the easiest choice! We could use 12, 16, or 20, but that would create larger numbers and make the problem unnecessarily complicated.

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