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

Q: Why can't I just add 1 + 4 and 4 + 8?

Fractions represent parts of a whole, not separate numbers. You can only add fractions when they have the same denominator because they represent the same-sized pieces.

Q: How do I know which number is the LCD?

The LCD is the smallest number that both denominators divide into evenly. For 4 and 8, since 8 ÷ 4 = 2 exactly, 8 is already the LCD!

Q: Do I always multiply the whole fraction?

Yes! When converting $ \frac{1}{4} $ to eighths, multiply both the numerator and denominator by 2: $ \frac{1 \times 2}{4 \times 2} = \frac{2}{8} $

Q: Should I simplify my final answer?

It depends on the problem! $ \frac{6}{8} $ can be simplified to $ \frac{3}{4} $, but both answers are mathematically correct. Check if your teacher prefers simplified form.

Q: What if the denominators are both different from the LCD?

Convert both fractions to the LCD. For example, with $ \frac{1}{3} + \frac{1}{6} $, convert the first to $ \frac{2}{6} $ and keep the second as $ \frac{1}{6} $.

Fraction Addition with Common Denominators

Solve the following exercise:

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

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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 multiply the fraction by 2, so we can find a common denominator.

00:14 Remember to multiply both the top number and the bottom number. Great job so far!

00:20 Now, let's calculate these products. Keep going!

00:25 Add them together using the common denominator.

00:29 Next, let's work out the final numerator. Almost there!

00:34 And this is how we solve the problem. Great work, everyone!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

Let's try to find the lowest common denominator between 4 and 8

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 8

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{4\times2}+\frac{4\times1}{8\times1}=\frac{2}{8}+\frac{4}{8}$

Now we'll combine and get:

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

Final Answer

$\frac{6}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the LCD before adding fractions with different denominators
Technique: Convert $\frac{1}{4}$ to $\frac{2}{8}$ using LCD of 8
Check: Verify $\frac{2}{8} + \frac{4}{8} = \frac{6}{8}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{4} + \frac{4}{8} = \frac{5}{12}$ ! This treats fractions like whole numbers and gives completely wrong results. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why can't I just add 1 + 4 and 4 + 8?

Fractions represent parts of a whole, not separate numbers. You can only add fractions when they have the same denominator because they represent the same-sized pieces.

How do I know which number is the LCD?

The LCD is the smallest number that both denominators divide into evenly. For 4 and 8, since 8 ÷ 4 = 2 exactly, 8 is already the LCD!

Do I always multiply the whole fraction?

Yes! When converting $\frac{1}{4}$ to eighths, multiply both the numerator and denominator by 2: $\frac{1 \times 2}{4 \times 2} = \frac{2}{8}$

Should I simplify my final answer?

It depends on the problem! $\frac{6}{8}$ can be simplified to $\frac{3}{4}$ , but both answers are mathematically correct. Check if your teacher prefers simplified form.

What if the denominators are both different from the LCD?

Convert both fractions to the LCD. For example, with $\frac{1}{3} + \frac{1}{6}$ , convert the first to $\frac{2}{6}$ and keep the second as $\frac{1}{6}$ .

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