Solve the Fraction Addition: 1/4 + 3/8

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

Fractions represent parts of a whole. You can only add parts when they're the same size! $ \frac{1}{4} $ means 1 piece out of 4, while $ \frac{3}{8} $ means 3 pieces out of 8. These are different sized pieces, so you need a common denominator first.

Q: How do I know what common denominator to use?

Look for the Least Common Multiple (LCM) of the denominators. For 4 and 8, since 8 is already a multiple of 4, the LCD is 8. This makes conversion easier!

Q: Do I need to simplify my final answer?

Always check if your answer can be simplified! In this case, $ \frac{5}{8} $ is already in lowest terms since 5 and 8 share no common factors.

Q: Can I use decimals instead of fractions?

You could convert to decimals ($ \frac{1}{4} = 0.25 $, $ \frac{3}{8} = 0.375 $), but keeping fractions is usually more exact and preferred in math class.

Fraction Addition with Unlike Denominators

Solve the following exercise:

$\frac{1}{4}+\frac{3}{8}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Alright, let's solve the problem step by step.

00:12 First, we need a common denominator. So, multiply the fraction by 2.

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

00:25 Great! Now, let's do the multiplications.

00:31 Next, add them together using the common denominator.

00:35 Now, calculate the numerator after the addition.

00:39 And that's it! You've solved the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{4}+\frac{3}{8}=\text{?}$

Step-by-step solution

To solve this addition problem involving fractions, we first need to ensure both fractions have a common denominator.

Step 1: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8.

To do this, we need to multiply both the numerator and denominator of $\frac{1}{4}$ by 2 to achieve the desired denominator:

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

Step 2: Now we can add the fractions $\frac{2}{8}$ and $\frac{3}{8}$ since they have a common denominator.

$\frac{2}{8} + \frac{3}{8} = \frac{2 + 3}{8} = \frac{5}{8}$

Therefore, the sum of $\frac{1}{4}$ and $\frac{3}{8}$ is $\frac{5}{8}$ .

Thus, the correct answer to the problem is $\frac{5}{8}$ .

Final Answer

$\frac{5}{8}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator Rule: Find LCD before adding fractions with different denominators
Conversion Technique: Multiply $\frac{1}{4}$ by $\frac{2}{2}$ to get $\frac{2}{8}$
Verify Addition: Check that $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$ by adding numerators only ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1 + 3 = 4 and 4 + 8 = 12 to get $\frac{4}{12}$ ! This gives a completely wrong answer because you're not following fraction addition rules. Always find a common denominator first, then add only the numerators.

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?

Fractions represent parts of a whole. You can only add parts when they're the same size! $\frac{1}{4}$ means 1 piece out of 4, while $\frac{3}{8}$ means 3 pieces out of 8. These are different sized pieces, so you need a common denominator first.

How do I know what common denominator to use?

Look for the Least Common Multiple (LCM) of the denominators. For 4 and 8, since 8 is already a multiple of 4, the LCD is 8. This makes conversion easier!

What if both fractions need to be converted?

Sometimes both fractions need conversion! For example, with $\frac{1}{3} + \frac{1}{4}$ , you'd convert both to twelfths: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

Do I need to simplify my final answer?

Always check if your answer can be simplified! In this case, $\frac{5}{8}$ is already in lowest terms since 5 and 8 share no common factors.

Can I use decimals instead of fractions?

You could convert to decimals ( $\frac{1}{4} = 0.25$ , $\frac{3}{8} = 0.375$ ), but keeping fractions is usually more exact and preferred in math class.

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