Adding Unlike Fractions: Calculate 1/2 Plus 3/8

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

Because $ \frac{1}{2} $ means 1 out of 2 parts, while $ \frac{3}{8} $ means 3 out of 8 parts. These are different sized pieces! You need to convert them to the same size pieces first.

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

Look for the least common multiple (LCM) of the denominators. Since 8 is already a multiple of 2, we use 8 as our common denominator. This makes the math simpler!

Q: What if both fractions need to be converted?

Convert both fractions to the common denominator! For example, if adding $ \frac{1}{3} + \frac{1}{4} $, convert both to twelfths: $ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} $.

Q: Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $ \frac{7}{8} $ cannot be reduced further since 7 and 8 share no common factors.

Q: What's the easiest way to convert fractions?

Ask yourself: "What do I multiply the smaller denominator by to get the larger one?" Here, 2 × 4 = 8, so multiply both parts of $ \frac{1}{2} $ by 4.

Fraction Addition with Common Denominators

$\frac{1}{2}+\frac{3}{8}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 Therefore we'll multiply by 4 to get the common denominator 8

00:09 Remember to multiply both numerator and denominator

00:15 Let's calculate the multiplications

00:20 Add under the common denominator

00:28 Calculate the numerator

00:31 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

$\frac{1}{2}+\frac{3}{8}=$

Step-by-step solution

To solve this problem, we need to add the fractions $\frac{1}{2}$ and $\frac{3}{8}$ .

Step 1: Convert $\frac{1}{2}$ to a fraction with a denominator of 8. We do this by determining the equivalent fraction $\frac{1}{2} = \frac{4}{8}$ . We achieve this by multiplying the numerator and denominator by 4.
Step 2: Now, add the fractions $\frac{4}{8}$ and $\frac{3}{8}$ : $\frac{4}{8} + \frac{3}{8} = \frac{4 + 3}{8} = \frac{7}{8}$ This step involves adding the numerators while keeping the common denominator.

Therefore, the sum of $\frac{1}{2}$ and $\frac{3}{8}$ is $\frac{7}{8}$ .

Final Answer

$\frac{7}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to same denominator before adding numerators
Technique: Convert $\frac{1}{2}$ to $\frac{4}{8}$ by multiplying by $\frac{4}{4}$
Check: Verify $\frac{4}{8} + \frac{3}{8} = \frac{7}{8}$ by adding numerators only ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{2} + \frac{3}{8}$ as $\frac{1+3}{2+8} = \frac{4}{10}$ ! 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 numerators and denominators straight across?

Because $\frac{1}{2}$ means 1 out of 2 parts, while $\frac{3}{8}$ means 3 out of 8 parts. These are different sized pieces! You need to convert them to the same size pieces first.

How do I know what common denominator to use?

Look for the least common multiple (LCM) of the denominators. Since 8 is already a multiple of 2, we use 8 as our common denominator. This makes the math simpler!

What if both fractions need to be converted?

Convert both fractions to the common denominator! For example, if adding $\frac{1}{3} + \frac{1}{4}$ , convert both to twelfths: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $\frac{7}{8}$ cannot be reduced further since 7 and 8 share no common factors.

What's the easiest way to convert fractions?

Ask yourself: "What do I multiply the smaller denominator by to get the larger one?" Here, 2 × 4 = 8, so multiply both parts of $\frac{1}{2}$ by 4.

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