Solve the Fraction Addition: 1/2 + 1/2 Step-by-Step

Q: Why don't I add the denominators too?

The denominator tells you what type of pieces you have (halves, thirds, etc.). When adding $ \frac{1}{2} + \frac{1}{2} $, you're adding halves, so the pieces stay halves - only the quantity changes!

Q: When do I need to find a common denominator?

Only when the denominators are different! Since both fractions here have denominator 2, you can add directly. If you had $ \frac{1}{2} + \frac{1}{3} $, then you'd need a common denominator.

Q: How do I know when to simplify my answer?

Always check if your fraction can be simplified! If the numerator and denominator have common factors, divide both by their greatest common factor. Here, $ \frac{2}{2} = 1 $.

Q: Can I use this method for any fractions with the same denominator?

Yes! Whether it's $ \frac{3}{7} + \frac{4}{7} $ or $ \frac{15}{23} + \frac{8}{23} $, just add the numerators and keep the denominator the same.

Fraction Addition with Same Denominators

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Add under the common denominator

00:07 Calculate the numerator

00:11 Any number divided by itself always equals 1

00:15 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

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

Step-by-step solution

To solve this problem, we follow these steps:

Step 1: Identify the numerators of the fractions. Here, both numerators are 1, as we have $\frac{1}{2}$ and $\frac{1}{2}$ .
Step 2: Add the numerators. We calculate $1 + 1 = 2$ .
Step 3: Keep the common denominator. The denominator remains 2.
Step 4: Write the result as a single fraction. This gives us $\frac{2}{2}$ .
Step 5: Simplify the fraction. Since $\frac{2}{2}$ simplifies to 1, the final result is 1.

Therefore, the solution to $\frac{1}{2} + \frac{1}{2}$ is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are equal, add only the numerators
Technique: Calculate $1 + 1 = 2$ then write $\frac{2}{2}$
Check: Simplify the result: $\frac{2}{2} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 1+1=2 and 2+2=4 to get 2/4! This creates a completely wrong fraction. The denominators stay the same when they're equal. Always add only the numerators and keep the common denominator unchanged.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why don't I add the denominators too?

The denominator tells you what type of pieces you have (halves, thirds, etc.). When adding $\frac{1}{2} + \frac{1}{2}$ , you're adding halves, so the pieces stay halves - only the quantity changes!

When do I need to find a common denominator?

Only when the denominators are different! Since both fractions here have denominator 2, you can add directly. If you had $\frac{1}{2} + \frac{1}{3}$ , then you'd need a common denominator.

How do I know when to simplify my answer?

Always check if your fraction can be simplified! If the numerator and denominator have common factors, divide both by their greatest common factor. Here, $\frac{2}{2} = 1$ .

What if I get an improper fraction?

That's okay! If your numerator is bigger than your denominator, you can leave it as an improper fraction or convert it to a mixed number depending on what the problem asks for.

Can I use this method for any fractions with the same denominator?

Yes! Whether it's $\frac{3}{7} + \frac{4}{7}$ or $\frac{15}{23} + \frac{8}{23}$ , just add the numerators and keep the denominator the same.

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