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

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

The denominator tells us what type of pieces we're working with (halves, thirds, etc.). When adding $ \frac{1}{2} + \frac{1}{2} $, we're adding halves, so we keep working with halves!

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

Always check if your final fraction can be simplified! If the numerator and denominator have common factors, divide both by the greatest common factor.

Q: Can I use this method for all fraction addition?

Only when denominators are identical! If denominators are different, you must first find a common denominator before adding the numerators.

Q: How can I visualize this problem?

Think of pizza slices! $ \frac{1}{2} $ is half a pizza. Adding another $ \frac{1}{2} $ gives you one whole pizza (1).

Fraction Addition with Same Denominators

Solve the following exercise:

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

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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 add the fractions under a common denominator

00:08 Let's calculate the numerator

00:13 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:

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

Step-by-step solution

To solve this problem, we need to add the two fractions $\frac{1}{2} + \frac{1}{2}$ . Since the fractions have the same denominator, we apply fraction addition rules by:

Add the numerators: $1 + 1 = 2$ .
Keep the denominator the same: $2$ .
The resulting fraction is $\frac{2}{2}$ .
Simplify $\frac{2}{2}$ to $1$ since the numerator and denominator are equal.

Therefore, the sum of $\frac{1}{2} + \frac{1}{2}$ is $1$ .

The correct answer is option 3: 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators when denominators are the same
Technique: $\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2} = \frac{2}{2}$
Check: Simplify final fraction: $\frac{2}{2} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add both parts: 1/2 + 1/2 = 2/4! This creates a completely wrong fraction. When denominators are the same, only add the numerators and keep the 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 us what type of pieces we're working with (halves, thirds, etc.). When adding $\frac{1}{2} + \frac{1}{2}$ , we're adding halves, so we keep working with halves!

How do I know when to simplify my answer?

Always check if your final fraction can be simplified! If the numerator and denominator have common factors, divide both by the greatest common factor.

What if I get an improper fraction?

Improper fractions (where numerator ≥ denominator) are fine! You can leave them as fractions or convert to mixed numbers or whole numbers like $\frac{2}{2} = 1$ .

Can I use this method for all fraction addition?

Only when denominators are identical! If denominators are different, you must first find a common denominator before adding the numerators.

How can I visualize this problem?

Think of pizza slices! $\frac{1}{2}$ is half a pizza. Adding another $\frac{1}{2}$ gives you one whole pizza (1).

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