Solve the Addition: 1/5 + 1/5 with Same Denominators

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

The denominator tells us the size of each piece. Since both fractions have pieces of the same size (fifths), we keep that size unchanged. We only add how many pieces we have!

Q: What if the visual diagram confuses me?

Focus on the math first! The diagram shows 1 shaded part + 1 shaded part = 2 shaded parts out of 5 total parts. This matches our calculation of $ \frac{2}{5} $.

Q: Is there a shortcut for same denominators?

Yes! When denominators are identical, just add the numerators and write the result over the same denominator. It's that simple!

Q: What if I got a different answer?

Double-check that you only added the numerators (1 + 1 = 2) and kept the denominator as 5. The most common mistake is accidentally adding denominators too.

Fraction Addition with Identical Denominators

Solve the following exercise:

$\frac{1}{5}+\frac{1}{5}=\text{?}$

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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 divide our whole rectangle into 5 parts

00:08 Let's color the appropriate parts for each fraction

00:11 Let's combine all the colored parts and place in the numerator

00:19 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:

$\frac{1}{5}+\frac{1}{5}=\text{?}$

Step-by-step solution

To solve this problem, we'll add two fractions with a common denominator:

Step 1: Identify the numerators and the common denominator of the fractions.
Step 2: Add the numerators, keeping the denominator unchanged.

Let's do this for our given fractions:

We have the fractions $\frac{1}{5}$ and $\frac{1}{5}$ . Both have the same denominator, which is 5.
Step 1: The numerators are 1 and 1, and the common denominator is 5.

Step 2: Add the numerators while keeping the denominator same:
$\frac{1}{5} + \frac{1}{5} = \frac{1 + 1}{5} = \frac{2}{5}$ .

Thus, the solution to the problem is $\frac{2}{5}$ .

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators and keep the same denominator unchanged
Technique: $\frac{1}{5} + \frac{1}{5} = \frac{1+1}{5} = \frac{2}{5}$
Check: Count visual parts: 1 part + 1 part = 2 parts out of 5 total ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators: $\frac{1}{5} + \frac{1}{5} = \frac{2}{10}$ is wrong! This creates a completely different fraction with a different value. Always keep the denominator the same and only add 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 don't I add the denominators too?

The denominator tells us the size of each piece. Since both fractions have pieces of the same size (fifths), we keep that size unchanged. We only add how many pieces we have!

What if the visual diagram confuses me?

Focus on the math first! The diagram shows 1 shaded part + 1 shaded part = 2 shaded parts out of 5 total parts. This matches our calculation of $\frac{2}{5}$ .

Is there a shortcut for same denominators?

Yes! When denominators are identical, just add the numerators and write the result over the same denominator. It's that simple!

How can I check my answer is right?

Use the visual: count the total shaded sections (2) out of total sections (5). This gives you $\frac{2}{5}$ , confirming your calculation!

What if I got a different answer?

Double-check that you only added the numerators (1 + 1 = 2) and kept the denominator as 5. The most common mistake is accidentally adding denominators too.

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