Solve 2/5 + 1/5: Adding Fractions with Common Denominators

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

The denominator tells you what size pieces you're working with. Since both fractions are already fifths, you're adding pieces of the same size. Adding denominators would change the piece size!

Q: How do I know when fractions have the same denominator?

Just look at the bottom numbers! In $ \frac{2}{5} + \frac{1}{5} $, both bottom numbers are 5, so they're the same denominator.

Q: What if I get confused about which numbers to add?

Remember: numerators (top numbers) get added, denominators (bottom numbers) stay the same. Think of it as counting pieces of the same size.

Q: Can I simplify my answer further?

$ \frac{3}{5} $ is already in simplest form because 3 and 5 don't share any common factors other than 1. Always check if your final fraction can be reduced!

Q: How does the visual diagram help me understand this?

The diagram shows a rectangle divided into 5 equal parts. You're taking 2 parts plus 1 part, which gives you 3 parts out of 5 total parts = $ \frac{3}{5} $!

Fraction Addition with Same Denominators

$\frac{2}{5}+\frac{1}{5}=$

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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 color the appropriate number of squares, according to the given data

00:11 Now let's count and add to the numerator in the new fraction

00:15 The denominator equals the number of cells we divided

00:18 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

$\frac{2}{5}+\frac{1}{5}=$

Step-by-step solution

To solve the problem of adding the fractions $\frac{2}{5}$ and $\frac{1}{5}$ , we will utilize the fact that these fractions have the same denominator.

Here are the steps we will follow:

Step 1: Identify the fractions to be added. We have $\frac{2}{5}$ and $\frac{1}{5}$ .
Step 2: Notice that both fractions have the same denominator, which is 5.
Step 3: Add the numerators of the fractions while keeping the denominator unchanged.
Step 4: The sum of the numerators is $2 + 1 = 3$ .
Step 5: Therefore, place the sum of the numerators over the common denominator 5, giving us $\frac{3}{5}$ .

Thus, the sum of $\frac{2}{5}$ and $\frac{1}{5}$ is $\frac{3}{5}$ .

Final Answer

$\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are the same, add only the numerators
Technique: Keep denominator 5 unchanged, add numerators: 2 + 1 = 3
Check: Verify $\frac{3}{5}$ equals 2 parts plus 1 part of 5 ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 2+1 AND 5+5 to get $\frac{3}{10}$ ! This changes the size of each piece, making your answer wrong. Always keep the same denominator when fractions have equal denominators.

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 size pieces you're working with. Since both fractions are already fifths, you're adding pieces of the same size. Adding denominators would change the piece size!

How do I know when fractions have the same denominator?

Just look at the bottom numbers! In $\frac{2}{5} + \frac{1}{5}$ , both bottom numbers are 5, so they're the same denominator.

What if I get confused about which numbers to add?

Remember: numerators (top numbers) get added, denominators (bottom numbers) stay the same. Think of it as counting pieces of the same size.

Can I simplify my answer further?

$\frac{3}{5}$ is already in simplest form because 3 and 5 don't share any common factors other than 1. Always check if your final fraction can be reduced!

How does the visual diagram help me understand this?

The diagram shows a rectangle divided into 5 equal parts. You're taking 2 parts plus 1 part, which gives you 3 parts out of 5 total parts = $\frac{3}{5}$ !

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