Solve the Fraction Addition: 2/5 + 3/5 Step-by-Step

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

The denominator tells you the size of each piece. When you have $ \frac{2}{5} $ and $ \frac{3}{5} $, you're adding 2 fifths plus 3 fifths, which gives you 5 fifths total - not 5 tenths!

Q: What if my final answer is an improper fraction?

That's perfectly normal! Always simplify improper fractions to mixed numbers or whole numbers. Like $ \frac{5}{5} = 1 $ or $ \frac{7}{5} = 1\frac{2}{5} $.

Q: How can I visualize this problem?

Think of a pizza cut into 5 slices! You eat 2 slices and your friend eats 3 slices. Together you ate 5 out of 5 slices = the whole pizza = 1!

Q: What if the fractions have different denominators?

Then you need to find a common denominator first! Only when denominators match can you add the numerators directly.

Fraction Addition with Same Denominators

Solve the following exercise:

$\frac{2}{5}+\frac{3}{5}=\text{?}$

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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

00:10 Let's color the parts corresponding to each fraction

00:23 Let's combine all the colored parts and place in the numerator

00:30 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:

$\frac{2}{5}+\frac{3}{5}=\text{?}$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the denominators of the fractions. Both $\frac{2}{5}$ and $\frac{3}{5}$ have the denominator 5.
Step 2: When adding fractions with the same denominator, we only need to add the numerators.
Step 3: Calculate $\frac{2}{5} + \frac{3}{5} = \frac{2 + 3}{5} = \frac{5}{5}$ .
Step 4: Simplify $\frac{5}{5}$ , which equals 1.

Therefore, the solution to the problem is 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Same Denominators: Add numerators, keep the denominator unchanged
Technique: $\frac{2}{5} + \frac{3}{5} = \frac{2+3}{5} = \frac{5}{5}$
Check: Simplify final fraction - $\frac{5}{5} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 2/5 + 3/5 = 5/10! This gives wrong answers because you're changing the value of each fraction. Always keep the same denominator and only add the numerators when denominators match.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

FAQ

Everything you need to know about this question

Why don't I add the denominators together?

The denominator tells you the size of each piece. When you have $\frac{2}{5}$ and $\frac{3}{5}$ , you're adding 2 fifths plus 3 fifths, which gives you 5 fifths total - not 5 tenths!

What if my final answer is an improper fraction?

That's perfectly normal! Always simplify improper fractions to mixed numbers or whole numbers. Like $\frac{5}{5} = 1$ or $\frac{7}{5} = 1\frac{2}{5}$ .

How can I visualize this problem?

Think of a pizza cut into 5 slices! You eat 2 slices and your friend eats 3 slices. Together you ate 5 out of 5 slices = the whole pizza = 1!

What if the fractions have different denominators?

Then you need to find a common denominator first! Only when denominators match can you add the numerators directly.

How do I check if my answer is correct?

Convert your answer back to the original denominator and see if it makes sense. Also, use the visual: 2 fifths + 3 fifths should equal 5 fifths = 1 whole ✓

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