Solve the Fraction Addition: 2/5 + 4/10 Step-by-Step

Q: Why can't I just add the numerators and denominators directly?

Because fractions represent parts of different wholes! Adding $ \frac{2}{5} + \frac{4}{10} $ is like adding 2 pieces of a 5-piece pie to 4 pieces of a 10-piece pie. You need the same size pieces first.

Q: How do I know which common denominator to use?

Look for the least common multiple (LCM) of the denominators. Since 10 is already a multiple of 5, we use 10. This keeps numbers smaller and easier to work with!

Q: Do I need to simplify my final answer?

Not always! $ \frac{8}{10} $ could be simplified to $ \frac{4}{5} $, but if the answer choices show tenths, leave it as $ \frac{8}{10} $. Match the format of the given options.

Q: Can I convert to decimals instead?

You could, but working with fractions is more precise! Converting $ \frac{2}{5} = 0.4 $ and $ \frac{4}{10} = 0.4 $ gives 0.8, but keeping fractions avoids rounding errors.

Fraction Addition with Common Denominators

Solve the following exercise:

$\frac{2}{5}+\frac{4}{10}=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 First, we need to find the least common denominator.

00:13 We'll multiply by two to get a common denominator of ten.

00:17 Remember, always multiply both the numerator and denominator.

00:22 Now, let's calculate these multiplications.

00:26 Then, add the fractions under the common denominator.

00:31 Next, calculate the numerator by adding them up.

00:35 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{2}{5}+\frac{4}{10}=\text{?}$

Step-by-step solution

To solve this problem, we will add the fractions by first finding a common denominator:

Step 1: Identify that the denominators are 5 and 10. Since 10 is a multiple of 5, we choose 10 as the common denominator.
Step 2: Convert $\frac{2}{5}$ into a fraction with a denominator of 10. Multiply both numerator and denominator by 2 to get $\frac{4}{10}$ .
Step 3: Now both fractions are over 10: $\frac{4}{10}$ and $\frac{4}{10}$ .
Step 4: Add the numerators: $4 + 4 = 8$ .
Step 5: The sum is $\frac{8}{10}$ .

Therefore, the solution to the problem is $\frac{8}{10}$ .

The correct answer choice is: $\frac{8}{10}$ .

Final Answer

$\frac{8}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions together
Technique: Convert $\frac{2}{5}$ to $\frac{4}{10}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{4}{10} + \frac{4}{10} = \frac{8}{10}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 2 + 4 = 6 and 5 + 10 = 15 to get $\frac{6}{15}$ ! This creates a completely wrong fraction that doesn't represent the actual sum. Always find a common denominator first, then add only 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 can't I just add the numerators and denominators directly?

Because fractions represent parts of different wholes! Adding $\frac{2}{5} + \frac{4}{10}$ is like adding 2 pieces of a 5-piece pie to 4 pieces of a 10-piece pie. You need the same size pieces first.

How do I know which common denominator to use?

Look for the least common multiple (LCM) of the denominators. Since 10 is already a multiple of 5, we use 10. This keeps numbers smaller and easier to work with!

Do I need to simplify my final answer?

Not always! $\frac{8}{10}$ could be simplified to $\frac{4}{5}$ , but if the answer choices show tenths, leave it as $\frac{8}{10}$ . Match the format of the given options.

What if the denominators don't have an obvious relationship?

Find the LCM by listing multiples or using prime factorization. For example, if you had denominators 6 and 8, the LCM would be 24, so you'd convert both fractions to have 24 in the denominator.

Can I convert to decimals instead?

You could, but working with fractions is more precise! Converting $\frac{2}{5} = 0.4$ and $\frac{4}{10} = 0.4$ gives 0.8, but keeping fractions avoids rounding errors.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime