Solve: Adding 3/5 and 6/10 - Fraction Addition Practice

Q: Why can't I just add the top numbers and bottom numbers?

Fractions represent parts of a whole. You can only add parts when they're the same size! $ \frac{3}{5} $ means 3 fifths, while $ \frac{6}{10} $ means 6 tenths - different sized pieces.

Q: How do I know which denominator to use?

Look for the Least Common Multiple (LCM) of both denominators. Since 10 is a multiple of 5, use 10 as your common denominator. Always choose the smallest number that both denominators divide into evenly.

Q: Do I always need to simplify my answer?

Yes! Always simplify to lowest terms. $ \frac{12}{10} $ and $ \frac{6}{5} $ are the same value, but $ \frac{6}{5} $ is the simplest form because 6 and 5 share no common factors.

Q: What if my answer is bigger than 1?

That's perfectly normal! $ \frac{6}{5} $ equals 1$ \frac{1}{5} $ or 1.2. Improper fractions (numerator larger than denominator) are valid answers in math problems.

Q: Can I convert to decimals instead?

You can check your work with decimals: $ \frac{3}{5} = 0.6 $ and $ \frac{6}{10} = 0.6 $, so 0.6 + 0.6 = 1.2 = $ \frac{6}{5} $. But keep your final answer as a simplified fraction unless asked otherwise.

Fraction Addition with Common Denominators

$\frac{3}{5}+\frac{6}{10}=$

❤️ 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

00:04 Let's solve this math problem step by step.

00:08 First, we need the smallest common denominator.

00:11 Next, multiply by two to make the denominator ten.

00:16 Remember, multiply both the top and bottom numbers.

00:22 Now, let's do the multiplications together.

00:30 Great! Now, add the fractions using the common denominator.

00:35 Let's find the total for the numerator.

00:38 Simplify the fraction as much as you can.

00:41 Don't forget to divide both the numerator and denominator.

00:50 And that's how we find the solution. Great work!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{3}{5}+\frac{6}{10}=$

Step-by-step solution

To solve this problem, we need to add the fractions $\frac{3}{5}$ and $\frac{6}{10}$ . Since $\frac{6}{10}$ is already expressed with the denominator of 10, we will convert $\frac{3}{5}$ to have the same denominator.

Step 1: Convert $\frac{3}{5}$ into a fraction with a denominator of 10. To do this, multiply both the numerator and the denominator by 2:

$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

Step 2: Add the fractions $\frac{6}{10}$ and $\frac{6}{10}$ :

$\frac{6}{10} + \frac{6}{10} = \frac{6 + 6}{10} = \frac{12}{10}$

Step 3: Simplify $\frac{12}{10}$ . Both numerator and denominator can be divided by 2:

$\frac{12}{10} = \frac{12 \div 2}{10 \div 2} = \frac{6}{5}$

Thus, the sum $\frac{3}{5} + \frac{6}{10}$ simplifies to $\frac{6}{5}$ .

Therefore, the correct answer is $\frac{6}{5}$ which corresponds to choice 3.

Final Answer

$\frac{6}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to same denominator before adding numerators
Technique: Convert $\frac{3}{5}$ to $\frac{6}{10}$ by multiplying by $\frac{2}{2}$
Check: Simplify final answer: $\frac{12}{10} = \frac{6}{5}$ by dividing by 2 ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{3}{5} + \frac{6}{10}$ as $\frac{3+6}{5+10} = \frac{9}{15}$ ! This breaks fraction rules and gives wrong results. Always find common denominators 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 top numbers and bottom numbers?

Fractions represent parts of a whole. You can only add parts when they're the same size! $\frac{3}{5}$ means 3 fifths, while $\frac{6}{10}$ means 6 tenths - different sized pieces.

How do I know which denominator to use?

Look for the Least Common Multiple (LCM) of both denominators. Since 10 is a multiple of 5, use 10 as your common denominator. Always choose the smallest number that both denominators divide into evenly.

Do I always need to simplify my answer?

Yes! Always simplify to lowest terms. $\frac{12}{10}$ and $\frac{6}{5}$ are the same value, but $\frac{6}{5}$ is the simplest form because 6 and 5 share no common factors.

What if my answer is bigger than 1?

That's perfectly normal! $\frac{6}{5}$ equals 1 $\frac{1}{5}$ or 1.2. Improper fractions (numerator larger than denominator) are valid answers in math problems.

Can I convert to decimals instead?

You can check your work with decimals: $\frac{3}{5} = 0.6$ and $\frac{6}{10} = 0.6$ , so 0.6 + 0.6 = 1.2 = $\frac{6}{5}$ . But keep your final answer as a simplified fraction unless asked otherwise.

🌟 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