Solve the Fraction Addition: 1/3 + 3/6 Step by Step

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

Fractions represent parts of a whole. You can only add fractions when they represent parts of the same-sized whole. $ \frac{1}{3} $ means 1 part out of 3, while $ \frac{3}{6} $ means 3 parts out of 6. These are different sized pieces!

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

Look for the Least Common Multiple (LCM) of the denominators. Since 6 is already a multiple of 3, we can use 6. If denominators were 4 and 6, the LCM would be 12.

Q: What if both fractions need to be converted?

Convert both fractions to the common denominator! For example, $ \frac{1}{4} + \frac{1}{6} $ becomes $ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $ using LCD of 12.

Q: Do I always need to simplify my final answer?

Yes, always simplify! Check if the numerator and denominator share common factors. In this problem, $ \frac{5}{6} $ is already in simplest form since 5 and 6 share no common factors.

Q: What's the easiest way to find equivalent fractions?

Use the rule: whatever you do to the numerator, do to the denominator. To convert $ \frac{1}{3} $ to sixths, multiply both top and bottom by 2: $ \frac{1 \times 2}{3 \times 2} = \frac{2}{6} $.

Fraction Addition with Mixed Denominators

Solve the following exercise:

$\frac{1}{3}+\frac{3}{6}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together.

00:08 First, we need to find the least common denominator.

00:12 So, we multiply by 2 to get a common denominator of 6.

00:17 Remember, multiply both the top and bottom numbers.

00:21 Now, let's do the multiplication.

00:28 Add the fractions using the common denominator.

00:32 After that, calculate the top number.

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{3}+\frac{3}{6}=\text{?}$

Step-by-step solution

To solve the problem of adding the fractions $\frac{1}{3}$ and $\frac{3}{6}$ , we must find a common denominator:

Step 1: Identify a common denominator. Since the denominators are 3 and 6, and 6 is a multiple of 3, we can use 6 as the common denominator.
Step 2: Convert $\frac{1}{3}$ to a fraction with a denominator of 6. To do this, multiply both the numerator and denominator of $\frac{1}{3}$ by 2 to get: $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$ .
Step 3: Now, add the converted fraction $\frac{2}{6}$ to $\frac{3}{6}$ . Since they have the same denominator, we can add the numerators: $\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}$ .

The answer to the problem is therefore $\frac{5}{6}$ . This result matches choice id 3: $\frac{5}{6}$ .

Final Answer

$\frac{5}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions with different denominators
Technique: Convert $\frac{1}{3}$ to $\frac{2}{6}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$ and simplify if needed ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{3} + \frac{3}{6}$ as $\frac{1+3}{3+6} = \frac{4}{9}$ ! This ignores the need for common denominators and gives completely wrong results. Always convert to the same 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?

Fractions represent parts of a whole. You can only add fractions when they represent parts of the same-sized whole. $\frac{1}{3}$ means 1 part out of 3, while $\frac{3}{6}$ means 3 parts out of 6. These are different sized pieces!

How do I know which common denominator to use?

Look for the Least Common Multiple (LCM) of the denominators. Since 6 is already a multiple of 3, we can use 6. If denominators were 4 and 6, the LCM would be 12.

What if both fractions need to be converted?

Convert both fractions to the common denominator! For example, $\frac{1}{4} + \frac{1}{6}$ becomes $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$ using LCD of 12.

Do I always need to simplify my final answer?

Yes, always simplify! Check if the numerator and denominator share common factors. In this problem, $\frac{5}{6}$ is already in simplest form since 5 and 6 share no common factors.

What's the easiest way to find equivalent fractions?

Use the rule: whatever you do to the numerator, do to the denominator. To convert $\frac{1}{3}$ to sixths, multiply both top and bottom by 2: $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$ .

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