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

Q: Why can't I just add the tops and bottoms separately?

Because fractions represent parts of a whole. $ \frac{1}{3} $ means 1 piece out of 3, while $ \frac{1}{6} $ means 1 piece out of 6. These are different-sized pieces, so you need to make them the same size first!

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

Look for the Least Common Multiple (LCM) of the denominators. In this case, since 6 is already a multiple of 3, we can use 6 as our common denominator. This keeps the numbers simple!

Q: Do I always multiply the first fraction to match the second?

Not always! Sometimes you need to convert both fractions. For example, with $ \frac{1}{4} + \frac{1}{6} $, you'd convert both to twelfths: $ \frac{3}{12} + \frac{2}{12} $.

Q: Should I simplify my final answer?

Yes! Always check if your answer can be simplified. While $ \frac{3}{6} $ is correct, it can be simplified to $ \frac{1}{2} $ by dividing both numerator and denominator by 3.

Fraction Addition with Common Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 Therefore multiply by 2 for the common denominator 6

00:09 Remember to multiply both numerator and denominator

00:14 Calculate the multiplications

00:20 Add under common denominator

00:23 Calculate the numerator

00:27 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:

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

Step-by-step solution

To solve $\frac{1}{3} + \frac{1}{6}$ , follow these steps:

Step 1: Identify a common denominator for the fractions.
Since $6$ is a multiple of $3$ , $6$ is the common denominator.
Step 2: Convert $\frac{1}{3}$ to a fraction with denominator $6$ .
Multiply both the numerator and denominator of $\frac{1}{3}$ by $2$ :

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

Step 3: Add the fractions $\frac{2}{6} + \frac{1}{6}$ .
Simply add the numerators and keep the common denominator:

$\frac{2}{6} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6}$

Thus, after solving the addition, we get $\frac{3}{6}$ .

Final Answer

$\frac{3}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions together
Technique: Convert $\frac{1}{3}$ to $\frac{2}{6}$ by multiplying by 2
Check: Verify $\frac{2}{6} + \frac{1}{6} = \frac{3}{6}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{3} + \frac{1}{6}$ as $\frac{2}{9}$ by adding 1+1=2 and 3+6=9! This gives a completely wrong answer because you can't add fractions with different denominators directly. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just add the tops and bottoms separately?

Because fractions represent parts of a whole. $\frac{1}{3}$ means 1 piece out of 3, while $\frac{1}{6}$ means 1 piece out of 6. These are different-sized pieces, so you need to make them the same size first!

How do I know what common denominator to use?

Look for the Least Common Multiple (LCM) of the denominators. In this case, since 6 is already a multiple of 3, we can use 6 as our common denominator. This keeps the numbers simple!

Do I always multiply the first fraction to match the second?

Not always! Sometimes you need to convert both fractions. For example, with $\frac{1}{4} + \frac{1}{6}$ , you'd convert both to twelfths: $\frac{3}{12} + \frac{2}{12}$ .

Should I simplify my final answer?

Yes! Always check if your answer can be simplified. While $\frac{3}{6}$ is correct, it can be simplified to $\frac{1}{2}$ by dividing both numerator and denominator by 3.

What if the denominators are really big numbers?

The same method works! Just find the LCM of the denominators, convert each fraction, then add. Break it down into small steps and double-check your arithmetic.

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