Solve the Fraction Addition: 2/3 + 1/6 Step by Step

Q: Why can't I just add 2+1=3 and 3+6=9?

Because fractions represent parts of wholes! $ \frac{2}{3} $ means 2 parts out of 3, while $ \frac{1}{6} $ means 1 part out of 6. These are different sized pieces, so you need a common denominator first.

Q: Do I always multiply the first fraction when finding LCD?

Not always! Only multiply when needed. Here, $ \frac{2}{3} $ becomes $ \frac{4}{6} $ (multiply by 2), but $ \frac{1}{6} $ stays the same since it already has denominator 6.

Q: Can I simplify the answer further?

Check if the numerator and denominator share any common factors. Since 5 and 6 share no common factors except 1, $ \frac{5}{6} $ is already in simplest form!

Q: What if I get a different LCD?

Any common multiple works, but using the LCD makes calculations easier. If you used 12 instead of 6, you'd get $ \frac{8}{12} + \frac{2}{12} = \frac{10}{12} $, which simplifies to the same answer: $ \frac{5}{6} $.

Fraction Addition with Different Denominators

Solve the following equation:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this math problem.

00:08 First, multiply the fraction by 2 to find a common denominator.

00:13 Be sure to multiply both the numerator and the denominator.

00:17 Now, calculate the products and write them down.

00:23 Then, add the fractions together using the common denominator.

00:27 Go ahead and calculate the numerator.

00:31 And there you have it! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

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

Step-by-step solution

Let's begin by identifying the lowest common denominator between 3 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 6.

In this case, the common denominator is 6.

Let's proceed to multiply each fraction by the appropriate number in order to reach the denominator 6.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{3\times2}+\frac{1\times1}{6\times1}=\frac{4}{6}+\frac{1}{6}$

Finally we'll combine and obtain the following result:

$\frac{4+1}{6}=\frac{5}{6}$

Final Answer

$\frac{5}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the LCD before adding fractions with different denominators
Technique: Convert $\frac{2}{3}$ to $\frac{4}{6}$ using LCD of 6
Check: Verify $\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$ is in simplest form ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add straight across like $\frac{2}{3} + \frac{1}{6} = \frac{3}{9}$ ! This ignores that fractions represent parts of different-sized wholes. Always find the LCD first, then convert both fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why can't I just add 2+1=3 and 3+6=9?

Because fractions represent parts of wholes! $\frac{2}{3}$ means 2 parts out of 3, while $\frac{1}{6}$ means 1 part out of 6. These are different sized pieces, so you need a common denominator first.

How do I find the LCD of 3 and 6?

List multiples of each number: 3, 6, 9, 12... and 6, 12, 18, 24... The smallest number that appears in both lists is 6. Since 6 is already a multiple of 3, the LCD is 6!

Do I always multiply the first fraction when finding LCD?

Not always! Only multiply when needed. Here, $\frac{2}{3}$ becomes $\frac{4}{6}$ (multiply by 2), but $\frac{1}{6}$ stays the same since it already has denominator 6.

Can I simplify the answer further?

Check if the numerator and denominator share any common factors. Since 5 and 6 share no common factors except 1, $\frac{5}{6}$ is already in simplest form!

What if I get a different LCD?

Any common multiple works, but using the LCD makes calculations easier. If you used 12 instead of 6, you'd get $\frac{8}{12} + \frac{2}{12} = \frac{10}{12}$ , which simplifies to the same answer: $\frac{5}{6}$ .

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Solve the Fraction Addition: 2/3 + 1/6 Step by Step

Fraction Addition with Different Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just add 2+1=3 and 3+6=9?

How do I find the LCD of 3 and 6?

Do I always multiply the first fraction when finding LCD?

Can I simplify the answer further?

What if I get a different LCD?

🌟 Unlock Your Math Potential

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