Solve: Adding 2/3 and 1/6 Using Common Denominators

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

Because fractions represent parts of different-sized wholes! $ \frac{2}{3} $ means 2 parts out of 3, while $ \frac{1}{6} $ means 1 part out of 6. You need same-sized pieces before adding.

Q: How do I find the least common denominator quickly?

Look for the larger denominator first. If the smaller denominator divides evenly into it (like 3 into 6), that's your LCD! Otherwise, list multiples of both until you find a match.

Q: What if my LCD calculation gives me a bigger number than expected?

Double-check by trying the larger denominator first. In this problem, 6 works as the LCD because 3 divides into 6. You don't always need to multiply denominators together!

Q: Do I need to simplify my final answer?

Always check if you can! Look for common factors in the numerator and denominator. In this case, $ \frac{5}{6} $ is already in simplest form since 5 and 6 share no common factors.

Q: What's the difference between LCD and LCM?

They're the same thing! LCD (Least Common Denominator) is just the LCM (Least Common Multiple) of the denominators. Both help you find the smallest shared denominator.

Fraction Addition with Equivalent Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's multiply the fraction by 2 to get a common denominator

00:11 Remember to multiply both numerator and denominator

00:17 Let's calculate the multiplications

00:23 Let's add under the common denominator

00:26 Let's calculate the numerator

00:29 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:

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

Step-by-step solution

To solve the problem of adding $\frac{2}{3}$ and $\frac{1}{6}$ , we will first find a common denominator:

Step 1: Identify the least common denominator (LCD), which is 6 for the fractions $\frac{2}{3}$ and $\frac{1}{6}$ .
Step 2: Convert $\frac{2}{3}$ to an equivalent fraction with a denominator of 6. To do this, multiply both the numerator and the denominator by 2: $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
Step 3: Now, add the fractions $\frac{4}{6}$ and $\frac{1}{6}$ : $\frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}$

As we see, both fractions have been added correctly. The sum is already in its simplest form.

Therefore, the solution to the problem is $\frac{5}{6}$ .

Final Answer

$\frac{5}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to common denominator before adding numerators
Technique: Multiply $\frac{2}{3}$ by 2 to get $\frac{4}{6}$
Check: Verify LCD is smallest: 6 divides evenly into both 3 and 6 ✓

Common Mistakes

Avoid these frequent errors

Adding denominators together with numerators
Don't add $\frac{2}{3} + \frac{1}{6}$ as $\frac{3}{9}$ ! This completely ignores how fractions represent parts of a whole. Always find the LCD first, convert both fractions, 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 2+1 and 3+6 directly?

Because fractions represent parts of different-sized wholes! $\frac{2}{3}$ means 2 parts out of 3, while $\frac{1}{6}$ means 1 part out of 6. You need same-sized pieces before adding.

How do I find the least common denominator quickly?

Look for the larger denominator first. If the smaller denominator divides evenly into it (like 3 into 6), that's your LCD! Otherwise, list multiples of both until you find a match.

What if my LCD calculation gives me a bigger number than expected?

Double-check by trying the larger denominator first. In this problem, 6 works as the LCD because 3 divides into 6. You don't always need to multiply denominators together!

Do I need to simplify my final answer?

Always check if you can! Look for common factors in the numerator and denominator. In this case, $\frac{5}{6}$ is already in simplest form since 5 and 6 share no common factors.

What's the difference between LCD and LCM?

They're the same thing! LCD (Least Common Denominator) is just the LCM (Least Common Multiple) of the denominators. Both help you find the smallest shared denominator.

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