Solve the Addition: 2/6 + 2/6 Step-by-Step Solution

Q: Why don't I add the denominators too?

The denominator tells us how many equal parts the whole is divided into. Adding denominators would change the size of each piece! When denominators are the same, we're just counting more pieces of the same size.

Q: How can I visualize this problem?

Think of a rectangle divided into 6 equal parts. You start with 2 parts shaded, then add 2 more shaded parts. You end up with 4 parts shaded out of 6 total - that's $ \frac{4}{6} $!

Q: Should I simplify my answer?

The question asks for the sum, so $ \frac{4}{6} $ is correct as written. However, you could simplify it to $ \frac{2}{3} $ by dividing both 4 and 6 by their greatest common factor of 2.

Q: What if the denominators were different?

If denominators don't match, you'd need to find a common denominator first. But in this problem, both fractions already have the same denominator (6), so you can add directly!

Q: How do I know which answer choice is correct?

Look for the fraction that has 4 in the numerator and 6 in the denominator. Since 2 + 2 = 4, the answer must be $ \frac{4}{6} $, which matches choice 4.

Fraction Addition with Same Denominators

Solve the following exercise:

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

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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 divide our complete rectangle into 6 parts

00:09 Let's color the parts corresponding to each fraction

00:16 Let's combine all the colored parts and place in the numerator

00:24 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:

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

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Confirm that the denominators are the same.
Step 2: Add the numerators while keeping the denominator unchanged.
Step 3: Write down the result as a new fraction.

Now, let's work through the solution:

Step 1: We observe that both fractions have the same denominator, which is 6.

Step 2: Add the numerators. The numerators are both 2, so $2 + 2 = 4$ .

Step 3: Write the sum of the numerators over the common denominator:
$\frac{4}{6}$

Thus, the correct answer is $\frac{4}{6}$ , which corresponds to choice 4.

Final Answer

$\frac{4}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, add only the numerators together
Technique: Add numerators: 2 + 2 = 4, keep denominator 6
Check: Visual model shows 4 out of 6 parts shaded ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 2+2=4 and 6+6=12 to get 4/12! This changes the size of each piece and gives a completely different value. Always keep the denominator the same when adding fractions with identical denominators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why don't I add the denominators too?

The denominator tells us how many equal parts the whole is divided into. Adding denominators would change the size of each piece! When denominators are the same, we're just counting more pieces of the same size.

How can I visualize this problem?

Think of a rectangle divided into 6 equal parts. You start with 2 parts shaded, then add 2 more shaded parts. You end up with 4 parts shaded out of 6 total - that's $\frac{4}{6}$ !

Should I simplify my answer?

The question asks for the sum, so $\frac{4}{6}$ is correct as written. However, you could simplify it to $\frac{2}{3}$ by dividing both 4 and 6 by their greatest common factor of 2.

What if the denominators were different?

If denominators don't match, you'd need to find a common denominator first. But in this problem, both fractions already have the same denominator (6), so you can add directly!

How do I know which answer choice is correct?

Look for the fraction that has 4 in the numerator and 6 in the denominator. Since 2 + 2 = 4, the answer must be $\frac{4}{6}$ , which matches choice 4.

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