Solve: Adding Fractions 1/6 + 3/6 with Common Denominators

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

The denominator tells you the size of each piece. If you're adding pieces of the same size (like sixths), the piece size stays the same! You're just counting how many pieces you have total.

Q: How does the visual model help me understand this?

The rectangle is divided into 6 equal parts. You start with 1 shaded part, add 3 more shaded parts, and end up with 4 shaded parts out of 6 total - that's $ \frac{4}{6} $!

Q: Do I need to simplify my answer?

The question asks for $ \frac{4}{6} $, so that's your final answer. However, knowing that $ \frac{4}{6} = \frac{2}{3} $ when simplified is always helpful!

Q: What if the fractions had different denominators?

Then you'd need to find a common denominator first! But this problem is easier because both fractions already have the same denominator of 6.

Q: Can I use this same method for subtracting fractions?

Yes! When denominators are the same, subtract the numerators and keep the denominator. For example: $ \frac{5}{6} - \frac{2}{6} = \frac{3}{6} $

Fraction Addition with Same Denominators

Solve the following exercise:

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

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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

00:14 Let's combine all the colored parts and place in the numerator

00:21 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:

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

Step-by-step solution

To solve this problem, let's add the two fractions: $\frac{1}{6} + \frac{3}{6}$ .

Step 1: Confirm the denominators are the same. In this case, both fractions have the denominator of 6.

Step 2: Add the numerators while keeping the common denominator:

Numerators: $1 + 3 = 4$
Denominator: 6

Step 3: Combine the result from Step 2:

$\frac{1}{6} + \frac{3}{6} = \frac{4}{6}$

Thus, the solution to the problem is $\frac{4}{6}$ .

Final Answer

$\frac{4}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, add numerators and keep denominator unchanged
Technique: Add numerators: 1 + 3 = 4, keep denominator 6
Check: Visual model shows 4 out of 6 equal parts shaded ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 1+3=4 AND 6+6=12 to get 4/12 = wrong answer! This changes the size of the parts. Always keep the denominator the same when adding fractions with common 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 together?

The denominator tells you the size of each piece. If you're adding pieces of the same size (like sixths), the piece size stays the same! You're just counting how many pieces you have total.

How does the visual model help me understand this?

The rectangle is divided into 6 equal parts. You start with 1 shaded part, add 3 more shaded parts, and end up with 4 shaded parts out of 6 total - that's $\frac{4}{6}$ !

Do I need to simplify my answer?

The question asks for $\frac{4}{6}$ , so that's your final answer. However, knowing that $\frac{4}{6} = \frac{2}{3}$ when simplified is always helpful!

What if the fractions had different denominators?

Then you'd need to find a common denominator first! But this problem is easier because both fractions already have the same denominator of 6.

Can I use this same method for subtracting fractions?

Yes! When denominators are the same, subtract the numerators and keep the denominator. For example: $\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$

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