Solve the Fraction Addition: 1/7 + 2/7 Step-by-Step

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

When denominators are the same, they represent equal-sized pieces. Adding $ \frac{1}{7} + \frac{2}{7} $ means you have 1 seventh-piece plus 2 seventh-pieces, which equals 3 seventh-pieces total!

Q: What if the denominators were different?

If denominators differ, you must first find a common denominator by finding the LCD, then convert both fractions before adding. Same denominators make it much easier!

Q: How do I know if my answer needs to be simplified?

Check if the numerator and denominator share any common factors. Since 3 and 7 are both prime numbers, $ \frac{3}{7} $ is already in simplest form.

Q: Can I convert these to decimals instead?

You could, but working with fractions is more precise! $ \frac{1}{7} \approx 0.143 $ and $ \frac{2}{7} \approx 0.286 $ give approximate results, while $ \frac{3}{7} $ is exact.

Fraction Addition with Same Denominators

Solve the following exercise:

$\frac{1}{7}+\frac{2}{7}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Let's add the fractions under a common denominator

00:11 Let's calculate the numerator

00:15 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:

$\frac{1}{7}+\frac{2}{7}=\text{?}$

Step-by-step solution

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

Step 1: Identify that both fractions have the same denominator.
Step 2: Add the numerators while keeping the denominator constant.
Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions, $\frac{1}{7}$ and $\frac{2}{7}$ , have a common denominator of 7.
Step 2: Add the numerators: $1 + 2 = 3$ .
Step 3: Write the sum as a fraction with the denominator 7: $\frac{3}{7}$ .

Therefore, the solution to the problem is $\frac{3}{7}$ .

Final Answer

$\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Same Denominators: Add numerators and keep the common denominator
Technique: $1 + 2 = 3$ , denominator stays 7
Check: $\frac{3}{7}$ is in simplest form since 3 and 7 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add $\frac{1}{7} + \frac{2}{7}$ as $\frac{1+2}{7+7} = \frac{3}{14}$ ! This creates a completely different fraction with wrong value. Always keep the same denominator and only add the numerators when denominators match.

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?

When denominators are the same, they represent equal-sized pieces. Adding $\frac{1}{7} + \frac{2}{7}$ means you have 1 seventh-piece plus 2 seventh-pieces, which equals 3 seventh-pieces total!

What if the denominators were different?

If denominators differ, you must first find a common denominator by finding the LCD, then convert both fractions before adding. Same denominators make it much easier!

How do I know if my answer needs to be simplified?

Check if the numerator and denominator share any common factors. Since 3 and 7 are both prime numbers, $\frac{3}{7}$ is already in simplest form.

Can I convert these to decimals instead?

You could, but working with fractions is more precise! $\frac{1}{7} \approx 0.143$ and $\frac{2}{7} \approx 0.286$ give approximate results, while $\frac{3}{7}$ is exact.

What's the easiest way to remember this rule?

Think of it like pizza slices! If you have 1 slice of a 7-piece pizza plus 2 more slices from the same pizza, you have 3 slices total - still from that same 7-piece pizza.

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