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

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

The denominator tells you what size pieces you're working with. When you have sevenths + sevenths, you still have sevenths! Only the number of pieces (numerator) changes.

Q: What if the fractions had different denominators?

Then you'd need to find a common denominator first! But since both fractions are sevenths, you can add directly: $ \frac{2}{7} + \frac{2}{7} $ becomes $ \frac{4}{7} $.

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

Check if the numerator and denominator share any common factors. Since 4 and 7 don't share any factors other than 1, $ \frac{4}{7} $ is already in simplest form.

Q: Can I convert this to a decimal instead?

Yes! $ \frac{4}{7} $ equals approximately 0.571, but keeping it as a fraction is usually more precise and preferred in math class.

Q: What's the easiest way to remember this rule?

Think of it like counting objects: 2 apples + 2 apples = 4 apples. Same idea: $ \frac{2}{7} + \frac{2}{7} = \frac{4}{7} $ - you're just counting sevenths!

Fraction Addition with Like Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's add the fractions under a common denominator

00:08 Let's calculate the numerator

00:11 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:

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

Step-by-step solution

To solve the problem of adding $\frac{2}{7}$ and $\frac{2}{7}$ , we proceed with the following steps:

Step 1: Identify the common denominator, which is 7 in this case. Since both fractions have the same denominator, we can apply the formula directly for adding fractions with a common denominator:

$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$

Step 2: Add the numerators of the fractions. Combining the numerators, we have:

$2 + 2 = 4$

Step 3: Write the resulting fraction using the sum of the numerators and the common denominator. The resulting fraction becomes:

$\frac{4}{7}$

Conclusion: By adding the numerators and using the shared denominator, the sum of $\frac{2}{7} + \frac{2}{7}$ is $\frac{4}{7}$ .

The correct answer choice is $\frac{4}{7}$ , and this corresponds to choice 4.

Thus, the solution to the problem is $\frac{4}{7}$ .

Final Answer

$\frac{4}{7}$

Key Points to Remember

Essential concepts to master this topic

Like Denominators Rule: Add numerators, keep the same denominator unchanged
Technique: $\frac{2}{7} + \frac{2}{7} = \frac{2+2}{7} = \frac{4}{7}$
Check: Verify that $\frac{4}{7}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators together like $\frac{2}{7} + \frac{2}{7} = \frac{4}{14}$ ! This creates a completely different fraction value. Always keep the denominator the same when fractions have like 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 what size pieces you're working with. When you have sevenths + sevenths, you still have sevenths! Only the number of pieces (numerator) changes.

What if the fractions had different denominators?

Then you'd need to find a common denominator first! But since both fractions are sevenths, you can add directly: $\frac{2}{7} + \frac{2}{7}$ becomes $\frac{4}{7}$ .

How do I know if my answer can be simplified?

Check if the numerator and denominator share any common factors. Since 4 and 7 don't share any factors other than 1, $\frac{4}{7}$ is already in simplest form.

Can I convert this to a decimal instead?

Yes! $\frac{4}{7}$ equals approximately 0.571, but keeping it as a fraction is usually more precise and preferred in math class.

What's the easiest way to remember this rule?

Think of it like counting objects: 2 apples + 2 apples = 4 apples. Same idea: $\frac{2}{7} + \frac{2}{7} = \frac{4}{7}$ - you're just counting sevenths!

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