Solve the Fraction Addition: 2/7 + 3/7 Step by Step

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

The denominator tells us the size of each piece. When adding $ \frac{2}{7} + \frac{3}{7} $, you're combining pieces that are already the same size (sevenths), so you just count how many pieces total!

Q: What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But since both fractions here have 7 as the denominator, you can add directly!

Q: How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 2 slices, then get 3 more slices. You now have 5 slices out of 7 total, which is $ \frac{5}{7} $!

Q: Can I simplify this answer further?

Check if 5 and 7 have any common factors. Since 5 and 7 are both prime numbers, $ \frac{5}{7} $ is already in simplest form!

Q: What if I get confused about which numbers to add?

Remember: numerators (top numbers) get added, denominators (bottom numbers) stay the same when they're identical. Think "tops together, bottom stays"!

Fraction Addition with Same Denominators

Solve the following exercise:

$\frac{2}{7}+\frac{3}{7}=\text{?}$

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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 divide our complete rectangle into 7 parts

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

00:15 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:

$\frac{2}{7}+\frac{3}{7}=\text{?}$

Step-by-step solution

To solve this problem, we need to add the fractions $\frac{2}{7}$ and $\frac{3}{7}$ . Since both fractions have the same denominator, the process is simple:

Step 1: Verify the fractions have a common denominator, which is 7.
Step 2: Add the numerators together. Thus, $2 + 3 = 5$ .
Step 3: Keep the common denominator unchanged.

By adding the numerators $2$ and $3$ , we obtain $5$ , and the denominator remains $7$ . Therefore, the resulting fraction is $\frac{5}{7}$ .

This matches the given correct answer.

Hence, the solution to the problem is $\frac{5}{7}$ .

Final Answer

$\frac{5}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add numerators when denominators are identical
Technique: Calculate 2 + 3 = 5, keep denominator 7
Check: Verify $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$ using visual model ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't calculate $\frac{2}{7} + \frac{3}{7} = \frac{5}{14}$ ! Adding denominators changes the size of the pieces, giving a completely wrong answer. Always keep the common denominator unchanged and only add 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 don't I add the denominators too?

The denominator tells us the size of each piece. When adding $\frac{2}{7} + \frac{3}{7}$ , you're combining pieces that are already the same size (sevenths), so you just count how many pieces total!

What if the denominators were different?

If denominators are different, you'd need to find a common denominator first. But since both fractions here have 7 as the denominator, you can add directly!

How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 2 slices, then get 3 more slices. You now have 5 slices out of 7 total, which is $\frac{5}{7}$ !

Can I simplify this answer further?

Check if 5 and 7 have any common factors. Since 5 and 7 are both prime numbers, $\frac{5}{7}$ is already in simplest form!

What if I get confused about which numbers to add?

Remember: numerators (top numbers) get added, denominators (bottom numbers) stay the same when they're identical. Think "tops together, bottom stays"!

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