Solve the Fraction Addition: 4/7 + 2/7 Step by Step

Q: Why don't I add the denominators when they're the same?

Think of fractions like pieces of pizza! If you have 4 pieces of a 7-slice pizza plus 2 more pieces from the same pizza, you get 6 pieces total - but it's still the same 7-slice pizza!

Q: What if the denominators were different?

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

Q: What's the fastest way to add fractions with same denominators?

Simple! Just add the top numbers (numerators) and write the result over the same bottom number (denominator). It's like counting: 4 + 2 = 6 sevenths!

Fraction Addition with Same Denominators

Solve the following exercise:

$\frac{4}{7}+\frac{2}{7}=\text{?}$

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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 combine the fractions under a common denominator

00:09 Let's calculate the numerator

00:13 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:

$\frac{4}{7}+\frac{2}{7}=\text{?}$

Step-by-step solution

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

Step 1: Identify the given fractions $\frac{4}{7}$ and $\frac{2}{7}$ .
Step 2: Since the denominators are the same, add the numerators directly.
Step 3: Maintain the common denominator in the result.

Now, let's work through each step:
Step 1: The problem gives us the fractions $\frac{4}{7}$ and $\frac{2}{7}$ .
Step 2: Add the numerators: $4 + 2 = 6$ .
Step 3: The common denominator remains 7, so the result is $\frac{6}{7}$ .

Therefore, the solution to the problem is $\frac{6}{7}$ .

Final Answer

$\frac{6}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, add numerators and keep denominator
Technique: Add numerators: 4 + 2 = 6, keep denominator 7
Check: Verify $\frac{6}{7}$ equals $\frac{4}{7} + \frac{2}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 4 + 2 = 6 AND 7 + 7 = 14 to get $\frac{6}{14}$ ! This changes the value of the fractions completely. Always keep the same denominator 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 when they're the same?

Think of fractions like pieces of pizza! If you have 4 pieces of a 7-slice pizza plus 2 more pieces from the same pizza, you get 6 pieces total - but it's still the same 7-slice pizza!

What if the denominators were different?

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

Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $\frac{6}{7}$ cannot be reduced further since 6 and 7 share no common factors.

How can I visualize this problem?

Picture a circle divided into 7 equal parts. Color 4 parts, then color 2 more parts. You now have 6 out of 7 parts colored - that's $\frac{6}{7}$ !

What's the fastest way to add fractions with same denominators?

Simple! Just add the top numbers (numerators) and write the result over the same bottom number (denominator). It's like counting: 4 + 2 = 6 sevenths!

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