Solve the Fraction Addition: 4/7 + 1/7 Step by Step

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

The denominator tells you the size of each piece. Since both fractions have sevenths, you're adding pieces of the same size. Adding denominators would change the piece size, which is incorrect!

Q: What if the fractions had different denominators?

Then you'd need to find a common denominator first! Convert both fractions so they have the same denominator, then add the numerators.

Q: How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 4 slices plus 1 more slice, giving you 5 slices out of 7 total slices!

Q: Is there a shortcut for adding fractions with the same denominator?

Yes! When denominators match, just add the numerators and keep the denominator. It's the easiest type of fraction addition.

Fraction Addition with Like Denominators

$\frac{4}{7}+\frac{1}{7}=$

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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 under the common denominator

00:07 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

$\frac{4}{7}+\frac{1}{7}=$

Step-by-step solution

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

Step 1: Identify that both fractions, $\frac{4}{7}$ and $\frac{1}{7}$ , have a common denominator of 7.
Step 2: Add the numerators while keeping the denominator the same.

Let's work through each step:
Step 1: We have the two fractions $\frac{4}{7}$ and $\frac{1}{7}$ . Both fractions share the denominator of 7.
Step 2: Add the numerators: $4 + 1 = 5$ .
Thus, $\frac{4}{7} + \frac{1}{7} = \frac{5}{7}$ .

Therefore, 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 the same
Technique: Keep denominator 7, add numerators: 4 + 1 = 5
Check: Verify $\frac{5}{7}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 4/7 + 1/7 = 5/14! This creates a completely wrong answer because you're changing the size of the pieces. Always keep the same denominator and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

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. Since both fractions have sevenths, you're adding pieces of the same size. Adding denominators would change the piece size, which is incorrect!

What if the fractions had different denominators?

Then you'd need to find a common denominator first! Convert both fractions so they have the same denominator, then add the numerators.

Do I need to simplify my answer?

Always check if your answer can be simplified! In this case, $\frac{5}{7}$ is already in lowest terms since 5 and 7 share no common factors.

How can I visualize this problem?

Think of a pizza cut into 7 equal slices. You have 4 slices plus 1 more slice, giving you 5 slices out of 7 total slices!

Is there a shortcut for adding fractions with the same denominator?

Yes! When denominators match, just add the numerators and keep the denominator. It's the easiest type of fraction addition.

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