Solve the Fraction Addition: 4/11 + 5/11 Step by Step

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

The denominator tells us what size pieces we're working with. Since both fractions are already in elevenths, we're just counting how many elevenths we have total: 4 elevenths + 5 elevenths = 9 elevenths.

Q: What if the denominators were different?

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

Q: Do I need to simplify my answer?

Always check if you can simplify! For $ \frac{9}{11} $, since 9 and 11 share no common factors besides 1, it's already in simplest form.

Q: How can I double-check my work?

Convert to decimals: $ \frac{4}{11} \approx 0.364 $ and $ \frac{5}{11} \approx 0.455 $. Adding gives about 0.818, which equals $ \frac{9}{11} $!

Q: Is there a pattern I can remember?

Like denominators = Easy addition! Just think: Same bottom number stays the sameAdd the top numbers togetherCheck if you can simplify

Fraction Addition with Like Denominators

Solve the following exercise:

$\frac{4}{11}+\frac{5}{11}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together!

00:13 First, we add the fractions, using a common denominator.

00:19 Now, let's work out the numerator.

00:22 And that's how we find the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{4}{11}+\frac{5}{11}=\text{?}$

Step-by-step solution

To solve the problem of adding the fractions $\frac{4}{11} + \frac{5}{11}$ , we follow these steps:

Step 1: Identify that both fractions have the same denominator of 11.
Step 2: Since the denominators are the same, we can add their numerators directly:
$4 + 5 = 9$ .
Step 3: Keep the common denominator, which remains as 11.

Now we combine these results to find the sum of the fractions:

$\frac{4}{11} + \frac{5}{11} = \frac{9}{11}$

The solution to the problem is $\frac{9}{11}$ , which matches choice 3 in the provided options.

Final Answer

$\frac{9}{11}$

Key Points to Remember

Essential concepts to master this topic

Like Denominators Rule: Add numerators, keep the same denominator unchanged
Addition Technique: Calculate 4 + 5 = 9, place over common denominator 11
Check: Verify $\frac{9}{11}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add 4 + 5 = 9 AND 11 + 11 = 22 to get $\frac{9}{22}$ ! This creates a completely different fraction with wrong 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 too?

The denominator tells us what size pieces we're working with. Since both fractions are already in elevenths, we're just counting how many elevenths we have total: 4 elevenths + 5 elevenths = 9 elevenths.

What if the denominators were different?

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

Do I need to simplify my answer?

Always check if you can simplify! For $\frac{9}{11}$ , since 9 and 11 share no common factors besides 1, it's already in simplest form.

How can I double-check my work?

Convert to decimals: $\frac{4}{11} \approx 0.364$ and $\frac{5}{11} \approx 0.455$ . Adding gives about 0.818, which equals $\frac{9}{11}$ !

Is there a pattern I can remember?

Like denominators = Easy addition! Just think:

Same bottom number stays the same
Add the top numbers together
Check if you can simplify

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