Solve: Adding 6 and 5⅔ - Mixed Number Addition Problem

Q: Why don't I need to convert 6 to a mixed number?

Whole numbers are already in their simplest form! Since 6 has no fractional part, you can add it directly to the whole number part of $ 5\frac{2}{3} $.

Q: What if the fractional parts needed to be added too?

If both numbers had fractional parts (like $ 6\frac{1}{4} + 5\frac{2}{3} $), you'd add whole numbers first, then add fractions separately using a common denominator.

Q: Can I write the answer as an improper fraction instead?

Yes! $ 11\frac{2}{3} = \frac{35}{3} $ is mathematically correct, but mixed numbers are usually preferred for answers unless specifically asked for improper fractions.

Q: How do I know I added the whole numbers correctly?

Double-check: $ 6 + 5 = 11 $. Then verify your final answer makes sense - it should be larger than both original numbers since you're adding positive values!

Q: What's the fastest way to solve this type of problem?

Step 1: Add whole numbers: 6 + 5 = 11Step 2: Attach the fraction: $ \frac{2}{3} $Step 3: Write as mixed number: $ 11\frac{2}{3} $

Mixed Number Addition with Whole Numbers

$6+5\frac{2}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 First, let's break down each mixed fraction into a whole number and a fraction

00:13 Let's calculate the sum of the whole numbers

00:20 Now let's add the fraction to the sum of the numbers

00:23 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

$6+5\frac{2}{3}=$

Step-by-step solution

To solve the problem $6 + 5\frac{2}{3}$ , we will follow these steps:

Step 1: Identify the whole numbers: $6$ and $5$ .
Step 2: Add the whole numbers: $6 + 5 = 11$ .
Step 3: Recognize the fractional part: $\frac{2}{3}$ .
Step 4: Combine the whole number result with the fractional part: $11 + \frac{2}{3}$ .

Resultantly, when adding these components, the complete sum is $11\frac{2}{3}$ .

Therefore, the solution to the problem is $11\frac{2}{3}$ .

Final Answer

$11\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add whole numbers first, then attach the fractional part
Technique: $6 + 5 = 11$ , then combine with $\frac{2}{3}$
Check: Verify $11\frac{2}{3} = 11 + \frac{2}{3} = \frac{35}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Converting mixed numbers to improper fractions unnecessarily
Don't convert $5\frac{2}{3}$ to $\frac{17}{3}$ and then add = complicated fractions! This creates extra work with big numerators. Always add whole numbers directly when one addend is a whole number.

Practice Quiz

Test your knowledge with interactive questions

$2\frac{2}{5}+2\frac{2}{5}=$

FAQ

Everything you need to know about this question

Why don't I need to convert 6 to a mixed number?

Whole numbers are already in their simplest form! Since 6 has no fractional part, you can add it directly to the whole number part of $5\frac{2}{3}$ .

What if the fractional parts needed to be added too?

If both numbers had fractional parts (like $6\frac{1}{4} + 5\frac{2}{3}$ ), you'd add whole numbers first, then add fractions separately using a common denominator.

Can I write the answer as an improper fraction instead?

Yes! $11\frac{2}{3} = \frac{35}{3}$ is mathematically correct, but mixed numbers are usually preferred for answers unless specifically asked for improper fractions.

How do I know I added the whole numbers correctly?

Double-check: $6 + 5 = 11$ . Then verify your final answer makes sense - it should be larger than both original numbers since you're adding positive values!

What's the fastest way to solve this type of problem?

Step 1: Add whole numbers: 6 + 5 = 11
Step 2: Attach the fraction: $\frac{2}{3}$
Step 3: Write as mixed number: $11\frac{2}{3}$

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