Solve 2 + 3⅓: Adding Whole Numbers with Mixed Numbers

Q: What if I want to check my answer using improper fractions?

Great idea! Convert both numbers: $ 2 = \frac{14}{7} $ and $ 3\frac{3}{7} = \frac{24}{7} $. Then add: $ \frac{14}{7} + \frac{24}{7} = \frac{38}{7} = 5\frac{3}{7} $

Q: Can I add the whole number to the fractional part instead?

No! You can't add 2 directly to $ \frac{3}{7} $ because they have different units. Think of it like adding 2 whole pizzas to 3/7 of a pizza slice - you count the whole pizzas separately!

Q: What's the easiest way to remember this process?

Remember: "Whole with whole, fraction stays alone." Just add the whole numbers (2 + 3 = 5) and keep the original fraction ($ \frac{3}{7} $) to get $ 5\frac{3}{7} $.

Q: Would this work the same way with subtraction?

Yes! For something like $ 5 - 2\frac{1}{4} $, you'd subtract whole numbers (5 - 2 = 3) and keep the fraction, giving $ 3\frac{1}{4} $. Same principle applies!

Mixed Number Addition with Whole Numbers

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Break down into whole number and remainder

00:15 Add the whole numbers

00:20 Combine into a mixed number

00:24 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

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

Step-by-step solution

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

Step 1: Identify the whole and fractional parts of the mixed number.
Step 2: Add the whole numbers together.
Step 3: Combine the result with the fractional part.

Now, let's work through each step:
Step 1: The mixed number $3\frac{3}{7}$ consists of the whole number 3 and the fraction $\frac{3}{7}$ .
Step 2: Add the whole numbers: $3 + 2 = 5$ .
Step 3: The final result combines the sum of the whole numbers with the original fraction: $5 + \frac{3}{7} = 5\frac{3}{7}$ .

Therefore, the solution to the problem is $5\frac{3}{7}$ .

Final Answer

$5\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add whole numbers first, keep fractional part unchanged
Technique: $2 + 3\frac{3}{7}$ = (2 + 3) + $\frac{3}{7}$ = 5 + $\frac{3}{7}$
Check: Verify by converting to improper fractions: $\frac{14}{7} + \frac{24}{7} = \frac{38}{7} = 5\frac{3}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Adding the whole number to both the whole and fractional parts
Don't add 2 to both 3 and $\frac{3}{7}$ giving $5\frac{5}{7}$ ! This counts the 2 twice and inflates your answer. Always add whole numbers together first, then attach the original fraction unchanged.

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 anything when adding a whole number to a mixed number?

When adding a whole number to a mixed number, you only need to add the whole number parts together! The fraction stays exactly the same because you're not adding anything to it.

What if I want to check my answer using improper fractions?

Great idea! Convert both numbers: $2 = \frac{14}{7}$ and $3\frac{3}{7} = \frac{24}{7}$ . Then add: $\frac{14}{7} + \frac{24}{7} = \frac{38}{7} = 5\frac{3}{7}$

Can I add the whole number to the fractional part instead?

No! You can't add 2 directly to $\frac{3}{7}$ because they have different units. Think of it like adding 2 whole pizzas to 3/7 of a pizza slice - you count the whole pizzas separately!

What's the easiest way to remember this process?

Remember: "Whole with whole, fraction stays alone." Just add the whole numbers (2 + 3 = 5) and keep the original fraction ( $\frac{3}{7}$ ) to get $5\frac{3}{7}$ .

Would this work the same way with subtraction?

Yes! For something like $5 - 2\frac{1}{4}$ , you'd subtract whole numbers (5 - 2 = 3) and keep the fraction, giving $3\frac{1}{4}$ . Same principle applies!

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