Solve Mixed Number Addition: 5⅖ + 2⅕ Step by Step

Q: Why don't I need to find a common denominator?

Great observation! Since both fractions already have the same denominator ($ \frac{2}{5} $ and $ \frac{1}{5} $), you can add the numerators directly: 2 + 1 = 3.

Q: Can I add the whole numbers and fractions all together?

Always separate them first! Add whole numbers (5 + 2 = 7), then fractions ($ \frac{2}{5} + \frac{1}{5} = \frac{3}{5} $), then combine for $ 7\frac{3}{5} $.

Q: What if my fraction part gets bigger than 1?

If you get an improper fraction like $ \frac{7}{5} $, convert it to a mixed number and add to your whole number part. For example: $ 6\frac{7}{5} = 6 + 1\frac{2}{5} = 7\frac{2}{5} $.

Q: How can I check if my answer is right?

Convert both mixed numbers to improper fractions first: $ 5\frac{2}{5} = \frac{27}{5} $ and $ 2\frac{1}{5} = \frac{11}{5} $. Then add: $ \frac{27}{5} + \frac{11}{5} = \frac{38}{5} = 7\frac{3}{5} $!

Q: Why is this easier than adding different denominators?

When denominators are the same, you skip the hardest step! No need to find LCD or convert fractions - just add numerators directly and keep the denominator.

Mixed Number Addition with Same Denominators

$5\frac{2}{5}+2\frac{1}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 First, let's break down each mixed fraction into its whole number and fraction

00:18 Let's use the commutative property and arrange the exercise in a convenient way to solve

00:30 Let's calculate the sum of the whole numbers

00:36 Let's add using the common denominator

00:44 This is the sum of the fractions, now let's add it to the sum of the numbers

00:48 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

$5\frac{2}{5}+2\frac{1}{5}=$

Step-by-step solution

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

Step 1: Add the whole number parts.
Step 2: Add the fractional parts.
Step 3: Combine results and simplify if necessary.

Now, let's work through each step:
Step 1: The mixed numbers are $5\frac{2}{5}$ and $2\frac{1}{5}$ . First, add the whole number parts: $5 + 2 = 7$ .
Step 2: Next, add the fractional parts: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$ . Since the denominators are the same, just add the numerators.
Step 3: Combine these sums to form the mixed number: $7 + \frac{3}{5} = 7\frac{3}{5}$ .

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

Final Answer

$7\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Add whole numbers separately, then add fractions separately
Technique: Same denominators: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$
Check: Convert to improper: $\frac{27}{5} + \frac{11}{5} = \frac{38}{5} = 7\frac{3}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators instead of just numerators
Don't add $\frac{2}{5} + \frac{1}{5} = \frac{3}{10}$ ! This creates a wrong denominator and gives $7\frac{3}{10}$ instead of the correct answer. Always keep the same denominator and only add the numerators when denominators match.

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 find a common denominator?

Great observation! Since both fractions already have the same denominator ( $\frac{2}{5}$ and $\frac{1}{5}$ ), you can add the numerators directly: 2 + 1 = 3.

Can I add the whole numbers and fractions all together?

Always separate them first! Add whole numbers (5 + 2 = 7), then fractions ( $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$ ), then combine for $7\frac{3}{5}$ .

What if my fraction part gets bigger than 1?

If you get an improper fraction like $\frac{7}{5}$ , convert it to a mixed number and add to your whole number part. For example: $6\frac{7}{5} = 6 + 1\frac{2}{5} = 7\frac{2}{5}$ .

How can I check if my answer is right?

Convert both mixed numbers to improper fractions first: $5\frac{2}{5} = \frac{27}{5}$ and $2\frac{1}{5} = \frac{11}{5}$ . Then add: $\frac{27}{5} + \frac{11}{5} = \frac{38}{5} = 7\frac{3}{5}$ !

Why is this easier than adding different denominators?

When denominators are the same, you skip the hardest step! No need to find LCD or convert fractions - just add numerators directly and keep the denominator.

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