Solve Mixed Number Addition: 3¼ + 1½ Step by Step

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

Great observation! Both fractions already have the same denominator (fourths). When denominators match, you can directly add the numerators and keep the denominator unchanged.

Q: What if the whole number part gets bigger than expected?

Sometimes adding fractions creates an improper fraction that adds another whole number. For example, $ \frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4} $ would add 1 more to your whole number total.

Q: Can I convert to improper fractions instead?

Absolutely! You can convert $ 3\frac{1}{4} = \frac{13}{4} $ and $ 1\frac{2}{4} = \frac{6}{4} $, then add: $ \frac{13}{4} + \frac{6}{4} = \frac{19}{4} = 4\frac{3}{4} $. Both methods work!

Q: How do I know which answer choice is correct?

Work through the problem step-by-step, then double-check your arithmetic. Here: 3 + 1 = 4 (whole numbers) and $ \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $ (fractions), giving $ 4\frac{3}{4} $.

Q: Should I simplify the fraction part?

Always check if you can simplify! In this case, $ \frac{3}{4} $ is already in lowest terms since 3 and 4 share no common factors other than 1.

Mixed Number Addition with Common Denominators

$3\frac{1}{4}+1\frac{2}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 First, break down each mixed fraction into a whole number and a fraction

00:14 We'll use the commutative property and arrange the exercise in a convenient way to solve

00:34 Let's calculate the sum of the whole numbers

00:40 Add with common denominator

00:46 This is the sum of fractions, now let's add it to the sum of numbers

00:50 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

$3\frac{1}{4}+1\frac{2}{4}=$

Step-by-step solution

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

Step 1: Extract the whole number and fraction parts from each mixed number.
Step 2: Add the whole numbers together.
Step 3: Add the fractions together using their common denominator.
Step 4: Combine the results, checking if any simplification is needed.

Now, let's work through each step:
Step 1: From $3\frac{1}{4}$ , the whole number is $3$ and the fraction is $\frac{1}{4}$ . From $1\frac{2}{4}$ , the whole number is $1$ and the fraction is $\frac{2}{4}$ .
Step 2: Add the whole numbers: $3 + 1 = 4$ .
Step 3: Add the fractions $\frac{1}{4} + \frac{2}{4}$ . Since the denominators are the same, we add the numerators: $\frac{1+2}{4} = \frac{3}{4}$ .
Step 4: Combine the results from Steps 2 and 3 to get $4 + \frac{3}{4} = 4\frac{3}{4}$ .

Therefore, the solution to the problem is $4\frac{3}{4}$ , which matches choice 3.

Final Answer

$4\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Structure: Separate whole numbers from fractions before adding
Technique: Add whole numbers (3 + 1 = 4) and fractions separately
Check: Verify $4\frac{3}{4} = 4 + \frac{3}{4} = \frac{19}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add $\frac{1}{4} + \frac{2}{4} = \frac{3}{8}$ ! This gives wrong denominators and incorrect results. Always keep the common denominator and only add the numerators: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ .

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 here?

Great observation! Both fractions already have the same denominator (fourths). When denominators match, you can directly add the numerators and keep the denominator unchanged.

What if the whole number part gets bigger than expected?

Sometimes adding fractions creates an improper fraction that adds another whole number. For example, $\frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4}$ would add 1 more to your whole number total.

Can I convert to improper fractions instead?

Absolutely! You can convert $3\frac{1}{4} = \frac{13}{4}$ and $1\frac{2}{4} = \frac{6}{4}$ , then add: $\frac{13}{4} + \frac{6}{4} = \frac{19}{4} = 4\frac{3}{4}$ . Both methods work!

How do I know which answer choice is correct?

Work through the problem step-by-step, then double-check your arithmetic. Here: 3 + 1 = 4 (whole numbers) and $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ (fractions), giving $4\frac{3}{4}$ .

Should I simplify the fraction part?

Always check if you can simplify! In this case, $\frac{3}{4}$ is already in lowest terms since 3 and 4 share no common factors other than 1.

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