Solve Mixed Number Addition: 1¼ + 2½ Step by Step

Q: Why can't I just add the whole numbers and fractions separately?

You can add whole numbers separately, but the fractions must have the same denominator first! So add 1 + 2 = 3, then convert $ \frac{1}{4} + \frac{1}{2} $ to $ \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $.

Q: What's the fastest way to find the common denominator?

Look at your denominators (4 and 2). Since 4 is a multiple of 2, the LCD is simply 4! Convert $ \frac{1}{2} $ to $ \frac{2}{4} $ by multiplying top and bottom by 2.

Q: How do I convert an improper fraction back to a mixed number?

Divide the numerator by the denominator. For $ \frac{15}{4} $: 15 ÷ 4 = 3 remainder 3, so the answer is $ 3\frac{3}{4} $.

Q: Can I solve this problem without converting to improper fractions?

Yes! Add whole numbers: 1 + 2 = 3. Then add fractions with common denominator: $ \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $. Final answer: $ 3\frac{3}{4} $.

Mixed Number Addition with Common Denominators

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve a math problem together!

00:07 Here's how to change a mixed fraction into a regular fraction. It's easy!

00:15 We'll use this method in our example. Let's convert it into a fraction.

00:34 First, multiply to find the common denominator. That's important!

00:46 Next, multiply each part by this common denominator.

00:52 Great job! Now, let's change it back into a mixed fraction.

00:57 Think of number fifteen as twelve plus three.

01:01 Break this fraction into a whole number and a remainder.

01:05 Convert the whole fraction to a whole number, then mix them together.

01:10 And there you have it! That's how we find the answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

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

Step 1: Convert the mixed numbers to improper fractions.
Step 2: Find a common denominator and perform the addition.
Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:
Step 1: Convert each mixed number to an improper fraction:

$1\frac{1}{4}$ becomes $\frac{5}{4}$ because $1 \times 4 + 1 = 5$ .
$2\frac{1}{2}$ becomes $\frac{5}{2}$ because $2 \times 2 + 1 = 5$ .

Step 2: Find a common denominator and add the fractions:
The least common denominator of 4 and 2 is 4.
Convert

\frac{5}{2}

\frac{10}{4}

by multiplying the numerator and the denominator by 2.
Now, add the fractions:

\frac{5}{4} + \frac{10}{4} = \frac{15}{4}

.

Step 3: Convert the improper fraction back to a mixed number:
Divide 15 by 4. The whole number is 3, and the remainder is 3.
So,

\frac{15}{4} = 3\frac{3}{4}

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

Final Answer

$3\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Convert First: Transform mixed numbers to improper fractions before adding
Common Denominator: Change $\frac{5}{2}$ to $\frac{10}{4}$ using LCD of 4
Check Result: Verify $3\frac{3}{4} = 1\frac{1}{4} + 2\frac{1}{2}$ by converting back ✓

Common Mistakes

Avoid these frequent errors

Adding whole numbers and fractions separately without finding common denominators
Don't add 1 + 2 = 3, then $\frac{1}{4} + \frac{1}{2} = \frac{2}{6}$ = wrong answer $3\frac{2}{6}$ ! This ignores that fractions need the same denominator to add correctly. Always convert fractions to common denominators first, then add numerators.

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 can't I just add the whole numbers and fractions separately?

You can add whole numbers separately, but the fractions must have the same denominator first! So add 1 + 2 = 3, then convert $\frac{1}{4} + \frac{1}{2}$ to $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ .

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. For $1\frac{1}{4}$ : multiply 1 × 4 = 4, then add 1 to get $\frac{5}{4}$ .

What's the fastest way to find the common denominator?

Look at your denominators (4 and 2). Since 4 is a multiple of 2, the LCD is simply 4! Convert $\frac{1}{2}$ to $\frac{2}{4}$ by multiplying top and bottom by 2.

How do I convert an improper fraction back to a mixed number?

Divide the numerator by the denominator. For $\frac{15}{4}$ : 15 ÷ 4 = 3 remainder 3, so the answer is $3\frac{3}{4}$ .

Can I solve this problem without converting to improper fractions?

Yes! Add whole numbers: 1 + 2 = 3. Then add fractions with common denominator: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ . Final answer: $3\frac{3}{4}$ .

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