Solve Mixed Number Subtraction: 4½ - 2½

Q: What if the fractions were different, like 1/2 and 1/3?

Then you'd need to find a common denominator for the fractions first, or convert both mixed numbers to improper fractions. The separate component method only works when fractions are identical.

Q: Can the answer ever be just a whole number?

Yes! When the fraction parts are identical (like both $ \frac{1}{2} $), they subtract to zero, leaving only the whole number difference. This is exactly what happened in our problem.

Q: How do I check if my answer is correct?

Add your answer to the second mixed number: $ 2 + 2\frac{1}{2} = 4\frac{1}{2} $ ✓. If you get the first mixed number back, your subtraction is correct!

Q: What if I need to borrow from the whole number?

That happens when the first fraction is smaller than the second fraction. In our problem, both fractions were $ \frac{1}{2} $, so no borrowing was needed.

Mixed Number Subtraction with Identical Fractions

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 First, let's break down each mixed fraction into its whole number and fraction

00:19 Subtract

00:25 Use the commutative property and arrange the exercise in a convenient way to solve

00:34 Calculate the difference between the whole numbers

00:40 Subtract with common denominator

00:43 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

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

Step-by-step solution

To solve the problem $4\frac{1}{2} - 2\frac{1}{2}$ , we need to follow these steps:

Step 1: Identify the components of each mixed number.
$4\frac{1}{2}$ consists of a whole number $4$ and a fraction $\frac{1}{2}$ .
$2\frac{1}{2}$ consists of a whole number $2$ and a fraction $\frac{1}{2}$ .
Step 2: Subtract the whole numbers.
Subtract the whole number of the second from the first: $4 - 2 = 2$ .
Step 3: Subtract the fractions.
Since both fractions are $\frac{1}{2}$ , subtract them: $\frac{1}{2} - \frac{1}{2} = 0$ .
Step 4: Combine the results.
The result from the whole numbers is $2$ , and the result from the fractions is $0$ . So, $2 + 0 = 2$ .

Therefore, the answer to the problem $4\frac{1}{2} - 2\frac{1}{2}$ is $2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Components: Subtract whole numbers separately, then subtract fraction parts
Technique: $4 - 2 = 2$ and $\frac{1}{2} - \frac{1}{2} = 0$
Check: Convert answer back to mixed form: $2 + 0 = 2$ ✓

Common Mistakes

Avoid these frequent errors

Converting to improper fractions unnecessarily
Don't convert $4\frac{1}{2}$ to $\frac{9}{2}$ when fractions are identical = extra work and potential errors! When both mixed numbers have the same fraction part, you can subtract components separately. Always work with mixed numbers directly when fractions 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 can I subtract the whole numbers and fractions separately?

When both mixed numbers have the same fraction part, you can treat them as separate components. Think of it like $(4 + \frac{1}{2}) - (2 + \frac{1}{2})$ , which becomes $4 - 2 + \frac{1}{2} - \frac{1}{2}$ .

What if the fractions were different, like 1/2 and 1/3?

Then you'd need to find a common denominator for the fractions first, or convert both mixed numbers to improper fractions. The separate component method only works when fractions are identical.

Can the answer ever be just a whole number?

Yes! When the fraction parts are identical (like both $\frac{1}{2}$ ), they subtract to zero, leaving only the whole number difference. This is exactly what happened in our problem.

How do I check if my answer is correct?

Add your answer to the second mixed number: $2 + 2\frac{1}{2} = 4\frac{1}{2}$ ✓. If you get the first mixed number back, your subtraction is correct!

What if I need to borrow from the whole number?

That happens when the first fraction is smaller than the second fraction. In our problem, both fractions were $\frac{1}{2}$ , so no borrowing was needed.

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