Solve Mixed Number Subtraction: 10½ - ½

Q: Why don't I need to borrow from the whole number?

You only borrow when the fraction you're subtracting is larger than the fraction part of the mixed number. Since $ \frac{1}{2} - \frac{1}{2} = 0 $, no borrowing needed!

Q: What if the denominators were different?

Then you'd need to find a common denominator first. But in this problem, both fractions have the same denominator (2), so you can subtract directly.

Q: Should I always convert mixed numbers to improper fractions?

Not always! When denominators match like here, working with the mixed number is faster and less error-prone. Only convert when you need to multiply or divide.

Q: How do I know when my final answer should be a mixed number?

If your result is a whole number (like 10), leave it as is. You only need mixed number form when there's a remaining fraction part after calculation.

Q: What if I got 9 as my answer instead?

Check your work! A common error is subtracting $ \frac{1}{2} $ from the whole number instead of from the fraction part. Remember: only subtract like parts!

Mixed Number Subtraction with Like Denominators

$10\frac{1}{2}-\frac{1}{2}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Break down each mixed fraction into a whole number and remainder

00:14 Reduce what is possible

00:21 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

$10\frac{1}{2}-\frac{1}{2}=$

Step-by-step solution

Let's solve the problem step-by-step:

Step 1: Identify the parts of the mixed number $10\frac{1}{2}$ . It consists of the whole number $10$ and the fraction $\frac{1}{2}$ .
Step 2: We'll subtract $\frac{1}{2}$ (the fraction we are given to subtract) from the fraction part of the mixed number:

$\frac{1}{2} - \frac{1}{2} = 0$

Step 3: After performing the subtraction, the fractional part becomes $0$ .

Step 4: This leaves us with the whole part of the mixed number on its own, which is $10$ .

Therefore, the solution to the problem is $10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtract fraction parts separately from whole number parts
Technique: $\frac{1}{2} - \frac{1}{2} = 0$ , leaving whole number unchanged
Check: $10\frac{1}{2} - \frac{1}{2} = 10 + 0 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Converting the mixed number to improper fraction unnecessarily
Don't convert $10\frac{1}{2}$ to $\frac{21}{2}$ = creates harder arithmetic! This makes simple problems complicated and increases chance of calculation errors. Always work directly with the mixed number when denominators are the same.

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 borrow from the whole number?

You only borrow when the fraction you're subtracting is larger than the fraction part of the mixed number. Since $\frac{1}{2} - \frac{1}{2} = 0$ , no borrowing needed!

What if the denominators were different?

Then you'd need to find a common denominator first. But in this problem, both fractions have the same denominator (2), so you can subtract directly.

Should I always convert mixed numbers to improper fractions?

Not always! When denominators match like here, working with the mixed number is faster and less error-prone. Only convert when you need to multiply or divide.

How do I know when my final answer should be a mixed number?

If your result is a whole number (like 10), leave it as is. You only need mixed number form when there's a remaining fraction part after calculation.

What if I got 9 as my answer instead?

Check your work! A common error is subtracting $\frac{1}{2}$ from the whole number instead of from the fraction part. Remember: only subtract like parts!

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