Solve Mixed Number Subtraction: 2⅓ - 1⅔ Step-by-Step

Q: Why can't I just subtract the fractions and get a negative result?

Mixed numbers represent positive values, so negative fractional parts don't make sense. When $ \frac{1}{3} - \frac{2}{3} $ gives $ -\frac{1}{3} $, you need to borrow from the whole number first!

Q: When do I need to borrow in mixed number subtraction?

Borrow whenever the top fraction is smaller than the bottom fraction. If \( \frac{1}{3} , you need to borrow before subtracting!

Q: Can my final answer be just a fraction?

Yes! If your result is a proper fraction (numerator smaller than denominator), leave it as is. Only convert to mixed numbers when you have improper fractions.

Q: What if both mixed numbers have the same whole number part?

The same borrowing rules apply! Even $ 3\frac{1}{4} - 3\frac{3}{4} $ requires borrowing because $ \frac{1}{4} . The result would be \( \frac{2}{4} = \frac{1}{2} $.

Mixed Number Subtraction with Regrouping

$2\frac{1}{3}-1\frac{2}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Break down each mixed fraction into a whole number and remainder

00:26 Convert from whole numbers to appropriate proper fractions

00:42 Add using the common denominator

01:00 Subtract using the common denominator

01:14 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

$2\frac{1}{3}-1\frac{2}{3}=$

Step-by-step solution

To solve the problem $2\frac{1}{3} - 1\frac{2}{3}$ , we'll perform the following steps:

Step 1: Subtract the integer parts: $2 - 1 = 1$ .
Step 2: Subtract the fractional parts: $\frac{1}{3} - \frac{2}{3}$ .

To calculate $\frac{1}{3} - \frac{2}{3}$ :

Since the fractions have a common denominator, subtract only the numerators:
$1 - 2 = -1$ .
Therefore, $\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$ .

Now combine the results:

The subtraction results in $1 - \frac{1}{3}$ .

To simplify, note $1 = \frac{3}{3}$ .

Thus, $1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$ .

Therefore, the solution to $2\frac{1}{3} - 1\frac{2}{3}$ is $\frac{2}{3}$ .

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When top fraction is smaller, borrow 1 from whole number
Technique: Convert $1 = \frac{3}{3}$ so $1 - \frac{1}{3} = \frac{2}{3}$
Check: Convert answer back to mixed: $\frac{2}{3}$ stays as proper fraction ✓

Common Mistakes

Avoid these frequent errors

Subtracting fractions without considering borrowing
Don't calculate $\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$ and leave it negative = wrong final answer! Negative fractional parts create incorrect results. Always borrow from the whole number when the top fraction is smaller than the bottom fraction.

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 subtract the fractions and get a negative result?

Mixed numbers represent positive values, so negative fractional parts don't make sense. When $\frac{1}{3} - \frac{2}{3}$ gives $-\frac{1}{3}$ , you need to borrow from the whole number first!

How do I borrow from the whole number part?

Take 1 from the whole number and convert it to a fraction with the same denominator. For example: $2\frac{1}{3}$ becomes $1\frac{4}{3}$ because $1 = \frac{3}{3}$ and $\frac{1}{3} + \frac{3}{3} = \frac{4}{3}$ .

When do I need to borrow in mixed number subtraction?

Borrow whenever the top fraction is smaller than the bottom fraction. If $\frac{1}{3} < \frac{2}{3}$ , you need to borrow before subtracting!

Can my final answer be just a fraction?

Yes! If your result is a proper fraction (numerator smaller than denominator), leave it as is. Only convert to mixed numbers when you have improper fractions.

What if both mixed numbers have the same whole number part?

The same borrowing rules apply! Even $3\frac{1}{4} - 3\frac{3}{4}$ requires borrowing because $\frac{1}{4} < \frac{3}{4}$ . The result would be $\frac{2}{4} = \frac{1}{2}$ .

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