Solve the Fraction Subtraction: 5/3 minus 2/3

Q: Why don't I subtract the denominators too?

The denominator tells us what size pieces we're working with. Since both fractions use thirds, we keep working with thirds! Only the number of pieces (numerators) changes when we subtract.

Q: Do I always need to simplify my answer?

Yes, always simplify! $ \frac{3}{3} $ equals 1, which is much cleaner than leaving it as an improper fraction. Look for common factors to reduce.

Q: What if the numerators were different, like 2 - 5?

You'd get $ \frac{2-5}{3} = \frac{-3}{3} = -1 $. Negative answers are perfectly fine in fraction subtraction! Just follow the same steps.

Q: How do I know when fractions have the same denominator?

Look at the bottom numbers. In $ \frac{5}{3} - \frac{2}{3} $, both denominators are 3, so they're the same! This makes subtraction much easier.

Fraction Subtraction with Same Denominators

Solve the following exercise:

$\frac{5}{3}-\frac{2}{3}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Subtract in the common denominator

00:08 Calculate the numerator

00:11 Any number divided by itself always equals 1

00:14 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

Solve the following exercise:

$\frac{5}{3}-\frac{2}{3}=\text{?}$

Step-by-step solution

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

Step 1: Recognize that both fractions have the same denominator, which allows direct subtraction of the numerators.
Step 2: Subtract the numerator of the second fraction ( $2$ ) from the numerator of the first fraction ( $5$ ).
Step 3: Place the result over the common denominator.

Now, let's work through each step:
Step 1: We have $\frac{5}{3} - \frac{2}{3}$ . Both denominators are 3.
Step 2: Subtract the numerators: $5 - 2 = 3$ .
Step 3: The resulting fraction is $\frac{3}{3}$ .

Finally, simplify $\frac{3}{3} = 1$ .

Therefore, the solution to the problem is 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Same Denominator Rule: Subtract numerators directly, keep common denominator unchanged
Technique: For $\frac{5}{3} - \frac{2}{3}$ , calculate 5 - 2 = 3
Check: Simplify final result $\frac{3}{3} = 1$ and verify answer ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators instead of keeping them the same
Don't subtract both numerators AND denominators like 5-2 and 3-3 = 3/0! This creates undefined results or wrong answers. Always keep the common denominator unchanged and only subtract the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

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

FAQ

Everything you need to know about this question

Why don't I subtract the denominators too?

The denominator tells us what size pieces we're working with. Since both fractions use thirds, we keep working with thirds! Only the number of pieces (numerators) changes when we subtract.

Do I always need to simplify my answer?

Yes, always simplify! $\frac{3}{3}$ equals 1, which is much cleaner than leaving it as an improper fraction. Look for common factors to reduce.

What if the numerators were different, like 2 - 5?

You'd get $\frac{2-5}{3} = \frac{-3}{3} = -1$ . Negative answers are perfectly fine in fraction subtraction! Just follow the same steps.

How do I know when fractions have the same denominator?

Look at the bottom numbers. In $\frac{5}{3} - \frac{2}{3}$ , both denominators are 3, so they're the same! This makes subtraction much easier.

Can I convert this to a mixed number instead?

Since our answer is 1 (a whole number), there's no need for a mixed number here. But if you got something like $\frac{7}{3}$ , you could write it as $2\frac{1}{3}$ .

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