Solve Fraction Subtraction: 10/13 minus 5/13 Step-by-Step

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

The denominator tells us what size pieces we're working with. Since both fractions are thirteenths, we keep thirteenths and just change how many we have: 10 pieces minus 5 pieces = 5 pieces.

Q: What if the denominators were different?

Then you'd need to find a common denominator first! But in this problem, both fractions already have the same denominator (13), so you can subtract directly.

Q: How do I know if my answer needs to be simplified?

Check if the numerator and denominator share any common factors. Since 5 and 13 are both prime numbers, $ \frac{5}{13} $ is already in simplest form.

Q: Can the answer ever be bigger than the first fraction?

Never! When you subtract fractions, your answer must be smaller than what you started with. If you get a bigger answer, double-check your work.

Q: What if I get zero as my answer?

That's possible! If you subtract $ \frac{5}{13} - \frac{5}{13} $, you get $ \frac{0}{13} = 0 $. Zero is a valid answer in fraction subtraction.

Fraction Subtraction with Same Denominators

Solve the following exercise:

$\frac{10}{13}-\frac{5}{13}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Subtract with common denominator

00:07 Calculate the numerator

00:11 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:

$\frac{10}{13}-\frac{5}{13}=\text{?}$

Step-by-step solution

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

Step 1: Identify the given fractions and ensure they have a common denominator.
Step 2: Subtract the numerators while keeping the denominator the same.
Step 3: Simplify the result if necessary.

Let's work through each step:
Step 1: The fractions given are $\frac{10}{13}$ and $\frac{5}{13}$ , both having a denominator of 13.
Step 2: Apply the subtraction formula for fractions with common denominators: $\frac{10}{13} - \frac{5}{13} = \frac{10 - 5}{13} = \frac{5}{13}$ Step 3: No further simplification is needed since $\frac{5}{13}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{5}{13}$ .

Final Answer

$\frac{5}{13}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators match, subtract only the numerators
Technique: Keep denominator 13, subtract: 10 - 5 = 5
Check: Verify $\frac{5}{13}$ cannot simplify further since GCD(5,13) = 1 ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't calculate $\frac{10}{13} - \frac{5}{13} = \frac{5}{0}$ by subtracting both parts! This creates undefined fractions and meaningless answers. Always keep the common denominator unchanged and subtract only 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 we subtract the denominators too?

The denominator tells us what size pieces we're working with. Since both fractions are thirteenths, we keep thirteenths and just change how many we have: 10 pieces minus 5 pieces = 5 pieces.

What if the denominators were different?

Then you'd need to find a common denominator first! But in this problem, both fractions already have the same denominator (13), so you can subtract directly.

How do I know if my answer needs to be simplified?

Check if the numerator and denominator share any common factors. Since 5 and 13 are both prime numbers, $\frac{5}{13}$ is already in simplest form.

Can the answer ever be bigger than the first fraction?

Never! When you subtract fractions, your answer must be smaller than what you started with. If you get a bigger answer, double-check your work.

What if I get zero as my answer?

That's possible! If you subtract $\frac{5}{13} - \frac{5}{13}$ , you get $\frac{0}{13} = 0$ . Zero is a valid answer in fraction subtraction.

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