Solve the Fraction Subtraction: 3/5 minus 5/10

Q: Why can't I just subtract 3-5 and 5-10 separately?

You can only subtract fractions when they have the same denominator! Think of it like trying to subtract 3 apples from 5 oranges - you need to convert them to the same type first.

Q: How do I know which denominator to use as the common one?

Look for the Least Common Multiple (LCM) of the denominators. In this case, 10 is a multiple of 5, so 10 is the perfect common denominator to use.

Q: Is 5/10 the same as 1/2?

Yes! $ \frac{5}{10} = \frac{1}{2} $ when simplified. You could solve this problem as $ \frac{3}{5} - \frac{1}{2} $, but using 10 as the common denominator makes the calculation easier.

Fraction Subtraction with Common Denominators

Solve the following exercise:

$\frac{3}{5}-\frac{5}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's get started by solving the problem.

00:09 First, multiply everything by 2 to find the common denominator.

00:14 Make sure you multiply both the top number and the bottom number.

00:18 Now, let's calculate, the multiplications.

00:25 Continue by dividing the result by the common denominator.

00:31 Now, calculate the new top number.

00:35 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{3}{5}-\frac{5}{10}=\text{?}$

Step-by-step solution

To solve this problem, we'll follow a step-by-step approach:

Step 1: Convert both fractions to have the same denominator.
- The original fractions are $\frac{3}{5}$ and $\frac{5}{10}$ .
- Convert $\frac{3}{5}$ to a fraction with denominator 10. Multiply both numerator and denominator by 2:
$\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$ .
Step 2: Subtract the fractions now that they have a common denominator.
- The fractions to subtract are $\frac{6}{10} - \frac{5}{10}$ .
Step 3: Perform the subtraction by subtracting numerators.
- $\frac{6}{10} - \frac{5}{10} = \frac{6-5}{10} = \frac{1}{10}$ .
Step 4: Verify if simplification is necessary.
- The fraction $\frac{1}{10}$ is already in its simplest form.

Therefore, the solution to $\frac{3}{5}-\frac{5}{10}$ is $\frac{1}{10}$ .

Final Answer

$\frac{1}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to have the same denominator before subtracting
Technique: Convert $\frac{3}{5}$ to $\frac{6}{10}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{6}{10} - \frac{5}{10} = \frac{1}{10}$ is in simplest form ✓

Common Mistakes

Avoid these frequent errors

Subtracting fractions without finding common denominators
Don't subtract $\frac{3}{5} - \frac{5}{10} = \frac{3-5}{5-10} = \frac{-2}{-5}$ ! This creates wrong denominators and incorrect results. Always find a common denominator first by converting one or both fractions.

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 can't I just subtract 3-5 and 5-10 separately?

You can only subtract fractions when they have the same denominator! Think of it like trying to subtract 3 apples from 5 oranges - you need to convert them to the same type first.

How do I know which denominator to use as the common one?

Look for the Least Common Multiple (LCM) of the denominators. In this case, 10 is a multiple of 5, so 10 is the perfect common denominator to use.

Do I always multiply by 2/2 to convert fractions?

No! You multiply by whatever fraction equals 1 that gives you the target denominator. For $\frac{3}{5}$ to become tenths, multiply by $\frac{2}{2}$ because 5 × 2 = 10.

What if my answer can be simplified further?

Always check if your final fraction can be reduced! Look for common factors in the numerator and denominator. Since 1 and 10 share no common factors except 1, $\frac{1}{10}$ is already simplified.

Is 5/10 the same as 1/2?

Yes! $\frac{5}{10} = \frac{1}{2}$ when simplified. You could solve this problem as $\frac{3}{5} - \frac{1}{2}$ , but using 10 as the common denominator makes the calculation easier.

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