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

Q: Why can't I just subtract 3-3=0 from the numerators?

You can subtract numerators, but only after getting a common denominator! With different denominators like 5 and 10, you're subtracting different-sized pieces, which doesn't work.

Q: How do I find the common denominator?

Find the Least Common Multiple (LCM) of the denominators. For 5 and 10, list multiples: 5, 10, 15... and 10, 20, 30... The smallest common one is 10!

Q: What if both fractions need to be converted?

Convert both fractions to the common denominator. For example, if subtracting $ \frac{2}{3} - \frac{1}{4} $, convert both to twelfths: $ \frac{8}{12} - \frac{3}{12} $.

Q: Do I need to simplify my answer?

Always check if your answer can be simplified! $ \frac{3}{10} $ is already in lowest terms since 3 and 10 share no common factors besides 1.

Q: Can I convert the other way, making 10 into 5?

No! You can only convert to a larger denominator that both original denominators divide into evenly. Since 10 ÷ 5 = 2 but 5 ÷ 10 = 0.5, use 10 as the common denominator.

Fraction Subtraction with Different Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Multiply the fraction by 2 to get to the common denominator

00:07 Make sure to multiply both numerator and denominator

00:13 Calculate the multiplications

00:19 Subtract with the common denominator

00:23 Calculate the numerator

00:26 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:

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

Step-by-step solution

To solve the problem $\frac{3}{5} - \frac{3}{10}$ , follow these steps:

Step 1: Find the common denominator:

The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10, so our common denominator is 10.

Step 2: Convert each fraction to have the common denominator:

Convert $\frac{3}{5}$ to a fraction with a denominator of 10:

Multiply both the numerator and denominator of $\frac{3}{5}$ by 2 to get $\frac{6}{10}$ .

Note: $\frac{3}{10}$ already has the common denominator of 10, so it remains unchanged.

Step 3: Perform the subtraction:

Subtract $\frac{3}{10}$ from $\frac{6}{10}$ :

$\frac{6}{10} - \frac{3}{10} = \frac{6 - 3}{10} = \frac{3}{10}$ .

Therefore, the solution to the problem is $\frac{3}{10}$ .

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before subtracting fractions
Technique: Convert $\frac{3}{5}$ to $\frac{6}{10}$ by multiplying by 2
Check: Verify $\frac{6}{10} - \frac{3}{10} = \frac{3}{10}$ by adding back ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract both numerators AND denominators like 3-3=0 and 5-10=-5 = $\frac{0}{-5}$ ! This completely ignores fraction rules and gives meaningless results. Always find a common denominator first, then 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 can't I just subtract 3-3=0 from the numerators?

You can subtract numerators, but only after getting a common denominator! With different denominators like 5 and 10, you're subtracting different-sized pieces, which doesn't work.

How do I find the common denominator?

Find the Least Common Multiple (LCM) of the denominators. For 5 and 10, list multiples: 5, 10, 15... and 10, 20, 30... The smallest common one is 10!

What if both fractions need to be converted?

Convert both fractions to the common denominator. For example, if subtracting $\frac{2}{3} - \frac{1}{4}$ , convert both to twelfths: $\frac{8}{12} - \frac{3}{12}$ .

Do I need to simplify my answer?

Always check if your answer can be simplified! $\frac{3}{10}$ is already in lowest terms since 3 and 10 share no common factors besides 1.

Can I convert the other way, making 10 into 5?

No! You can only convert to a larger denominator that both original denominators divide into evenly. Since 10 ÷ 5 = 2 but 5 ÷ 10 = 0.5, use 10 as the common denominator.

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