Solve the Fraction Subtraction: 3/5 minus 6/15 Step-by-Step

Q: Why can't I just subtract 3-6 and 5-15 directly?

Fractions represent parts of a whole. You can only subtract when the 'wholes' (denominators) are the same size! It's like trying to subtract 3 apples from 6 oranges - they're different units.

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

Look for the Least Common Multiple (LCM) of both denominators. In this case, 15 is already a multiple of 5, so 15 becomes our common denominator automatically!

Q: Do I always need to simplify my final answer?

Yes, always simplify! $ \frac{3}{15} $ and $ \frac{1}{5} $ are equal, but $ \frac{1}{5} $ is the simplest form and the expected answer.

Fraction Subtraction with Common Denominator Finding

Solve the following exercise:

$\frac{3}{5}-\frac{6}{15}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply by 3 to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:15 Calculate the multiplications

00:23 Subtract by the common denominator

00:29 Calculate the numerator

00:33 Reduce the fraction as much as possible

00:37 Make sure to divide both numerator and denominator

00:44 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:

$\frac{3}{5}-\frac{6}{15}=\text{?}$

Step-by-step solution

To solve $\frac{3}{5} - \frac{6}{15}$ , we need both fractions to have the same denominator. We observe that 15 is a multiple of 5, so it is already suitable as a common denominator.

Step 1: Convert
Convert $\frac{3}{5}$ to have a denominator of 15. Multiply both the numerator and the denominator by 3:

$\frac{3}{5} \times \frac{3}{3} = \frac{9}{15}$

Step 2: Subtract the fractions
Now, subtract $\frac{9}{15} - \frac{6}{15}$ :

$\frac{9}{15} - \frac{6}{15} = \frac{9 - 6}{15} = \frac{3}{15}$

Step 3: Simplify the result
Simplify $\frac{3}{15}$ by dividing both the numerator and the denominator by 3:

$\frac{3}{15} = \frac{1}{5}$

Therefore, the solution to the problem is $\frac{1}{5}$ .

Final Answer

$\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before subtracting fractions completely
Technique: Convert $\frac{3}{5}$ to $\frac{9}{15}$ by multiplying by 3
Check: Simplify final answer: $\frac{3}{15} = \frac{1}{5}$ by dividing by 3 ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators and denominators separately
Don't subtract 3-6 and 5-15 separately = $\frac{-3}{-10}$ ! This ignores the fundamental rule that fractions need common denominators. 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 3-6 and 5-15 directly?

Fractions represent parts of a whole. You can only subtract when the 'wholes' (denominators) are the same size! It's like trying to subtract 3 apples from 6 oranges - they're different units.

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

Look for the Least Common Multiple (LCM) of both denominators. In this case, 15 is already a multiple of 5, so 15 becomes our common denominator automatically!

Do I always need to simplify my final answer?

Yes, always simplify! $\frac{3}{15}$ and $\frac{1}{5}$ are equal, but $\frac{1}{5}$ is the simplest form and the expected answer.

What if the denominators don't have an obvious relationship?

When denominators like 4 and 6 don't divide evenly, find their LCM (which would be 12). Then convert both fractions: $\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{6} = \frac{2}{12}$ .

Can I check my work somehow?

Absolutely! Convert your answer back to a decimal and check: $\frac{1}{5} = 0.2$ . Also verify: $\frac{3}{5} - \frac{6}{15} = 0.6 - 0.4 = 0.2$ ✓

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