Solve Fraction Subtraction: 4/6 - 3/9 Step-by-Step

Q: Why can't I just subtract 4-3 and 6-9?

Because fractions represent parts of different-sized wholes! You can't subtract $ \frac{4}{6} $ and $ \frac{3}{9} $ directly - it's like trying to subtract 4 slices of a 6-piece pizza from 3 slices of a 9-piece pizza without making the pieces the same size first.

Q: What if I get a different common denominator?

Any common multiple works, but using the LCD keeps numbers smaller and makes calculations easier. For example, 36 would work too, but you'd get $ \frac{24}{36} - \frac{12}{36} = \frac{12}{36} $, which still simplifies to $ \frac{1}{3} $.

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

Yes! Always check if you can reduce your fraction to lowest terms. Divide both numerator and denominator by their greatest common factor. $ \frac{6}{18} $ becomes $ \frac{1}{3} $ when you divide both by 6.

Fraction Subtraction with Different Denominators

Solve the following exercise:

$\frac{4}{6}-\frac{3}{9}=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 Multiply by 3 and 2 respectively to find the common denominator

00:09 Make sure to multiply both numerator and denominator

00:19 Calculate the multiplications

00:27 Subtract with the common denominator

00:31 Calculate the numerator

00:38 Reduce the fraction as much as possible

00:42 Make sure to divide both numerator and denominator

00:45 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:

$\frac{4}{6}-\frac{3}{9}=\text{?}$

Step-by-step solution

To solve this problem, let's go step by step:

Step 1: Identify the Least Common Denominator (LCD).
- The denominators are 6 and 9.
- The multiples of 6 are 6, 12, 18, 24, ...
- The multiples of 9 are 9, 18, 27, 36, ...
- The smallest common multiple is 18.
Step 2: Rewrite the fractions with the common denominator of 18.
- $\frac{4}{6}$ can be converted by finding an equivalent fraction with a denominator of 18: $\frac{4 \times 3}{6 \times 3} = \frac{12}{18}$ .
- $\frac{3}{9}$ can be converted similarly: $\frac{3 \times 2}{9 \times 2} = \frac{6}{18}$ .
Step 3: Subtract the two fractions.
- Subtract the numerators: $12 - 6 = 6$ .
- The result is $\frac{6}{18}$ .
Step 4: Simplify the resulting fraction.
- $\frac{6}{18}$ simplifies to $\frac{1}{3}$ by dividing both the numerator and the denominator by 6.

Therefore, the solution to the problem is $\frac{1}{3}$ .

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find common denominator before subtracting fractions
Technique: Convert $\frac{4}{6}$ to $\frac{12}{18}$ and $\frac{3}{9}$ to $\frac{6}{18}$
Check: Simplify final answer: $\frac{6}{18} = \frac{1}{3}$ by dividing by 6 ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract 4-3 = 1 and 6-9 = -3 to get $\frac{1}{-3}$ ! This treats fractions like separate numbers instead of parts of wholes. Always find the LCD first, convert both fractions, 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 4-3 and 6-9?

Because fractions represent parts of different-sized wholes! You can't subtract $\frac{4}{6}$ and $\frac{3}{9}$ directly - it's like trying to subtract 4 slices of a 6-piece pizza from 3 slices of a 9-piece pizza without making the pieces the same size first.

How do I find the LCD of 6 and 9?

List the multiples of each number: 6: 6, 12, 18, 24... and 9: 9, 18, 27, 36... The smallest number that appears in both lists is 18, so that's your LCD!

What if I get a different common denominator?

Any common multiple works, but using the LCD keeps numbers smaller and makes calculations easier. For example, 36 would work too, but you'd get $\frac{24}{36} - \frac{12}{36} = \frac{12}{36}$ , which still simplifies to $\frac{1}{3}$ .

Do I always need to simplify my final answer?

Yes! Always check if you can reduce your fraction to lowest terms. Divide both numerator and denominator by their greatest common factor. $\frac{6}{18}$ becomes $\frac{1}{3}$ when you divide both by 6.

What if the first fraction is smaller than the second?

No problem! Just subtract normally and you'll get a negative result. For example, $\frac{2}{8} - \frac{5}{8} = \frac{-3}{8}$ or $-\frac{3}{8}$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime