Solve the Fraction Subtraction: 1/3 minus 1/6 Step by Step

Q: Why can't I just subtract 1/3 - 1/6 directly?

You can only subtract fractions when they have the same denominator. Think of it like subtracting different units - you can't subtract 2 apples from 3 oranges without converting to the same type first!

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

Use the smallest number that both denominators divide into evenly. Since 6 is already a multiple of 3, we use 6 as our common denominator. This keeps calculations simple!

Q: Can I use a different common denominator like 12?

Yes, but it makes more work! Using 12: $ \frac{4}{12} - \frac{2}{12} = \frac{2}{12} $, then you'd simplify to $ \frac{1}{6} $. The smallest common denominator is most efficient.

Fraction Subtraction with Common Denominators

Solve the following exercise:

$\frac{1}{3}-\frac{1}{6}=\text{?}$

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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 2 to find the common denominator

00:06 Make sure to multiply both numerator and denominator

00:14 Calculate the products

00:19 Subtract with the common denominator

00:26 Calculate the numerator

00:30 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:

$\frac{1}{3}-\frac{1}{6}=\text{?}$

Step-by-step solution

To solve this fraction subtraction problem, we need to follow these steps:

Step 1: Identify and adjust the fractions to have a common denominator. The given problem is $\frac{1}{3} - \frac{1}{6}$ .
Step 2: Find a common denominator. Since 6 is a multiple of 3, we can use 6 as the common denominator.
Step 3: Adjust $\frac{1}{3}$ to have a denominator of 6. Multiply both the numerator and denominator of $\frac{1}{3}$ by 2 to get $\frac{2}{6}$ .
Step 4: Subtract the fractions now having the same denominator: $\frac{2}{6} - \frac{1}{6}$ .
Step 5: Subtract the numerators: $2 - 1 = 1$ , keeping the denominator as 6, resulting in $\frac{1}{6}$ .

Therefore, the solution to $\frac{1}{3} - \frac{1}{6}$ is $\frac{1}{6}$ .

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Fractions need same denominators before subtracting numerators
Technique: Convert $\frac{1}{3}$ to $\frac{2}{6}$ by multiplying by 2
Check: Verify $\frac{2}{6} - \frac{1}{6} = \frac{1}{6}$ by adding back ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract both parts: 1-1 and 3-6 = 0/-3! This completely changes the value of fractions. Always keep the common denominator unchanged and only subtract 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 1/3 - 1/6 directly?

You can only subtract fractions when they have the same denominator. Think of it like subtracting different units - you can't subtract 2 apples from 3 oranges without converting to the same type first!

How do I know which common denominator to use?

Use the smallest number that both denominators divide into evenly. Since 6 is already a multiple of 3, we use 6 as our common denominator. This keeps calculations simple!

Do I need to simplify my final answer?

Always check if your answer can be simplified! In this case, $\frac{1}{6}$ is already in lowest terms since 1 and 6 share no common factors except 1.

What if the second fraction was bigger than the first?

If you get a negative result, that's perfectly fine! For example, $\frac{1}{6} - \frac{1}{3} = \frac{1}{6} - \frac{2}{6} = -\frac{1}{6}$ . Just follow the same steps.

Can I use a different common denominator like 12?

Yes, but it makes more work! Using 12: $\frac{4}{12} - \frac{2}{12} = \frac{2}{12}$ , then you'd simplify to $\frac{1}{6}$ . The smallest common denominator is most efficient.

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