Solve the Fraction Subtraction: 5/10 - 2/6 Step-by-Step

Q: Why can't I just subtract 5-2 and 10-6 directly?

Because $ \frac{5}{10} $ and $ \frac{2}{6} $ represent parts of different sized wholes! You need to convert them to the same denominator first, like converting dollars and euros before adding money.

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

Yes! Always check if your answer can be simplified. Divide both numerator and denominator by their greatest common divisor. Here, $ \frac{5}{30} $ becomes $ \frac{1}{6} $ when divided by 5.

Q: Can I reduce the fractions before subtracting?

Absolutely! $ \frac{5}{10} = \frac{1}{2} $ and $ \frac{2}{6} = \frac{1}{3} $. Then subtract $ \frac{1}{2} - \frac{1}{3} $ using LCD of 6 to get $ \frac{3}{6} - \frac{2}{6} = \frac{1}{6} $.

Fraction Subtraction with Different Denominators

Solve the following exercise:

$\frac{5}{10}-\frac{2}{6}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:10 First, we need to find the smallest common denominator.

00:14 Multiply the denominators, 3 and 5, to find it.

00:18 Remember, you must multiply both the numerator and denominator.

00:29 Now, let's calculate those multiplications.

00:37 Next, divide by the common denominator.

00:45 Calculate the new numerator.

00:49 Try to reduce the fraction as much as possible.

00:55 Divide both the numerator and the denominator if needed.

00:59 And there you have it! That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{5}{10}-\frac{2}{6}=\text{?}$

Step-by-step solution

We need to subtract the fractions $\frac{5}{10} - \frac{2}{6}$ .

Step 1: Find a common denominator for the fractions. The denominators are 10 and 6.

The Least Common Multiple (LCM) of 10 and 6 is 30.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 30.

For $\frac{5}{10}$ , multiply both the numerator and the denominator by 3 to get $\frac{15}{30}$ .
For $\frac{2}{6}$ , multiply both the numerator and the denominator by 5 to get $\frac{10}{30}$ .

Step 3: Subtract the fractions:

$\frac{15}{30} - \frac{10}{30} = \frac{15 - 10}{30} = \frac{5}{30}$ .

Step 4: Simplify the result:

The fraction $\frac{5}{30}$ can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 5.

$\frac{5}{30} = \frac{5 \div 5}{30 \div 5} = \frac{1}{6}$ .

Therefore, the answer to the subtraction $\frac{5}{10} - \frac{2}{6}$ is $\frac{1}{6}$ .

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before subtracting fractions with different denominators
Technique: Convert $\frac{5}{10}$ to $\frac{15}{30}$ and $\frac{2}{6}$ to $\frac{10}{30}$
Check: Simplify $\frac{5}{30}$ by dividing by GCD of 5 to get $\frac{1}{6}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators and denominators separately
Don't subtract 5-2=3 and 10-6=4 to get $\frac{3}{4}$ = wrong answer! This ignores that fractions represent parts of different wholes. Always find a common denominator first, then subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{8}{5}-\frac{4}{5}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just subtract 5-2 and 10-6 directly?

Because $\frac{5}{10}$ and $\frac{2}{6}$ represent parts of different sized wholes! You need to convert them to the same denominator first, like converting dollars and euros before adding money.

How do I find the LCD of 10 and 6?

List multiples: 10, 20, 30, 40... and 6, 12, 18, 24, 30... The first number that appears in both lists is your LCD. Or use prime factorization: 10 = 2×5, 6 = 2×3, so LCD = 2×3×5 = 30.

Do I always need to simplify my final answer?

Yes! Always check if your answer can be simplified. Divide both numerator and denominator by their greatest common divisor. Here, $\frac{5}{30}$ becomes $\frac{1}{6}$ when divided by 5.

What if the LCD seems really big?

Don't worry! Sometimes you get large denominators like 30. Just work through the steps carefully. The final simplified answer will usually be much simpler, like our $\frac{1}{6}$ .

Can I reduce the fractions before subtracting?

Absolutely! $\frac{5}{10} = \frac{1}{2}$ and $\frac{2}{6} = \frac{1}{3}$ . Then subtract $\frac{1}{2} - \frac{1}{3}$ using LCD of 6 to get $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$ .

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