Solve the Fraction Subtraction: 3/6 - 1/4

Q: Why can't I just subtract 3-1 and 6-4?

Because $ \frac{3}{6} $ and $ \frac{1}{4} $ represent different sized pieces! You can only subtract fractions when they have the same denominator - like subtracting slices from pizzas cut the same way.

Q: What do I multiply each fraction by?

Divide the LCD by each denominator: $ \frac{3}{6} $ multiply by $ \frac{2}{2} $ (since 12÷6=2)$ \frac{1}{4} $ multiply by $ \frac{3}{3} $ (since 12÷4=3)

Q: Can I simplify the answer further?

$ \frac{3}{12} $ can be simplified! Since both 3 and 12 are divisible by 3, you get $ \frac{1}{4} $. Always check if your final answer can be reduced to lowest terms.

Fraction Subtraction with Unlike Denominators

Solve the following equation:

$\frac{3}{6}-\frac{1}{4}=$

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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.

00:09 First, multiply each fraction by 3 and 2 to get the same denominator.

00:15 Remember, multiply both the top and bottom numbers of each fraction.

00:23 Now, calculate the new numerators by doing the multiplications.

00:33 Next, subtract the fractions with the common denominator.

00:38 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{3}{6}-\frac{1}{4}=$

Step-by-step solution

Let's try to find the lowest common denominator between 4 and 6

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 6

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 2

We'll multiply the second fraction by 3

$\frac{3\times2}{6\times2}-\frac{1\times3}{4\times3}=\frac{6}{12}-\frac{3}{12}$

Now let's subtract:

$\frac{6-3}{12}=\frac{3}{12}$

Final Answer

$\frac{3}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before subtracting fractions with different denominators
Technique: Convert $\frac{3}{6}$ to $\frac{6}{12}$ and $\frac{1}{4}$ to $\frac{3}{12}$
Check: Verify $\frac{6}{12} - \frac{3}{12} = \frac{3}{12}$ by adding back: $\frac{3}{12} + \frac{3}{12} = \frac{6}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators and denominators separately
Don't subtract 3-1=2 and 6-4=2 to get $\frac{2}{2}$ = wrong answer! This ignores that fractions represent parts of different-sized wholes. Always find the LCD first to make denominators the same.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why can't I just subtract 3-1 and 6-4?

Because $\frac{3}{6}$ and $\frac{1}{4}$ represent different sized pieces! You can only subtract fractions when they have the same denominator - like subtracting slices from pizzas cut the same way.

How do I find the LCD of 6 and 4?

List multiples of each number: 6: 6, 12, 18, 24... and 4: 4, 8, 12, 16, 20, 24... The first number that appears in both lists is your LCD. Here it's 12!

What do I multiply each fraction by?

Divide the LCD by each denominator:

$\frac{3}{6}$ multiply by $\frac{2}{2}$ (since 12÷6=2)
$\frac{1}{4}$ multiply by $\frac{3}{3}$ (since 12÷4=3)

Can I simplify the answer further?

$\frac{3}{12}$ can be simplified! Since both 3 and 12 are divisible by 3, you get $\frac{1}{4}$ . Always check if your final answer can be reduced to lowest terms.

What if the denominators are already the same?

Lucky you! When denominators match, just subtract the numerators and keep the same denominator. For example: $\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$

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