Solve the Fraction Problem: 5/6 - 1/4 - 3/12 Step by Step

Q: Why can't I just subtract the numerators and denominators separately?

Fractions represent parts of a whole, not separate numbers! You need the same-sized pieces (same denominator) before you can subtract. It's like trying to subtract 2 apples from 3 oranges - you need to convert to the same unit first.

Q: How do I find the LCD when there are three different denominators?

List the multiples of each denominator until you find the smallest number that appears in all lists. For 6, 4, and 12: multiples of 12 (12, 24...) already include 6 and 4 as factors, so 12 is the LCD!

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

Yes, always simplify! Look for the greatest common factor of the numerator and denominator. For $\frac{4}{12}$, both 4 and 12 are divisible by 4, giving us $\frac{1}{3}$.

Q: What if one fraction already has the LCD as its denominator?

Great! That fraction stays the same. In this problem, $\frac{3}{12}$ already had denominator 12, so we only needed to convert the other fractions.

Q: I got a different answer than what's shown as correct. What went wrong?

Check these common errors: Did you find the correct LCD? Did you multiply both numerator and denominator by the same number? Did you subtract all numerators correctly? Did you simplify the final fraction?

Q: Is there a shortcut for problems like this?

The systematic approach IS the shortcut! Find LCD → Convert → Subtract → Simplify. Trying to skip steps usually leads to mistakes and takes longer to fix.

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 Therefore we'll multiply by 2 and 3 respectively to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:21 Let's calculate the multiplications

00:36 Subtract under the common denominator

00:42 Calculate the numerator

00:49 Reduce the fraction as much as possible

00:53 Remember to divide both numerator and denominator

00:57 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following exercise:

$\frac{5}{6}-\frac{1}{4}-\frac{3}{12}=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the least common denominator (LCD).
Step 2: Convert each fraction to have the common denominator.
Step 3: Subtract the numerators and simplify the final result.

Now, let's work through each step:
Step 1: The denominators are $6$ , $4$ , and $12$ . The smallest number that is a multiple of all these denominators is $12$ , so our LCD is $12$ .
Step 2: Convert each fraction to have a denominator of $12$ :

$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$
$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
$\frac{3}{12}$ already has the denominator $12$ .

Step 3: Subtract the fractions, now rewritten as having the same denominator:

$\frac{10}{12} - \frac{3}{12} - \frac{3}{12}$ .

Subtract the numerators:

10 - 3 - 3 = 4.

The resulting fraction is $\frac{4}{12}$ .

We simplify $\frac{4}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $4$ :

$\frac{4 \div 4}{12 \div 4} = \frac{1}{3}$ .

Therefore, the simplified result of the operation is $\frac{1}{3}$ .

3

Final Answer

$\frac{5}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before subtracting fractions with different denominators
Technique: Convert to common denominator: $\frac{5}{6} = \frac{10}{12}$
Check: Verify LCD is smallest common multiple: 12 ÷ 6 = 2, 12 ÷ 4 = 3 ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract 5-1-3 and 6-4-12 separately = $\frac{1}{-10}$ which is wrong! This treats fractions like whole numbers. Always find LCD first, convert all fractions to same denominator, then subtract only numerators.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{3}+\frac{1}{4}=$

FAQ

Everything you need to know about this question

Why can't I just subtract the numerators and denominators separately?

+

Fractions represent parts of a whole, not separate numbers! You need the same-sized pieces (same denominator) before you can subtract. It's like trying to subtract 2 apples from 3 oranges - you need to convert to the same unit first.

How do I find the LCD when there are three different denominators?

+

List the multiples of each denominator until you find the smallest number that appears in all lists. For 6, 4, and 12: multiples of 12 (12, 24...) already include 6 and 4 as factors, so 12 is the LCD!

Do I always need to simplify my final answer?

+

Yes, always simplify! Look for the greatest common factor of the numerator and denominator. For $\frac{4}{12}$ , both 4 and 12 are divisible by 4, giving us $\frac{1}{3}$ .

What if one fraction already has the LCD as its denominator?

+

Great! That fraction stays the same. In this problem, $\frac{3}{12}$ already had denominator 12, so we only needed to convert the other fractions.

I got a different answer than what's shown as correct. What went wrong?

+

Check these common errors: Did you find the correct LCD? Did you multiply both numerator and denominator by the same number? Did you subtract all numerators correctly? Did you simplify the final fraction?

Is there a shortcut for problems like this?

+

The systematic approach IS the shortcut! Find LCD → Convert → Subtract → Simplify. Trying to skip steps usually leads to mistakes and takes longer to fix.

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Solve the Fraction Problem: 5/6 - 1/4 - 3/12 Step by Step

Fraction Subtraction with Mixed Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just subtract the numerators and denominators separately?

How do I find the LCD when there are three different denominators?

Do I always need to simplify my final answer?

What if one fraction already has the LCD as its denominator?

I got a different answer than what's shown as correct. What went wrong?

Is there a shortcut for problems like this?

🌟 Unlock Your Math Potential

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