Solve: 5/6 - 2/4 - 1/12 | Multiple Fraction Subtraction

Q: Why do I multiply the first fraction by 2 but the second by 3?

You need to make each denominator equal 12. Since $ 6 \times 2 = 12 $, multiply the first fraction by 2. Since $ 4 \times 3 = 12 $, multiply the second by 3. The third fraction already has denominator 12!

Q: Can I simplify my answer further?

Yes! $ \frac{3}{12} $ can be simplified by dividing both numerator and denominator by their GCD of 3, giving $ \frac{1}{4} $.

Q: Do I always need to convert to the same denominator?

Always! You cannot add or subtract fractions unless they have the same denominator. Think of it like trying to subtract apples from oranges - you need the same 'units' first!

Fraction Subtraction with Common Denominators

$\frac{5}{6}-\frac{2}{4}-\frac{1}{12}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each fraction by 2 and 3 respectively to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:18 Calculate the multiplications

00:33 Add with the common denominator

00:40 Calculate the numerator

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

$\frac{5}{6}-\frac{2}{4}-\frac{1}{12}=$

Step-by-step solution

Let's try to find the lowest common denominator between 6 and 4 and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 4, and 12

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

We'll multiply the third fraction by 1

$\frac{5\times2}{6\times2}-\frac{2\times3}{4\times3}-\frac{1\times1}{12\times1}=\frac{10}{12}-\frac{6}{12}-\frac{1}{12}$

Now let's subtract:

$\frac{10-6-1}{12}=\frac{4-1}{12}=\frac{3}{12}$

Final Answer

$\frac{3}{12}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find least common denominator for all fractions first
Technique: Convert $\frac{5}{6}$ to $\frac{10}{12}$ by multiplying by 2
Check: Verify $\frac{10}{12} - \frac{6}{12} - \frac{1}{12} = \frac{3}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting fractions with different denominators directly
Don't subtract $\frac{5}{6} - \frac{2}{4} = \frac{3}{2}$ ! This gives completely wrong answers because you can't combine fractions with different denominators. Always find the LCD first and convert all fractions to equivalent fractions with the same denominator.

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

How do I find the LCD of 6, 4, and 12?

List the multiples of each number: 6: 6, 12, 18... 4: 4, 8, 12, 16... 12: 12, 24, 36... The smallest number that appears in all lists is 12!

Why do I multiply the first fraction by 2 but the second by 3?

You need to make each denominator equal 12. Since $6 \times 2 = 12$ , multiply the first fraction by 2. Since $4 \times 3 = 12$ , multiply the second by 3. The third fraction already has denominator 12!

Can I simplify my answer further?

Yes! $\frac{3}{12}$ can be simplified by dividing both numerator and denominator by their GCD of 3, giving $\frac{1}{4}$ .

What if I get a negative answer?

Negative answers are possible in subtraction! If you're subtracting larger fractions from smaller ones, you'll get a negative result. Just follow the same steps with the LCD.

Do I always need to convert to the same denominator?

Always! You cannot add or subtract fractions unless they have the same denominator. Think of it like trying to subtract apples from oranges - you need the same 'units' first!

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