Solve the Triple Fraction Subtraction: 5/6 - 2/4 - 3/12

Q: Why is 12 the LCD of 6, 4, and 12?

The LCD is the smallest number that all denominators divide into evenly. Since 12 ÷ 6 = 2, 12 ÷ 4 = 3, and 12 ÷ 12 = 1, we know 12 works!

Q: Do I subtract from left to right like regular subtraction?

Yes! Once you have the same denominator, work left to right: $ \frac{10}{12} - \frac{6}{12} - \frac{3}{12} = \frac{10-6-3}{12} = \frac{1}{12} $

Q: What if my answer comes out negative?

Negative answers are totally normal! If you get $ \frac{-2}{12} $, just simplify it to $ -\frac{1}{6} $. Always check your arithmetic carefully.

Q: Can I simplify fractions before finding the LCD?

Yes, but be careful! You could simplify $ \frac{2}{4} = \frac{1}{2} $ first, but then you'd need LCD of 6, 2, and 12, which is still 12. Sometimes it's easier to work with the original fractions.

Q: How do I know if my final answer can be simplified?

Check if the numerator and denominator share any common factors. Since 1 and 12 share no common factors except 1, $ \frac{1}{12} $ is already in simplest form!

Fraction Subtraction with Multiple Terms

$\frac{5}{6}-\frac{2}{4}-\frac{3}{12}=$

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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

00:22 Let's calculate the multiplications

00:31 Subtract under the common denominator

00:36 Let's calculate the numerator

00:46 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{5}{6}-\frac{2}{4}-\frac{3}{12}=$

Step-by-step solution

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

$\frac{5\times2}{6\times2}-\frac{2\times3}{4\times3}-\frac{3\times1}{12\times1}=\frac{10}{12}-\frac{6}{12}-\frac{3}{12}$

Now we'll subtract and get:

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

Final Answer

$\frac{1}{12}$

Key Points to Remember

Essential concepts to master this topic

LCD Method: Find common denominator to combine all fractions together
Technique: Convert fractions: $\frac{5}{6} = \frac{10}{12}, \frac{2}{4} = \frac{6}{12}$
Check: Verify numerator calculation: 10 - 6 - 3 = 1 ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract 5/6 - 2/4 - 3/12 by doing (5-2-3)/(6-4-12) = 0/(-10)! This treats fractions like whole numbers and gives completely wrong results. Always find the LCD first, then only subtract the numerators.

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 is 12 the LCD of 6, 4, and 12?

The LCD is the smallest number that all denominators divide into evenly. Since 12 ÷ 6 = 2, 12 ÷ 4 = 3, and 12 ÷ 12 = 1, we know 12 works!

Do I subtract from left to right like regular subtraction?

Yes! Once you have the same denominator, work left to right: $\frac{10}{12} - \frac{6}{12} - \frac{3}{12} = \frac{10-6-3}{12} = \frac{1}{12}$

What if my answer comes out negative?

Negative answers are totally normal! If you get $\frac{-2}{12}$ , just simplify it to $-\frac{1}{6}$ . Always check your arithmetic carefully.

Can I simplify fractions before finding the LCD?

Yes, but be careful! You could simplify $\frac{2}{4} = \frac{1}{2}$ first, but then you'd need LCD of 6, 2, and 12, which is still 12. Sometimes it's easier to work with the original fractions.

How do I know if my final answer can be simplified?

Check if the numerator and denominator share any common factors. Since 1 and 12 share no common factors except 1, $\frac{1}{12}$ is already in simplest form!

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Solve the Triple Fraction Subtraction: 5/6 - 2/4 - 3/12

Fraction Subtraction with Multiple Terms

❤️ 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 is 12 the LCD of 6, 4, and 12?

Do I subtract from left to right like regular subtraction?

What if my answer comes out negative?

Can I simplify fractions before finding the LCD?

How do I know if my final answer can be simplified?

🌟 Unlock Your Math Potential

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