Solve the Fraction Expression: 3/6 - 1/3 - 1/12 Step-by-Step

Fraction Operations with Mixed Denominators

36−13−112= \frac{3}{6}-\frac{1}{3}-\frac{1}{12}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's find the solution.
00:07 First, we need the least common denominator.
00:11 So, we'll multiply by two, and by four, to find it.
00:14 Remember, always multiply both the numerator and the denominator.
00:27 Now, let's do the multiplications.
00:37 Subtract under the common denominator.
00:44 Calculate the new numerator.
00:49 And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

36−13−112= \frac{3}{6}-\frac{1}{3}-\frac{1}{12}=

2

Step-by-step solution

Let's try to find the least common denominator between 6, 3, and 12

To find the least common denominator, we need to find a number that is divisible by 6, 3, 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 4

We'll multiply the third fraction by 1

3×26×2−1×43×4−1×112×1=612−412−112 \frac{3\times2}{6\times2}-\frac{1\times4}{3\times4}-\frac{1\times1}{12\times1}=\frac{6}{12}-\frac{4}{12}-\frac{1}{12}

Now let's subtract:

6−4−112=2−112=112 \frac{6-4-1}{12}=\frac{2-1}{12}=\frac{1}{12}

3

Final Answer

112 \frac{1}{12}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find least common denominator before adding or subtracting fractions
  • Technique: Convert 36 \frac{3}{6} to 612 \frac{6}{12} and 13 \frac{1}{3} to 412 \frac{4}{12}
  • Check: Verify 612−412−112=112 \frac{6}{12} - \frac{4}{12} - \frac{1}{12} = \frac{1}{12} by cross-checking LCD work ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions without finding common denominators
    Don't try to subtract 36−13 \frac{3}{6} - \frac{1}{3} directly = wrong answer like 23 \frac{2}{3} ! You can't combine fractions with different denominators because they represent different-sized pieces. Always find the LCD first to make all 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

How do I find the LCD of 6, 3, and 12?

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List the multiples of each number until you find the smallest number that appears in all lists:

  • 6: 6, 12, 18...
  • 3: 3, 6, 9, 12...
  • 12: 12, 24...

The LCD is 12 since it's the smallest multiple they all share!

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

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Because fractions represent parts of different-sized wholes! 13 \frac{1}{3} means 1 out of 3 pieces, while 16 \frac{1}{6} means 1 out of 6 pieces. You need the same-sized pieces (same denominator) to combine them correctly.

What if I simplified 3/6 to 1/2 first?

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That's a great approach! Simplifying 36=12 \frac{3}{6} = \frac{1}{2} first makes the problem 12−13−112 \frac{1}{2} - \frac{1}{3} - \frac{1}{12} . You'd still need LCD = 12, giving the same final answer.

How do I know which number to multiply each fraction by?

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Divide the LCD by each denominator:

  • 36 \frac{3}{6} : 12 ÷ 6 = 2, so multiply by 22 \frac{2}{2}
  • 13 \frac{1}{3} : 12 ÷ 3 = 4, so multiply by 44 \frac{4}{4}
  • 112 \frac{1}{12} : 12 ÷ 12 = 1, so multiply by 11 \frac{1}{1}

Can I check my answer a different way?

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Yes! Convert your answer to a decimal: 112≈0.083 \frac{1}{12} ≈ 0.083 . Then check: 36=0.5 \frac{3}{6} = 0.5 , 13≈0.333 \frac{1}{3} ≈ 0.333 , 112≈0.083 \frac{1}{12} ≈ 0.083 . So 0.5 - 0.333 - 0.083 ≈ 0.084, which matches 112 \frac{1}{12} !

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