Solve the Fraction Equation: 2/3 - 1/6 - 6/12

Fraction Operations with Common Denominators

23−16−612= \frac{2}{3}-\frac{1}{6}-\frac{6}{12}=

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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 step by step.
00:09 First, we'll find the least common denominator.
00:13 So, multiply 4 and 2 to get a common denominator.
00:18 Remember, multiply both the numerator and the denominator by these numbers.
00:27 Great job! Now let's compute these multiplications.
00:36 Next, subtract the values under the common denominator.
00:41 Alright, let's work on the numerator.
00:48 Remember, zero divided by any number is zero.
00:52 And that's how we find the answer. Great work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

23−16−612= \frac{2}{3}-\frac{1}{6}-\frac{6}{12}=

2

Step-by-step solution

Let's try to find the lowest common multiple of 3, 6 and 12

To find the lowest common multiple, we find a number that is divisible by 3, 6 and 12

In this case, the common multiple is 12

Now let's multiply each number in the appropriate multiple to reach the multiple of 12

We will multiply the first number by 4

We will multiply the second number by 2

We will multiply the third number by 1

2×43×4−1×26×2−6×112×1=812−212−612 \frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}-\frac{6\times1}{12\times1}=\frac{8}{12}-\frac{2}{12}-\frac{6}{12}

Now let's subtract:

8−2−612=6−612=012 \frac{8-2-6}{12}=\frac{6-6}{12}=\frac{0}{12}

We will divide the numerator and the denominator by 0 and get:

012=0 \frac{0}{12}=0

3

Final Answer

0 0

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert all fractions to same denominator before subtracting
  • Technique: Find LCD of 3, 6, 12 = 12: 23=812 \frac{2}{3} = \frac{8}{12}
  • Check: Verify numerator arithmetic: 8 - 2 - 6 = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions with different denominators directly
    Don't compute 23−16=13 \frac{2}{3} - \frac{1}{6} = \frac{1}{3} by subtracting numerators and denominators separately = wrong answer! This ignores that fractions represent different-sized parts. Always find the LCD first and convert all fractions before performing operations.

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 the numerators and denominators separately?

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Fractions represent parts of different-sized wholes. 23 \frac{2}{3} means 2 parts of thirds, while 16 \frac{1}{6} means 1 part of sixths. You must make the parts the same size first!

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

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

  • Multiples of 3: 3, 6, 9, 12, 15...
  • Multiples of 6: 6, 12, 18...
  • Multiples of 12: 12, 24...

The LCD is 12!

Why does 612 \frac{6}{12} equal 12 \frac{1}{2} ?

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Both fractions represent the same amount! 612=6÷612÷6=12 \frac{6}{12} = \frac{6 ÷ 6}{12 ÷ 6} = \frac{1}{2} . Always simplify fractions by dividing both numerator and denominator by their greatest common factor.

What does it mean when the answer is 0?

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An answer of 0 means the fractions you subtracted had a total value of zero. This happens when the positive parts exactly cancel out the negative parts - perfectly balanced!

Do I always need to simplify my final answer?

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Yes! Always reduce fractions to lowest terms. For example, 012=0 \frac{0}{12} = 0 because any fraction with 0 in the numerator equals zero, regardless of the denominator.

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