Solve 2/3 - 1/6 - 3/12: Complete Fraction Subtraction Guide

Fraction Subtraction with Multiple Denominators

23−16−312= \frac{2}{3}-\frac{1}{6}-\frac{3}{12}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Alright, let's solve this problem together.
00:11 First, we need to find the least common denominator.
00:17 We'll multiply by four and two to get twelve.
00:22 Remember, multiply both the top and the bottom numbers.
00:30 Now, let's do these multiplication steps.
00:43 With the same denominator, we subtract.
00:49 Let's work out the top number, or the numerator.
00:55 Reduce the fraction as much as possible.
01:01 Divide both the numerator and the denominator.
01:06 Great job! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

23−16−312= \frac{2}{3}-\frac{1}{6}-\frac{3}{12}=

2

Step-by-step solution

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

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

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

2×43×4−1×26×2−3×112×1=812−212−312 \frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}-\frac{3\times1}{12\times1}=\frac{8}{12}-\frac{2}{12}-\frac{3}{12}

Now let's subtract:

8−2−312=6−312=312 \frac{8-2-3}{12}=\frac{6-3}{12}=\frac{3}{12}

Let's divide both numerator and denominator by 3 and we get:

3:312:3=14 \frac{3:3}{12:3}=\frac{1}{4}

3

Final Answer

14 \frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the LCD of all denominators before subtracting
  • Technique: Convert fractions: 23=812 \frac{2}{3} = \frac{8}{12} , 16=212 \frac{1}{6} = \frac{2}{12}
  • Check: Substitute: 812−212−312=312=14 \frac{8}{12} - \frac{2}{12} - \frac{3}{12} = \frac{3}{12} = \frac{1}{4} ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting denominators along with numerators
    Don't subtract 2/3 - 1/6 - 3/12 = (2-1-3)/(3-6-12) = -2/-15! This treats fractions like whole numbers and gives completely wrong results. Always find the LCD first, convert all fractions, then subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Determine the least common multiple of 8 and 12.

\( \boxed 8~~~\boxed{ 12} \)

FAQ

Everything you need to know about this question

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

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List the multiples of each number: 3: 3, 6, 9, 12... 6: 6, 12, 18... 12: 12, 24... The smallest number that appears in all lists is 12.

Why can't I just subtract the fractions as they are?

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You can only add or subtract fractions when they have the same denominator. Different denominators represent different-sized pieces, so you must convert them to the same size first.

What if I forget to simplify my final answer?

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Always check if your answer can be simplified! 312 \frac{3}{12} and 14 \frac{1}{4} are equal, but simplified form is preferred. Divide both numerator and denominator by their greatest common factor.

How do I convert each fraction to have denominator 12?

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Ask: "What times the original denominator equals 12?"

  • 23 \frac{2}{3} : 3 × 4 = 12, so multiply by 44 \frac{4}{4}
  • 16 \frac{1}{6} : 6 × 2 = 12, so multiply by 22 \frac{2}{2}
  • 312 \frac{3}{12} : Already has denominator 12!

Can I work left to right: first subtract 2/3 - 1/6, then subtract 3/12?

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Yes! Subtraction is performed left to right. First find 23−16=46−16=36=12 \frac{2}{3} - \frac{1}{6} = \frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2} , then 12−312=612−312=312=14 \frac{1}{2} - \frac{3}{12} = \frac{6}{12} - \frac{3}{12} = \frac{3}{12} = \frac{1}{4} .

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