Solve: 10/12 - 2/3 - 1/6 Triple Fraction Subtraction

Fraction Subtraction with Multiple Terms

10122316= \frac{10}{12}-\frac{2}{3}-\frac{1}{6}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:03 We want to find the smallest common denominator
00:06 Therefore, we'll multiply 4 and 2 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:19 Let's calculate the multiplications
00:31 We'll subtract under the common denominator
00:38 Let's calculate the numerator
00:42 0 divided by any number always equals 0
00:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

10122316= \frac{10}{12}-\frac{2}{3}-\frac{1}{6}=

2

Step-by-step solution

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

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

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 1

We'll multiply the second fraction by 4

We'll multiply the third fraction by 2

10×112×12×43×41×26×2=1012812212 \frac{10\times1}{12\times1}-\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}=\frac{10}{12}-\frac{8}{12}-\frac{2}{12}

Now let's subtract:

108212=2212=012 \frac{10-8-2}{12}=\frac{2-2}{12}=\frac{0}{12}

We'll divide both the numerator and 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
  • LCD Rule: Find common denominator to combine all fractions
  • Technique: Convert 23 \frac{2}{3} to 812 \frac{8}{12} when LCD is 12
  • Check: Verify: 1012812212=012=0 \frac{10}{12} - \frac{8}{12} - \frac{2}{12} = \frac{0}{12} = 0

Common Mistakes

Avoid these frequent errors
  • Adding/subtracting fractions without common denominator
    Don't subtract 101223=89 \frac{10}{12} - \frac{2}{3} = \frac{8}{9} ! This gives completely wrong results because you can't combine fractions with different denominators. 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 a whole, and different denominators mean different-sized parts! You must make all parts the same size (same denominator) before combining them.

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

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List multiples of the largest number: 12, 24, 36... Check if smaller numbers divide evenly. Since 3 and 6 both divide into 12, the LCD is 12!

What does it mean when my answer is 0?

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Getting 0 means the positive and negative parts completely cancel out! This is a valid mathematical result - check by substitution to confirm.

Can I simplify fractions before finding the LCD?

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Yes! 1012 \frac{10}{12} simplifies to 56 \frac{5}{6} , making the LCD 6 instead of 12. Either approach works!

What if I get confused with multiple subtractions?

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Work left to right: first do 101223 \frac{10}{12} - \frac{2}{3} , then subtract 16 \frac{1}{6} from that result. One step at a time!

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