Solve the Fraction Subtraction: 5/6 minus 7/12

Fraction Subtraction with Different Denominators

Solve the following exercise:

56712=? \frac{5}{6}-\frac{7}{12}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Multiply by 2 to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:16 Calculate the multiplications
00:23 Subtract with the common denominator
00:27 Calculate the numerator
00:31 Reduce the fraction as much as possible
00:35 Make sure to divide both numerator and denominator
00:41 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

56712=? \frac{5}{6}-\frac{7}{12}=\text{?}

2

Step-by-step solution

To solve the subtraction 56712\frac{5}{6} - \frac{7}{12}, we need a common denominator.

Step 1: Find the least common denominator (LCD) of the two fractions.
The denominators are 6 and 12. The least common multiple of 6 and 12 is 12.

Step 2: Convert 56\frac{5}{6} to an equivalent fraction with a denominator of 12.
We can multiply the numerator and the denominator by 2 to achieve this:
56=5×26×2=1012\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}.

Step 3: Now, subtract the fractions with a common denominator:
1012712=10712=312\frac{10}{12} - \frac{7}{12} = \frac{10 - 7}{12} = \frac{3}{12}.

Step 4: Simplify the result.
312\frac{3}{12} can be simplified by dividing both the numerator and the denominator by 3:
312=3÷312÷3=14\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}.

Therefore, the solution to the problem 56712\frac{5}{6} - \frac{7}{12} is 14\boxed{\frac{1}{4}}.

From the available choices, option 4, which is 14\frac{1}{4}, is the correct answer.

3

Final Answer

14 \frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find common denominator before subtracting fractions
  • Technique: Convert 56 \frac{5}{6} to 1012 \frac{10}{12} by multiplying by 2
  • Check: Simplify 312 \frac{3}{12} to 14 \frac{1}{4} by dividing by 3 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting numerators and denominators separately
    Don't subtract 56712 \frac{5}{6} - \frac{7}{12} as 57612=26 \frac{5-7}{6-12} = \frac{-2}{-6} ! This ignores the fundamental rule that fractions need common denominators. Always find the LCD first, then subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{3}{2}-\frac{1}{2}=\text{?} \)

FAQ

Everything you need to know about this question

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

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Fractions represent parts of a whole. You can't combine parts unless they're the same size! 56 \frac{5}{6} means 5 sixths, while 712 \frac{7}{12} means 7 twelfths - different sized pieces.

How do I find the LCD of 6 and 12?

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List the multiples: 6: 6, 12, 18... and 12: 12, 24, 36... The smallest common multiple is 12. Since 12 is already a multiple of 6, the LCD is 12!

What if I forget to simplify my answer?

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Your answer isn't wrong, just not in simplest form. 312 \frac{3}{12} equals 14 \frac{1}{4} , but teachers usually want the simplified version. Always check if you can divide both parts by the same number.

Can the LCD ever be smaller than both denominators?

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No! The LCD must be divisible by both original denominators, so it's always at least as large as the bigger denominator. In our case, LCD = 12, which equals the larger denominator.

What if my final answer is negative?

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That's totally normal! If you're subtracting a larger fraction from a smaller one, you'll get a negative result. Just follow the same steps and keep the negative sign in your final answer.

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