Simplify: \[$\frac{11}{12} - \frac{5}{6}\$\]Enter Your Answer As A Fraction In Simplest Form. Example Answer: 2/7

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Understanding the Problem

To simplify the given expression, we need to find a common denominator for the two fractions and then subtract the second fraction from the first. The common denominator for 12 and 6 is 12, as 6 is a factor of 12.

Finding the Common Denominator

The common denominator for the two fractions is 12. To make the denominator of the second fraction equal to 12, we can multiply both the numerator and the denominator by 2.

Simplifying the Expression

Now that we have a common denominator, we can subtract the second fraction from the first.

1112−56=1112−5×26×2=1112−1012\frac{11}{12} - \frac{5}{6} = \frac{11}{12} - \frac{5 \times 2}{6 \times 2} = \frac{11}{12} - \frac{10}{12}

Subtracting the Fractions

Now that the fractions have the same denominator, we can subtract the numerators.

1112−1012=11−1012=112\frac{11}{12} - \frac{10}{12} = \frac{11 - 10}{12} = \frac{1}{12}

Conclusion

The simplified expression is 112\frac{1}{12}.

Example Use Case

This problem can be used to demonstrate the concept of finding a common denominator and subtracting fractions with different denominators.

Step-by-Step Solution

  1. Find the common denominator for the two fractions.
  2. Make the denominator of the second fraction equal to the common denominator.
  3. Subtract the second fraction from the first.
  4. Simplify the resulting fraction.

Common Mistakes

  • Not finding the common denominator before subtracting the fractions.
  • Not making the denominator of the second fraction equal to the common denominator.
  • Not simplifying the resulting fraction.

Real-World Applications

This problem can be used to demonstrate the concept of finding a common denominator and subtracting fractions with different denominators in real-world applications such as finance, science, and engineering.

Additional Resources

For more practice problems and examples, see the following resources:

  • Khan Academy: Subtracting Fractions with Different Denominators
  • Mathway: Subtracting Fractions with Different Denominators
  • IXL: Subtracting Fractions with Different Denominators

Conclusion

In conclusion, simplifying the expression 1112−56\frac{11}{12} - \frac{5}{6} requires finding a common denominator, making the denominator of the second fraction equal to the common denominator, subtracting the second fraction from the first, and simplifying the resulting fraction. The simplified expression is 112\frac{1}{12}.

Frequently Asked Questions

Q: What is the common denominator for 12 and 6?

A: The common denominator for 12 and 6 is 12, as 6 is a factor of 12.

Q: Why do we need to find a common denominator?

A: We need to find a common denominator to be able to subtract the two fractions. If the fractions have different denominators, we cannot subtract them directly.

Q: How do we make the denominator of the second fraction equal to the common denominator?

A: To make the denominator of the second fraction equal to the common denominator, we can multiply both the numerator and the denominator by the necessary factor. In this case, we multiplied the numerator and denominator of the second fraction by 2.

Q: What is the simplified expression?

A: The simplified expression is 112\frac{1}{12}.

Q: Can we simplify the expression further?

A: No, the expression 112\frac{1}{12} is already in its simplest form.

Q: What is the difference between subtracting fractions with the same denominator and subtracting fractions with different denominators?

A: When subtracting fractions with the same denominator, we can simply subtract the numerators. However, when subtracting fractions with different denominators, we need to find a common denominator and then subtract the fractions.

Q: How do we know if the expression is in its simplest form?

A: To determine if the expression is in its simplest form, we need to check if the numerator and denominator have any common factors. If they do, we can simplify the expression further.

Q: What are some real-world applications of subtracting fractions with different denominators?

A: Some real-world applications of subtracting fractions with different denominators include finance, science, and engineering. For example, in finance, we may need to subtract fractions to calculate interest rates or investment returns. In science, we may need to subtract fractions to calculate concentrations or rates of reaction.

Q: Where can I find more practice problems and examples?

A: You can find more practice problems and examples on websites such as Khan Academy, Mathway, and IXL.

Additional Tips and Tricks

  • Always find the common denominator before subtracting fractions with different denominators.
  • Make sure to simplify the resulting fraction after subtracting the fractions.
  • Use a calculator or online tool to check your work and ensure that the expression is in its simplest form.

Conclusion

In conclusion, simplifying the expression 1112−56\frac{11}{12} - \frac{5}{6} requires finding a common denominator, making the denominator of the second fraction equal to the common denominator, subtracting the second fraction from the first, and simplifying the resulting fraction. The simplified expression is 112\frac{1}{12}. We hope this Q&A article has helped you understand the concept of subtracting fractions with different denominators and provided you with additional resources and tips to help you succeed.