Subtract. Write Your Answer As A Mixed Number In Simplest Form.${ 5 \frac{1}{6} - 1 \frac{5}{6} }$

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Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number part, and b/c is the fractional part. For example, 3 1/2 is a mixed number that represents 3 whole units and 1/2 of a unit.

Subtracting Mixed Numbers

To subtract mixed numbers, we need to follow a step-by-step process. The process involves converting the mixed numbers to improper fractions, subtracting the fractions, and then converting the result back to a mixed number.

Step 1: Convert the Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For the given problem, we have:

516−156{ 5 \frac{1}{6} - 1 \frac{5}{6} }

We will convert both mixed numbers to improper fractions:

516=(5×6)+16=30+16=316{ 5 \frac{1}{6} = \frac{(5 \times 6) + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6} }

156=(1×6)+56=6+56=116{ 1 \frac{5}{6} = \frac{(1 \times 6) + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6} }

Step 2: Subtract the Fractions

Now that we have both mixed numbers in improper fraction form, we can subtract them:

316−116=31−116=206{ \frac{31}{6} - \frac{11}{6} = \frac{31 - 11}{6} = \frac{20}{6} }

Step 3: Simplify the Result

The result of the subtraction is an improper fraction. To simplify it, we can divide the numerator by the denominator:

206=326{ \frac{20}{6} = 3 \frac{2}{6} }

We can further simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

326=313{ 3 \frac{2}{6} = 3 \frac{1}{3} }

Conclusion

To subtract mixed numbers, we need to convert them to improper fractions, subtract the fractions, and then convert the result back to a mixed number. In this problem, we subtracted 5 1/6 and 1 5/6 and obtained the result 3 1/3.

Tips and Tricks

  • When subtracting mixed numbers, make sure to convert them to improper fractions first.
  • When subtracting fractions, make sure to have the same denominator.
  • When simplifying the result, make sure to divide both the numerator and the denominator by their greatest common divisor.

Practice Problems

  • Subtract 2 3/4 and 1 1/4.
  • Subtract 4 2/3 and 2 1/3.
  • Subtract 3 5/6 and 2 3/6.

Real-World Applications

Subtracting mixed numbers is an essential skill in real-world applications, such as:

  • Cooking: When measuring ingredients, you may need to subtract mixed numbers to get the correct amount.
  • Building: When measuring materials, you may need to subtract mixed numbers to get the correct amount.
  • Finance: When calculating interest rates, you may need to subtract mixed numbers to get the correct amount.

Conclusion

Subtracting mixed numbers is a fundamental skill in mathematics that requires attention to detail and a step-by-step approach. By following the steps outlined in this article, you can master the skill of subtracting mixed numbers and apply it to real-world applications.

Frequently Asked Questions

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. The result is the new numerator, and the denominator remains the same.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, convert them to improper fractions, subtract the fractions, and then convert the result back to a mixed number.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide the numerator and the denominator by their greatest common divisor.

Q: What is the difference between subtracting fractions and subtracting mixed numbers?

A: Subtracting fractions involves subtracting the numerators and keeping the same denominator, while subtracting mixed numbers involves converting the mixed numbers to improper fractions, subtracting the fractions, and then converting the result back to a mixed number.

Q: Can I subtract a mixed number from a whole number?

A: Yes, you can subtract a mixed number from a whole number by converting the mixed number to an improper fraction and then subtracting the fractions.

Q: Can I subtract a mixed number from a fraction?

A: Yes, you can subtract a mixed number from a fraction by converting the mixed number to an improper fraction and then subtracting the fractions.

Q: What are some real-world applications of subtracting mixed numbers?

A: Subtracting mixed numbers is used in various real-world applications, such as cooking, building, and finance.

Q: How do I practice subtracting mixed numbers?

A: You can practice subtracting mixed numbers by using online resources, worksheets, or by working on real-world problems.

Q: What are some common mistakes to avoid when subtracting mixed numbers?

A: Some common mistakes to avoid when subtracting mixed numbers include:

  • Not converting the mixed numbers to improper fractions
  • Not having the same denominator
  • Not simplifying the result
  • Not dividing both the numerator and the denominator by their greatest common divisor

Additional Resources

  • Online resources: Khan Academy, Mathway, and IXL
  • Worksheets: available on websites such as Math Drills and Math Goodies
  • Real-world problems: use everyday situations to practice subtracting mixed numbers

Conclusion

Subtracting mixed numbers is a fundamental skill in mathematics that requires attention to detail and a step-by-step approach. By following the steps outlined in this article and practicing with real-world problems, you can master the skill of subtracting mixed numbers and apply it to various real-world applications.