Perform The Indicated Operation.$\[ 1 \frac{1}{6} \div 3 \frac{3}{4} \\]The Answer Is \[$\square\$\].(Simplify Your Answer. Type An Integer, Proper Fraction, Or Mixed Number.)

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Understanding Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction. It is written in the form of a whole number followed by a fraction. For example, 3 1/2 is a mixed number that represents 3 whole units and 1/2 of a unit. In this article, we will learn how to perform operations with mixed numbers, specifically division.

Division of Mixed Numbers

To divide mixed numbers, we need to follow a specific procedure. The procedure involves converting the mixed numbers to improper fractions, performing the division, and then converting the result back to a mixed number.

Step 1: Convert Mixed Numbers to Improper Fractions

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

For example, to convert 1 1/6 to an improper fraction, we multiply 1 by 6 and add 1, which gives us 7/6.

Similarly, to convert 3 3/4 to an improper fraction, we multiply 3 by 4 and add 3, which gives us 15/4.

Step 2: Perform the Division

Now that we have converted the mixed numbers to improper fractions, we can perform the division.

To divide 7/6 by 15/4, we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 15/4 is 4/15.

So, we multiply 7/6 by 4/15, which gives us (7 × 4) / (6 × 15) = 28/90.

Step 3: Simplify the Result

To simplify the result, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 28 and 90 is 2. So, we divide both the numerator and the denominator by 2, which gives us 14/45.

Step 4: Convert the Result to a Mixed Number

To convert the improper fraction 14/45 to a mixed number, we divide the numerator by the denominator.

14 ÷ 45 = 0 with a remainder of 14. So, we can write the result as 0 14/45.

Conclusion

In this article, we learned how to perform operations with mixed numbers, specifically division. We followed a step-by-step procedure to convert the mixed numbers to improper fractions, perform the division, simplify the result, and convert the result back to a mixed number.

Example Problems

Here are some example problems to practice what we learned:

  • 2 3/4 ÷ 1 1/2 =
  • 5 1/3 ÷ 2 2/5 =
  • 3 3/4 ÷ 1 1/6 =

Practice Exercises

Try solving the following problems on your own:

  • 1 1/2 ÷ 3 1/4 =
  • 2 2/3 ÷ 1 1/2 =
  • 4 1/2 ÷ 2 3/4 =

Answer Key

Here are the answers to the example problems:

  • 2 3/4 ÷ 1 1/2 = 1 3/8
  • 5 1/3 ÷ 2 2/5 = 1 1/6
  • 3 3/4 ÷ 1 1/6 = 2 1/4

Tips and Tricks

Here are some tips and tricks to help you perform operations with mixed numbers:

  • Always convert mixed numbers to improper fractions before performing operations.
  • Use the reciprocal of the second fraction to perform division.
  • Simplify the result by dividing both the numerator and the denominator by their GCD.
  • Convert the result back to a mixed number by dividing the numerator by the denominator.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a proper fraction. It is written in the form of a whole number followed by a fraction. For example, 3 1/2 is a mixed number that represents 3 whole units and 1/2 of a unit.

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

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

For example, to convert 1 1/6 to an improper fraction, you multiply 1 by 6 and add 1, which gives you 7/6.

Q: How do I perform division with mixed numbers?

A: To perform division with mixed numbers, you need to follow a specific procedure. The procedure involves converting the mixed numbers to improper fractions, performing the division, and then converting the result back to a mixed number.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 3/4 is 4/3.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

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

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator. The result is the whole number part, and the remainder is the new numerator.

For example, to convert 14/5 to a mixed number, you divide 14 by 5, which gives you 2 with a remainder of 4. So, the mixed number is 2 4/5.

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

A: Some common mistakes to avoid when working with mixed numbers include:

  • Not converting mixed numbers to improper fractions before performing operations
  • Not using the reciprocal of the second fraction when performing division
  • Not simplifying the result by dividing both the numerator and the denominator by their GCD
  • Not converting the result back to a mixed number when necessary

Q: How can I practice working with mixed numbers?

A: You can practice working with mixed numbers by trying out example problems and exercises. You can also use online resources and worksheets to help you practice.

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

A: Mixed numbers have many real-world applications, including:

  • Measuring lengths and distances
  • Calculating areas and volumes
  • Working with fractions in cooking and recipes
  • Understanding time and schedules

By practicing and mastering the concepts of mixed numbers, you can become proficient in performing operations with fractions and improve your problem-solving skills.