Carla Made Fancy Green Costume Decorations For Each Of The 4 Dancers In Her Year-end Dance Performance. She Cut 2 2/3 Yards Of Ribbon Into Equal Pieces To Make The Decorations. How Long Was Each Piece Of Ribbon? Write Your Answer As A Fraction Or As A

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Solving the Mystery of the Fancy Green Costume Decorations

In the world of mathematics, problems often arise in the most unexpected ways. For Carla, a year-end dance performance is a time to shine, and she wants to make it extra special with fancy green costume decorations. However, she faces a challenge when cutting 2 2/3 yards of ribbon into equal pieces for each of the 4 dancers. In this article, we will delve into the world of fractions and division to find out how long each piece of ribbon will be.

Carla has 2 2/3 yards of ribbon, which she wants to cut into equal pieces for each of the 4 dancers. To solve this problem, we need to convert the mixed number 2 2/3 into an improper fraction. An improper fraction is a fraction where the numerator is greater than the denominator.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. In this case, we have:

2 2/3 = (2 × 3) + 2/3 = 6 + 2/3 = 20/3

So, Carla has 20/3 yards of ribbon.

Dividing the Ribbon into Equal Pieces

Now that we have the improper fraction, we can divide it by 4 to find out how long each piece of ribbon will be. To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number. In this case, we have:

(20/3) ÷ 4 = (20/3) × (1/4) = 20/12 = 5/3

So, each piece of ribbon will be 5/3 yards long.

In conclusion, Carla's fancy green costume decorations will have 5/3 yards of ribbon each. This problem may seem simple, but it requires a good understanding of fractions and division. By converting the mixed number to an improper fraction and dividing it by 4, we were able to find the solution to the problem.

This problem may seem like a simple math exercise, but it has real-world applications. In the world of fashion, designers often need to calculate the amount of fabric needed for a garment. By understanding fractions and division, designers can ensure that they have the right amount of fabric for their designs.

  • When converting mixed numbers to improper fractions, remember to multiply the whole number by the denominator and add the numerator.
  • When dividing a fraction by a whole number, multiply the fraction by the reciprocal of the whole number.
  • Practice, practice, practice! The more you practice solving problems like this, the more comfortable you will become with fractions and division.
  • When converting mixed numbers to improper fractions, make sure to multiply the whole number by the denominator and add the numerator.
  • When dividing a fraction by a whole number, make sure to multiply the fraction by the reciprocal of the whole number.
  • Don't forget to simplify the fraction after dividing it by a whole number.

In conclusion, solving mystery of the fancy green costume decorations requires a good understanding of fractions and division. By converting the mixed number to an improper fraction and dividing it by 4, we were able to find the solution to the problem. This problem may seem simple, but it has real-world applications and requires practice to become proficient.
Frequently Asked Questions (FAQs) about Solving the Mystery of the Fancy Green Costume Decorations

A: The main concept behind solving the mystery of the fancy green costume decorations is to convert the mixed number 2 2/3 into an improper fraction and then divide it by 4 to find out how long each piece of ribbon will be.

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. In this case, we have:

2 2/3 = (2 × 3) + 2/3 = 6 + 2/3 = 20/3

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 the denominator.

A: To divide a fraction by a whole number, you multiply the fraction by the reciprocal of the whole number. In this case, we have:

(20/3) ÷ 4 = (20/3) × (1/4) = 20/12 = 5/3

A: The reciprocal of a whole number is 1 divided by that number. For example, the reciprocal of 4 is 1/4.

A: Yes, you can simplify the fraction after dividing it by a whole number. In this case, we have:

(20/3) ÷ 4 = (20/3) × (1/4) = 20/12 = 5/3

You can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

A: You can find the GCD of two numbers by listing the factors of each number and finding the largest factor that they have in common.

A: Yes, you can use a calculator to solve this problem. However, it's always a good idea to understand the concept behind the problem and to check your answer with a calculator.

A: This problem has real-world applications in the world of fashion, where designers need to calculate the amount of fabric needed for a garment. It also has applications in other fields, such as architecture and engineering.

A: Yes, you can use problem as a teaching tool to help students understand fractions and division. You can modify the problem to make it more challenging or to fit the needs of your students.

A: Some common mistakes that students make when solving this problem include:

  • Not converting the mixed number to an improper fraction
  • Not dividing the fraction by the whole number
  • Not simplifying the fraction after dividing it by a whole number
  • Not checking their answer with a calculator

A: You can help your students overcome these common mistakes by providing clear instructions and examples, by encouraging them to check their work, and by providing feedback and support.