A Strip Of Wood 66 Inches Long Is To Be Cut Into $5\frac{1}{2}$-inch Pieces. How Many Pieces Can Be Cut?A) 14 B) 33 C) 12 D) 30

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Introduction

When it comes to cutting a strip of wood into smaller pieces, it's essential to consider the length of the strip and the size of the pieces we want to cut. In this problem, we have a strip of wood that is 66 inches long, and we want to cut it into pieces that are $5\frac{1}{2}$ inches long. The question is, how many pieces can we cut from this strip of wood?

Understanding the Problem

To solve this problem, we need to understand the concept of division and how it applies to cutting a strip of wood into smaller pieces. Division is a mathematical operation that involves splitting a quantity into equal parts. In this case, we want to divide the 66-inch strip of wood into pieces that are $5\frac{1}{2}$ inches long.

Calculating the Number of Pieces

To calculate the number of pieces we can cut, we need to divide the length of the strip (66 inches) by the length of each piece ($5\frac{1}{2}$ inches). We can start by converting the mixed number $5\frac{1}{2}$ to an improper fraction. To do this, we multiply the whole number part (5) by the denominator (2), and then add the numerator (1). This gives us:

512=(5×2)+12=10+12=1125\frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}

Now that we have the length of each piece as an improper fraction, we can divide the length of the strip (66 inches) by the length of each piece ($\frac{11}{2}$ inches). To do this, we can multiply the numerator (66) by the reciprocal of the denominator ($\frac{2}{11}$). This gives us:

66112=66×211=66×211=13211\frac{66}{\frac{11}{2}} = 66 \times \frac{2}{11} = \frac{66 \times 2}{11} = \frac{132}{11}

Simplifying the Result

To simplify the result, we can divide the numerator (132) by the denominator (11). This gives us:

13211=12\frac{132}{11} = 12

Conclusion

Therefore, we can cut 12 pieces from the 66-inch strip of wood, each piece being $5\frac{1}{2}$ inches long.

Answer

The correct answer is C) 12.

Discussion

This problem requires a basic understanding of division and how it applies to cutting a strip of wood into smaller pieces. It also requires the ability to convert a mixed number to an improper fraction and to simplify the result of a division operation. The problem is a good example of how division can be used to solve real-world problems, such as cutting a strip of wood into smaller pieces.

Additional Examples

Here are a few additional examples of how division can be used to solve real-world problems:

  • A bakery has 18 dozen donuts to package. If each box can hold 6 donuts, how many boxes can the bakery fill?
  • A farmer has 24 acres of land to plant with wheat. If each acre can be planted with 4 rows of wheat, how many rows of wheat can the farmer plant?
  • A carpenter has 36 feet of lumber to cut into pieces that are 2 feet long. How many pieces can the carpenter cut?

These examples demonstrate how division can be used to solve a variety of real-world problems, from packaging donuts to planting wheat to cutting lumber.

Conclusion

In conclusion, the problem of cutting a strip of wood into $5\frac{1}{2}$-inch pieces is a classic example of how division can be used to solve real-world problems. By understanding the concept of division and how it applies to cutting a strip of wood into smaller pieces, we can solve this problem and many others like it.

Q&A

Q: What is the length of the strip of wood?

A: The length of the strip of wood is 66 inches.

Q: What is the length of each piece that we want to cut?

A: The length of each piece is $5\frac{1}{2}$ inches.

Q: How do we convert the mixed number $5\frac{1}{2}$ to an improper fraction?

A: To convert the mixed number $5\frac{1}{2}$ to an improper fraction, we multiply the whole number part (5) by the denominator (2), and then add the numerator (1). This gives us:

512=(5×2)+12=10+12=1125\frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}

Q: How do we divide the length of the strip (66 inches) by the length of each piece ($\frac{11}{2}$ inches)?

A: To divide the length of the strip (66 inches) by the length of each piece ($\frac{11}{2}$ inches), we can multiply the numerator (66) by the reciprocal of the denominator ($\frac{2}{11}$). This gives us:

66112=66×211=66×211=13211\frac{66}{\frac{11}{2}} = 66 \times \frac{2}{11} = \frac{66 \times 2}{11} = \frac{132}{11}

Q: How do we simplify the result of the division operation?

A: To simplify the result of the division operation, we can divide the numerator (132) by the denominator (11). This gives us:

13211=12\frac{132}{11} = 12

Q: How many pieces can we cut from the 66-inch strip of wood?

A: We can cut 12 pieces from the 66-inch strip of wood, each piece being $5\frac{1}{2}$ inches long.

Q: What is the correct answer to the problem?

A: The correct answer is C) 12.

Q: What is the main concept that we used to solve this problem?

A: The main concept that we used to solve this problem is division.

Q: What are some real-world examples of how division can be used to solve problems?

A: Some real-world examples of how division can be used to solve problems include:

  • A bakery has 18 dozen donuts to package. If each box can hold 6 donuts, how many boxes can the bakery fill?
  • A farmer has 24 acres of land to plant with wheat. If each acre can be planted with 4 rows of wheat, how many rows of wheat can the farmer plant?
  • A carpenter has 36 feet of lumber to cut into pieces that are 2 feet long. How many pieces can the carpenter cut?

Q: Why is it important to understand division and how it applies to real-world problems?

A: It is essential to understand division and how it applies to real-world problems because it allows us to solve a variety of problems that involve splitting a quantity into equal parts. This is a fundamental concept in mathematics and is used in many different areas of life.

Q: What are some tips for solving division problems?

A: Some tips for solving division problems include:

  • Make sure to read the problem carefully and understand what is being asked.
  • Convert mixed numbers to improper fractions if necessary.
  • Use the reciprocal of the denominator to divide the numerator.
  • Simplify the result of the division operation.
  • Check your answer to make sure it is reasonable.

Q: What are some common mistakes to avoid when solving division problems?

A: Some common mistakes to avoid when solving division problems include:

  • Not reading the problem carefully and understanding what is being asked.
  • Not converting mixed numbers to improper fractions if necessary.
  • Not using the reciprocal of the denominator to divide the numerator.
  • Not simplifying the result of the division operation.
  • Not checking your answer to make sure it is reasonable.

Q: How can we practice solving division problems?

A: We can practice solving division problems by working on a variety of problems that involve dividing a quantity into equal parts. We can also use online resources and practice tests to help us prepare for division problems.