A Wooden Flooring Strip Is $20 \frac{1}{2}$ Inches Long. If You Cut Off $4 \frac{3}{4}$ Inches From One End, What Will Be The New Length Of The Strip In Inches?

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Understanding the Problem

To find the new length of the wooden flooring strip, we need to subtract the length that was cut off from the original length. However, we need to make sure that we are working with the same units. In this case, both lengths are given in inches, so we can proceed with the calculation.

Converting Mixed Numbers to Improper Fractions

Before we can perform the subtraction, we need to convert the mixed numbers to improper fractions. The original length of the strip is $20 \frac{1}{2}$ inches, which can be converted to an improper fraction as follows:

2012=(20×2)+12=40+12=41220 \frac{1}{2} = \frac{(20 \times 2) + 1}{2} = \frac{40 + 1}{2} = \frac{41}{2}

Similarly, the length that was cut off is $4 \frac{3}{4}$ inches, which can be converted to an improper fraction as follows:

434=(4×4)+34=16+34=1944 \frac{3}{4} = \frac{(4 \times 4) + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}

Subtracting the Lengths

Now that we have converted the mixed numbers to improper fractions, we can proceed with the subtraction. To subtract the lengths, we need to find a common denominator, which is 4 in this case. We can rewrite the original length as follows:

412=41×22×2=824\frac{41}{2} = \frac{41 \times 2}{2 \times 2} = \frac{82}{4}

Now we can subtract the lengths as follows:

824−194=82−194=634\frac{82}{4} - \frac{19}{4} = \frac{82 - 19}{4} = \frac{63}{4}

Converting the Result Back to a Mixed Number

To make the result more understandable, we can convert the improper fraction back to a mixed number. We can do this by dividing the numerator by the denominator:

634=1534\frac{63}{4} = 15 \frac{3}{4}

Conclusion

In conclusion, if you cut off $4 \frac{3}{4}$ inches from one end of a wooden flooring strip that is $20 \frac{1}{2}$ inches long, the new length of the strip will be $15 \frac{3}{4}$ inches.

Real-World Applications

This problem has real-world applications in various fields, such as carpentry and construction. When working with wooden flooring strips, it's essential to calculate the new length accurately to ensure that the strips fit together properly and that the flooring is installed correctly.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

  • Make sure to convert the mixed numbers to improper fractions before performing the subtraction.
  • Find a common denominator to ensure that the subtraction is accurate.
  • Convert the result back to a mixed number to make it more understandable.

Practice Problems

Here are some practice problems to help you reinforce your understanding of this concept:

  • A wooden flooring strip is $25 \frac{1}{3}$ inches long. If you cut off $6 \frac{2}{3}$ inches from one end, what will be the new length of the strip in inches?
  • A wooden flooring strip is $18 \frac{3}{4}$ inches long. If you cut off $3 \frac{1}{2}$ inches from one end, what will be the new length of the strip in inches?

Common Mistakes

Here are some common mistakes to avoid when solving this problem:

  • Failing to convert the mixed numbers to improper fractions before performing the subtraction.
  • Not finding a common denominator to ensure that the subtraction is accurate.
  • Not converting the result back to a mixed number to make it more understandable.

Conclusion

In conclusion, this problem requires you to subtract the length that was cut off from the original length of a wooden flooring strip. To solve this problem, you need to convert the mixed numbers to improper fractions, find a common denominator, and then perform the subtraction. By following these steps, you can accurately calculate the new length of the strip.

Q&A

Q: What is the original length of the wooden flooring strip?

A: The original length of the wooden flooring strip is $20 \frac{1}{2}$ inches.

Q: What is the length that was cut off from the strip?

A: The length that was cut off from the strip is $4 \frac{3}{4}$ inches.

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert $20 \frac{1}{2}$ to an improper fraction, you would multiply 20 by 2 and then add 1, resulting in $\frac{41}{2}$.

Q: How do I subtract two improper fractions?

A: To subtract two improper fractions, you need to find a common denominator. In this case, the common denominator is 4. You can rewrite the first improper fraction as $\frac{82}{4}$ and then subtract the second improper fraction, resulting in $\frac{63}{4}$.

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

A: To convert an improper fraction back to a mixed number, you need to divide the numerator by the denominator. For example, to convert $\frac{63}{4}$ back to a mixed number, you would divide 63 by 4, resulting in $15 \frac{3}{4}$.

Q: What is the new length of the strip after cutting off $4 \frac{3}{4}$ inches?

A: The new length of the strip after cutting off $4 \frac{3}{4}$ inches is $15 \frac{3}{4}$ inches.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as carpentry and construction. When working with wooden flooring strips, it's essential to calculate the new length accurately to ensure that the strips fit together properly and that the flooring is installed correctly.

Q: What are some tips and tricks to help me solve this problem?

A: Here are some tips and tricks to help you solve this problem:

  • Make sure to convert the mixed numbers to improper fractions before performing the subtraction.
  • Find a common denominator to ensure that the subtraction is accurate.
  • Convert the result back to a mixed number to make it more understandable.

Q: What are some common mistakes to avoid when solving this problem?

A: Here are some common mistakes to avoid when solving this problem:

  • Failing to convert the mixed numbers to improper fractions before performing the subtraction.
  • Not finding a common denominator to ensure that the subtraction is accurate.
  • Not converting the result back to a mixed number to make it more understandable.

Q: How can I practice solving this type of problem?

A: You can practice solving this type of problem by working through the practice problems provided earlier. You can also try creating your own problems and solving them to reinforce your understanding of the concept.

Q: What are some additional resources that I can use to learn more about this topic?

A: Here are some additional resources that you can use to learn more about this topic:

  • Online math tutorials and videos
  • Math textbooks and workbooks
  • Online math communities and forums
  • Math apps and software

Conclusion

In conclusion, this problem requires you to subtract the length that was cut off from the original length of a wooden flooring strip. To solve this problem, you need to convert the mixed numbers to improper fractions, find a common denominator, and then perform the subtraction. By following these steps, you can accurately calculate the new length of the strip.