Calculating the Total Amount of Wood Needed

Oct 13, 2025 by talynt.org 65 views

Introduction

Building a sandbox can be a fun and rewarding project, but it also requires careful planning and measurement. In this article, we will explore a math problem related to building a sandbox, where Marco needs to cut wood to specific lengths to create a sandbox for his little brother.

The Problem

Marco needs to cut 2 pieces of wood that are 6 feet long each and 2 pieces of wood that are $$4 \frac{1}{5}$$ feet long each. He also has 4 pieces of wood that are 7 feet long each. The question is, how much wood will be left after Marco cuts the wood to the required lengths?

Calculating the Total Amount of Wood Needed

To calculate the total amount of wood needed, we need to add up the lengths of the wood that Marco needs to cut. We can start by converting the mixed number $$4 \frac{1}{5}$$ to an improper fraction.

4 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5}

Now, we can add up the lengths of the wood:

2 \times 6 + 2 \times \frac{21}{5} = 12 + \frac{42}{5}

To add these two fractions, we need to find a common denominator, which is 5 in this case. We can rewrite the whole number 12 as a fraction with a denominator of 5:

12 = \frac{12 \times 5}{5} = \frac{60}{5}

Now, we can add the two fractions:

\frac{60}{5} + \frac{42}{5} = \frac{102}{5}

So, the total amount of wood needed is $$\frac{102}{5}$$ feet.

Calculating the Total Amount of Wood Available

Marco has 4 pieces of wood that are 7 feet long each. To calculate the total amount of wood available, we can multiply the length of each piece by the number of pieces:

4 \times 7 = 28

So, the total amount of wood available is 28 feet.

Calculating the Amount of Wood Left

To calculate the amount of wood left, we need to subtract the total amount of wood needed from the total amount of wood available:

28 - \frac{102}{5}

To subtract a fraction from a whole number, we need to convert the whole number to a fraction with the same denominator. In this case, we can rewrite 28 as a fraction with a denominator of 5:

28 = \frac{28 \times 5}{5} = \frac{140}{5}

Now, we can subtract the two fractions:

\frac{140}{5} - \frac{102}{5} = \frac{38}{5}

So, the amount of wood left is $$\frac{38}{5}$$ feet.

Conclusion

In this article, we explored a math problem related to building a sandbox. We calculated the total amount of wood needed and the total amount of wood available, and then subtracted the two amounts to find the amount of wood left. The result is $$\frac{38}{5}$$ feet of wood left.

Final Answer

The final answer is $$\frac{38}{5}$$ feet.

Additional Information

To convert a mixed number to an improper fraction, we can multiply the whole number by the denominator and add the numerator.
To add fractions with different denominators, we need to find a common denominator.
To subtract a fraction from a whole number, we need to convert the whole number to a fraction with the same denominator.

References

Glossary

Improper Fraction: A fraction where the numerator is greater than or equal to the denominator.
Common Denominator: A denominator that is common to two or more fractions.
Mixed Number: A number that is a combination of a whole number and a fraction.
Q&A: Building a Sandbox - A Math Problem =============================================

Introduction

In our previous article, we explored a math problem related to building a sandbox. We calculated the total amount of wood needed and the total amount of wood available, and then subtracted the two amounts to find the amount of wood left. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the total amount of wood needed to build the sandbox?

A: The total amount of wood needed is $$\frac{102}{5}$$ feet.

Q: How much wood does Marco have available to build the sandbox?

A: Marco has 4 pieces of wood that are 7 feet long each, for a total of 28 feet.

Q: How much wood will be left after Marco cuts the wood to the required lengths?

A: The amount of wood left is $$\frac{38}{5}$$ feet.

Q: Why do we need to convert the mixed number $$4 \frac{1}{5}$$ to an improper fraction?

A: We need to convert the mixed number to an improper fraction because it is easier to add and subtract fractions with the same denominator.

Q: How do we add fractions with different denominators?

A: To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 5.

Q: How do we subtract a fraction from a whole number?

A: To subtract a fraction from a whole number, we need to convert the whole number to a fraction with the same denominator.

Q: What is the final answer to the problem?

A: The final answer is $$\frac{38}{5}$$ feet.

Q: What are some related topics to this problem?

A: Some related topics to this problem include fractions, decimals, and mathematical operations.

Q: Where can I find more information on this topic?

A: You can find more information on this topic at Math Open Reference and Khan Academy.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: What is a common denominator?

A: A common denominator is a denominator that is common to two or more fractions.

Q: What is a mixed number?

A: A mixed number is a number that is a combination of a whole number and a fraction.

Conclusion

In this article, we answered some frequently asked questions related to the math problem of building a sandbox. We hope that this article has been helpful in understanding the problem and its solution.

Glossary

Improper Fraction: A fraction where the numerator is greater than or equal to the denominator.
Common Denominator: A denominator that is common to two or more fractions.
Mixed Number: A number that is a combination of a whole number and a fraction.
Fractions: A way of expressing a part of a whole.
Decimals: A way of expressing a part of a whole using a decimal point.
Mathematical Operations: The basic operations of arithmetic, including addition, subtraction, multiplication, and division.