Multiplying the Numerators

Oct 13, 2025 by leolavanderia.com.br 119 views

Understanding the Problem

A rectangular prism is a three-dimensional shape with length, width, and height. In this problem, we are given the dimensions of a rectangular prism in fractional form. The length is $\frac{3}{8}$ centimeter, the width is $\frac{5}{8}$ centimeter, and the height is $\frac{7}{8}$ centimeter. We need to calculate the volume of this rectangular prism.

What is Volume?

The volume of a rectangular prism is the amount of space inside the prism. It is calculated by multiplying the length, width, and height of the prism. The formula for the volume of a rectangular prism is:

Volume = Length × Width × Height

Calculating the Volume

To calculate the volume of the rectangular prism, we need to multiply the length, width, and height. We can do this by multiplying the fractions:

Volume = $\frac{3}{8}$ × $\frac{5}{8}$ × $\frac{7}{8}$

To multiply fractions, we need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). Then, we need to divide the product of the numerators by the product of the denominators.

Multiplying the Numerators

The product of the numerators is:

3 × 5 × 7 = 105

Multiplying the Denominators

The product of the denominators is:

8 × 8 × 8 = 512

Dividing the Product of the Numerators by the Product of the Denominators

Now, we need to divide the product of the numerators by the product of the denominators:

Volume = $\frac{105}{512}$

Simplifying the Fraction

The fraction $\frac{105}{512}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 105 and 512 is 1, so the fraction cannot be simplified further.

Conclusion

The volume of the rectangular prism is $\frac{105}{512}$ cubic centimeters. This is the amount of space inside the prism.

Real-World Applications

Calculating the volume of a rectangular prism has many real-world applications. For example, architects use volume calculations to determine the amount of materials needed for a building project. Engineers use volume calculations to determine the amount of fuel needed for a vehicle. In addition, volume calculations are used in many other fields, such as medicine, physics, and engineering.

Tips and Tricks

When calculating the volume of a rectangular prism, make sure to multiply the length, width, and height. Also, make sure to simplify the fraction if possible. Finally, remember that the volume of a rectangular prism is always positive, even if the dimensions are negative.

Practice Problems

A rectangular prism has a length of 2 centimeters, a width of 3 centimeters, and a height of 4 centimeters. What is the volume of the prism?
A rectangular prism has a length of $\frac{1}{2}$ centimeter, a width of $\frac{2}{3}$ centimeter, and a height of $\frac{3}{4}$ centimeter. What is the volume of the prism?
A rectangular prism has a length of 5 centimeters, a width of 6 centimeters, and a height of 7 centimeters. What is the volume of the prism?

Answer Key

24 cubic centimeters
$\frac{1}{24}$ cubic centimeters
210 cubic centimeters
Frequently Asked Questions (FAQs) about Calculating the Volume of a Rectangular Prism =====================================================================================

Q: What is the formula for calculating the volume of a rectangular prism?

A: The formula for calculating the volume of a rectangular prism is:

Volume = Length × Width × Height

Q: How do I calculate the volume of a rectangular prism with fractional dimensions?

A: To calculate the volume of a rectangular prism with fractional dimensions, you need to multiply the fractions. To multiply fractions, you need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). Then, you need to divide the product of the numerators by the product of the denominators.

Q: What is the greatest common divisor (GCD) and how do I use it to simplify a fraction?

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

Q: Can I simplify a fraction with a negative numerator or denominator?

A: Yes, you can simplify a fraction with a negative numerator or denominator. To simplify a fraction with a negative numerator or denominator, you need to follow the same steps as simplifying a fraction with positive numerators and denominators.

Q: How do I calculate the volume of a rectangular prism with decimal dimensions?

A: To calculate the volume of a rectangular prism with decimal dimensions, you need to multiply the decimals. To multiply decimals, you need to multiply the numbers as if they were whole numbers, and then count the number of decimal places in the product. Finally, you need to place the decimal point in the product at the correct position.

Q: Can I use a calculator to calculate the volume of a rectangular prism?

A: Yes, you can use a calculator to calculate the volume of a rectangular prism. However, make sure to enter the dimensions correctly and follow the order of operations (PEMDAS).

Q: What are some real-world applications of calculating the volume of a rectangular prism?

A: Calculating the volume of a rectangular prism has many real-world applications, such as:

Determining the amount of materials needed for a building project
Calculating the amount of fuel needed for a vehicle
Determining the volume of a container or tank
Calculating the volume of a rectangular prism in a scientific experiment

Q: What are some tips and tricks for calculating the volume of a rectangular prism?

A: Here are some tips and tricks for calculating the volume of a rectangular prism:

Make sure to multiply the length, width, and height
Simplify the fraction if possible
Remember that the volume of a rectangular prism is always positive, even if the dimensions are negative
Use a calculator to check your work
Practice, practice, practice!

Q: What are some common mistakes to avoid when calculating the volume of a rectangular prism?

A: Here are some common mistakes to avoid when calculating the volume of a rectangular prism:

Forgetting to multiply the length, width, and height
Not simplifying the fraction if possible
Not remembering that the volume of a rectangular prism is always positive, even if the dimensions are negative
Not using a calculator to check your work
Not practicing, practicing, practicing!

Q: How can I practice calculating the volume of a rectangular prism?

A: Here are some ways to practice calculating the volume of a rectangular prism:

Use online calculators or worksheets to practice calculating the volume of a rectangular prism
Use real-world examples, such as calculating the volume of a container or tank
Practice calculating the volume of a rectangular prism with different dimensions, such as fractional, decimal, and whole numbers
Use a calculator to check your work and see where you went wrong
Practice, practice, practice!