Fractions in Measurements: Understanding 4 1/4 x 2 3/8 x 8 3/16
When working with measurements, it's not uncommon to encounter fractions. These can be confusing, especially when trying to perform calculations. In this article, we'll explore how to work with fractions in measurements, using the example of 4 1/4 x 2 3/8 x 8 3/16.
Breaking Down the Fractions
Let's start by breaking down each of the fractions in the equation:
- 4 1/4 = 4 and 1/4
- 2 3/8 = 2 and 3/8
- 8 3/16 = 8 and 3/16
To work with these fractions, we need to convert them to improper fractions.
Converting to Improper Fractions
An improper fraction is a fraction where the numerator (the top number) is greater than the denominator (the bottom number). To convert our mixed numbers to improper fractions, we'll follow these steps:
- 4 1/4 = (4 x 4) + 1 = 17/4
- 2 3/8 = (2 x 8) + 3 = 19/8
- 8 3/16 = (8 x 16) + 3 = 131/16
Now that we have our improper fractions, we can multiply them together.
Multiplying the Fractions
To multiply the fractions, we'll multiply the numerators (the top numbers) together and multiply the denominators (the bottom numbers) together.
- Numerators: 17 x 19 x 131 = 43,303
- Denominators: 4 x 8 x 16 = 512
Now, we can write our answer as an improper fraction:
43,303/512
Simplifying the Answer
To simplify our answer, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD is 1, so our answer remains the same:
43,303/512
Conclusion
Working with fractions in measurements can be challenging, but by breaking them down, converting them to improper fractions, and multiplying them together, we can arrive at the correct answer. In this case, our final answer is 43,303/512.
