Fractions in Real-World Applications: Understanding 1 1/4 x 1 3/8
In mathematics, fractions are an essential concept that helps us understand proportions and ratios. However, many people struggle to apply fractions to real-world scenarios. In this article, we will delve into the world of fractions and explore the calculation of 1 1/4 x 1 3/8.
What are Mixed Numbers?
Before we dive into the calculation, it's essential to understand mixed numbers. A mixed number is a combination of a whole number and a fraction. For example, 1 1/4 is a mixed number, where 1 is the whole number and 1/4 is the fraction.
Multiplying Mixed Numbers
Now that we have a basic understanding of mixed numbers, let's move on to multiplying them. When multiplying mixed numbers, we need to follow the order of operations (PEMDAS) and convert the mixed numbers into improper fractions.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and then add the numerator.
- 1 1/4 = (1 * 4) + 1 = 5/4
- 1 3/8 = (1 * 8) + 3 = 11/8
Multiplying Improper Fractions
Now that we have converted the mixed numbers to improper fractions, we can multiply them together.
- 5/4 x 11/8 = (5 * 11) / (4 * 8) = 55/32
Simplifying the Answer
Our final answer is 55/32. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
- GCD of 55 and 32 is 1, so the simplified answer remains 55/32.
Real-World Applications
Now that we have calculated the product of 1 1/4 x 1 3/8, let's explore a real-world application of this calculation. Imagine you're a carpenter working on a construction project. You need to cut a piece of wood that is 1 1/4 inches thick and 1 3/8 inches wide. To find the area of the wood, you need to multiply the length and width. Using our calculation, we can find the area of the wood, which is approximately 55/32 square inches.
Conclusion
In conclusion, multiplying mixed numbers may seem daunting, but it's a crucial skill to master. By converting mixed numbers to improper fractions and following the order of operations, we can simplify complex calculations and apply them to real-world scenarios. Whether you're a student or a professional, understanding fractions and mixed numbers is essential for problem-solving and critical thinking.
