Fraction Operations: Understanding 5 1/2 x 4 3/4
In mathematics, fractions are an essential concept that can be challenging to grasp, especially when it comes to operations like multiplication. In this article, we will explore the calculation of 5 1/2 x 4 3/4, breaking it down step by step to ensure a clear understanding of the process.
What are Mixed Numbers?
Before diving into the calculation, it's essential to understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 5 1/2 is a mixed number, where 5 is the whole number and 1/2 is the fraction.
Converting Mixed Numbers to Improper Fractions
To multiply mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator (the top number) is greater than the denominator (the bottom number).
Let's convert our mixed numbers:
- 5 1/2 = 11/2 (convert 5 to 10/2 and add 1/2)
- 4 3/4 = 19/4 (convert 4 to 16/4 and add 3/4)
Multiplying Fractions
Now that we have our improper fractions, we can multiply them:
- 11/2 × 19/4 = ?
To multiply fractions, we multiply the numerators (11 and 19) and multiply the denominators (2 and 4). Then, we simplify the fraction:
- Numerators: 11 × 19 = 209
- Denominators: 2 × 4 = 8
- Result: 209/8
The Final Answer
So, 5 1/2 x 4 3/4 = 209/8. This is an improper fraction, and we can convert it back to a mixed number if needed.
By following these steps, you should now have a better understanding of how to multiply mixed numbers. Remember to convert them to improper fractions, multiply the numerators and denominators, and simplify the result.
