59 1/2 x 25 5/8: Calculating Mixed Numbers and Fractions
In mathematics, mixed numbers and fractions are essential concepts that help us understand and work with numerical values. In this article, we will explore the calculation of 59 1/2 x 25 5/8, which involves multiplying a mixed number with a fraction.
Understanding Mixed Numbers and Fractions
Before we dive into the calculation, let's quickly review what mixed numbers and fractions are:
- Mixed Numbers: A mixed number is a combination of a whole number and a fraction. For example, 2 1/2 is a mixed number, where 2 is the whole number and 1/2 is the fraction.
- Fractions: A fraction is a way to express a part of a whole. For example, 1/2 is a fraction, where 1 is the numerator (top number) and 2 is the denominator (bottom number).
Converting Mixed Numbers to Improper Fractions
To perform calculations involving mixed numbers, it's often helpful to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.
Let's convert our mixed numbers to improper fractions:
- 59 1/2: To convert this mixed number to an improper fraction, we multiply the whole number (59) by the denominator (2) and add the numerator (1). This gives us: 59 x 2 + 1 = 119/2
- 25 5/8: Following the same process, we get: 25 x 8 + 5 = 205/8
Multiplying Fractions
Now that we have our improper fractions, we can multiply them:
119/2 x 205/8
To multiply fractions, we multiply the numerators (top numbers) and denominators (bottom numbers) separately:
- Numerators: 119 x 205 = 24,395
- Denominators: 2 x 8 = 16
So, our result is: 24,395/16
Simplifying the Result
The final step is to simplify our result. We can do this by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 24,395 and 16 is 1, so our simplified result is:
24,395/16
And that's the result of multiplying 59 1/2 x 25 5/8!
