Calculating Fractions: 3 1/2 x 4 5/8
When working with fractions, multiplication can be a bit tricky. In this article, we will explore how to calculate the product of two mixed numbers: 3 1/2 and 4 5/8.
Converting Mixed Numbers to Improper Fractions
To multiply these mixed numbers, we first need to convert them into improper fractions.
3 1/2
To convert 3 1/2 to an improper fraction, we multiply the whole number part (3) by the denominator (2) and then add the numerator (1).
(3 x 2) + 1 = 7 So, 3 1/2 = 7/2
4 5/8
To convert 4 5/8 to an improper fraction, we multiply the whole number part (4) by the denominator (8) and then add the numerator (5).
(4 x 8) + 5 = 37 So, 4 5/8 = 37/8
Multiplying Improper Fractions
Now that we have our improper fractions, we can multiply them.
7/2 x 37/8
To multiply fractions, we multiply the numerators (7 and 37) and multiply the denominators (2 and 8).
Numerators: 7 x 37 = 259 Denominators: 2 x 8 = 16 So, 7/2 x 37/8 = 259/16
Simplifying the Fraction
We can simplify the fraction 259/16 by dividing both the numerator and denominator by their greatest common divisor (GCD).
GCD of 259 and 16 is 1 So, 259/16 = 259/16 (cannot be simplified further)
Therefore, the product of 3 1/2 and 4 5/8 is 259/16.
