Calculating the Product of 19 1/4 and 22 1/2
When dealing with mixed numbers, it's essential to understand how to multiply them correctly. In this article, we'll guide you through the step-by-step process of calculating the product of 19 1/4 and 22 1/2.
Converting Mixed Numbers to Improper Fractions
Before we begin the multiplication process, we need to convert both mixed numbers to improper fractions.
19 1/4
To convert 19 1/4 to an improper fraction, we'll multiply the whole number part (19) by the denominator (4) and then add the numerator (1).
(19 × 4) + 1 = 77
So, 19 1/4 is equal to 77/4.
22 1/2
Similarly, to convert 22 1/2 to an improper fraction, we'll multiply the whole number part (22) by the denominator (2) and then add the numerator (1).
(22 × 2) + 1 = 45
So, 22 1/2 is equal to 45/2.
Multiplying the Improper Fractions
Now that we have both mixed numbers converted to improper fractions, we can multiply them.
(77/4) × (45/2)
To multiply fractions, we'll multiply the numerators (77 and 45) and multiply the denominators (4 and 2).
(77 × 45) = 3465
(4 × 2) = 8
So, the product of (77/4) and (45/2) is 3465/8.
Simplifying the Fraction
To simplify the fraction 3465/8, we can divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 3465 and 8 is 1, so the fraction remains the same.
Final Answer
The product of 19 1/4 and 22 1/2 is 3465/8.
