Fraction Multiplication: 17 1/2 x 32/33
In this article, we will explore the multiplication of fractions, particularly the problem of multiplying 17 1/2 by 32/33. We will walk you through the step-by-step process of solving this problem and provide a detailed explanation of the calculations involved.
Converting Mixed Numbers to Improper Fractions
Before we dive into the multiplication, let's convert the mixed number 17 1/2 to an improper fraction.
17 1/2 = 35/2
Now we can proceed with the multiplication.
Multiplying Fractions
To multiply fractions, we need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), then simplify the resulting fraction.
Step 1: Multiply the Numerators
35/2 × 32/33 = (35 × 32) / (2 × 33)
Step 2: Multiply the Denominators
35/2 × 32/33 = 1120 / 66
Step 3: Simplify the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 1120 and 66 is 2.
1120 ÷ 2 = 560 66 ÷ 2 = 33
So, the simplified result is:
560/33
Final Answer
Therefore, the result of multiplying 17 1/2 by 32/33 is 560/33.
