4 3/4×3 1/2: Understanding Mixed Number Multiplication
When it comes to multiplication, mixed numbers can often be a source of confusion. In this article, we will explore the multiplication of two mixed numbers: 4 3/4 and 3 1/2.
What are Mixed Numbers?
Before we dive into the multiplication, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 4 3/4 is a mixed number because it consists of the whole number 4 and the fraction 3/4.
Multiplying Mixed Numbers
To multiply mixed numbers, we need to follow a specific procedure. Here's how to multiply 4 3/4 and 3 1/2:
Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
- 4 3/4 = 19/4 (convert 4 to 16/4 and add 3/4)
- 3 1/2 = 7/2 (convert 3 to 6/2 and add 1/2)
Step 2: Multiply the Fractions
Now, we can multiply the two fractions:
- 19/4 × 7/2 = ?
To multiply fractions, we multiply the numerators (19 and 7) and multiply the denominators (4 and 2). Then, we simplify the fraction:
- 19 × 7 = 133
- 4 × 2 = 8
- 133/8
Step 3: Simplify the Fraction
Our result is an improper fraction, but we can simplify it to a mixed number:
- 133/8 = 16 5/8
And that's our final answer! 4 3/4 × 3 1/2 = 16 5/8.
Conclusion
Multiplying mixed numbers can seem daunting, but by converting them to improper fractions and following the correct procedure, we can achieve the correct result. Remember to simplify your answer to a mixed number to make it easier to understand. With practice, you'll become a pro at multiplying mixed numbers!
