Fraction Operations: 2 1/2 x 2 3/4
In this article, we will explore how to perform a multiplication operation involving mixed numbers, specifically 2 1/2 and 2 3/4.
What 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.
Step-by-Step Solution
To multiply 2 1/2 and 2 3/4, we need to follow these steps:
Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both mixed numbers to improper fractions.
- 2 1/2 = (2 * 2 + 1) / 2 = 5/2
- 2 3/4 = (2 * 4 + 3) / 4 = 11/4
Step 2: Multiply the Fractions
Now, we can multiply the two fractions:
- (5/2) × (11/4) = ?
To multiply fractions, we need to multiply the numerators (numbers on top) and multiply the denominators (numbers at the bottom), then simplify the result.
- Numerators: 5 × 11 = 55
- Denominators: 2 × 4 = 8
- Result: 55/8
Step 3: Simplify the Result (Optional)
In this case, the result is already in its simplest form. However, if the result were not in its simplest form, we would need to simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD).
Final Answer
The final answer is:
2 1/2 × 2 3/4 = 55/8
Alternatively, we can convert the improper fraction back to a mixed number:
55/8 = 6 7/8
Therefore, 2 1/2 × 2 3/4 is equal to 6 7/8.
