Multiplying Mixed Numbers: 1 1/2 x 2 1/2
Multiplying mixed numbers can seem daunting, but it's actually quite simple once you break it down. Here's how to multiply 1 1/2 by 2 1/2 and express the answer as a fraction:
Step 1: Convert Mixed Numbers to Improper Fractions
- 1 1/2: Multiply the whole number (1) by the denominator (2) and add the numerator (1): (1 * 2) + 1 = 3. Keep the same denominator: 3/2
- 2 1/2: Multiply the whole number (2) by the denominator (2) and add the numerator (1): (2 * 2) + 1 = 5. Keep the same denominator: 5/2
Step 2: Multiply the Fractions
Now that we have improper fractions, we can multiply them directly:
(3/2) * (5/2) = (3 * 5) / (2 * 2) = 15/4
Step 3: Simplify to a Mixed Number (Optional)
The fraction 15/4 is an improper fraction (numerator is larger than the denominator). We can simplify it to a mixed number:
- Divide the numerator (15) by the denominator (4): 15 / 4 = 3 with a remainder of 3.
- The quotient (3) becomes the whole number part of the mixed number.
- The remainder (3) becomes the numerator of the fraction part.
- The denominator remains the same.
Therefore, 15/4 is equal to 3 3/4.
In Conclusion
1 1/2 multiplied by 2 1/2 is equal to 15/4 or 3 3/4. By converting the mixed numbers into improper fractions, multiplying, and simplifying the result, we can confidently calculate the answer.