Multiplying Mixed Numbers: Finding 1 1/3 Times 2 1/2
This article explores how to multiply mixed numbers, focusing on finding the product of 1 1/3 and 2 1/2 in fraction form.
Converting Mixed Numbers to Fractions
The first step is to convert both mixed numbers into improper fractions.
1. 1 1/3:
- Multiply the whole number (1) by the denominator of the fraction (3): 1 * 3 = 3
- Add the numerator (1) to the result: 3 + 1 = 4
- Keep the same denominator (3): 4/3
2. 2 1/2:
- Multiply the whole number (2) by the denominator of the fraction (2): 2 * 2 = 4
- Add the numerator (1) to the result: 4 + 1 = 5
- Keep the same denominator (2): 5/2
Multiplying Fractions
Now that we have improper fractions, we can multiply them:
(4/3) * (5/2) = (4 * 5) / (3 * 2) = 20/6
Simplifying the Result
The fraction 20/6 can be simplified. Find the greatest common factor (GCF) of 20 and 6, which is 2. Divide both the numerator and denominator by 2:
20/6 = (20 / 2) / (6 / 2) = 10/3
Converting Back to a Mixed Number (Optional)
The final answer in fraction form is 10/3. If you prefer, you can convert it back to a mixed number:
- Divide the numerator (10) by the denominator (3): 10 / 3 = 3 with a remainder of 1
- The whole number part of the mixed number is 3. The remainder (1) becomes the numerator of the fraction, and the denominator remains 3.
Therefore, 10/3 is equivalent to 3 1/3.
Conclusion
Multiplying 1 1/3 by 2 1/2 results in 10/3 or 3 1/3. By converting the mixed numbers to improper fractions, multiplying, and simplifying, we arrive at the solution.