Multiplying Mixed Numbers: 1 2/3 x 2 3/5
This article will guide you through the process of multiplying mixed numbers, specifically focusing on the problem 1 2/3 x 2 3/5.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. To perform multiplication, we first need to convert these mixed numbers into improper fractions.
Converting to Improper Fractions
1. Multiply the whole number by the denominator:
- 1 x 3 = 3 2. Add the numerator:
- 3 + 2 = 5 3. Keep the same denominator:
- 1 2/3 = 5/3
Similarly, for 2 3/5:
- 2 x 5 = 10
- 10 + 3 = 13
- 2 3/5 = 13/5
Multiplying the Improper Fractions
Now we have 5/3 x 13/5. To multiply fractions, we simply multiply the numerators and the denominators:
- (5 x 13) / (3 x 5) = 65/15
Simplifying the Result
The fraction 65/15 can be simplified. Both the numerator and denominator are divisible by 5:
- 65/15 = (65/5) / (15/5) = 13/3
Converting Back to a Mixed Number
Finally, we can convert the improper fraction 13/3 back to a mixed number:
- 13 divided by 3 is 4 with a remainder of 1.
- This gives us 4 1/3.
Conclusion
Therefore, 1 2/3 x 2 3/5, expressed in its simplest form, is 4 1/3.