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 example of 1 2/3 x 2 3/5.
Understanding Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. For example, 1 2/3 represents one whole and two-thirds of another.
Converting Mixed Numbers to Improper Fractions
Before multiplying mixed numbers, it's essential to convert them to improper fractions. Here's how:
- Multiply the denominator of the fraction by the whole number: In our case, 3 x 1 = 3.
- Add the numerator of the fraction: 3 + 2 = 5.
- Keep the same denominator: The improper fraction for 1 2/3 becomes 5/3.
Following the same steps for 2 3/5, we get:
- 5 x 2 = 10
- 10 + 3 = 13
- Keep the denominator: The improper fraction for 2 3/5 becomes 13/5.
Multiplying Improper Fractions
Now we have 5/3 x 13/5. To multiply fractions:
- Multiply the numerators: 5 x 13 = 65
- Multiply the denominators: 3 x 5 = 15
This gives us 65/15.
Simplifying the Result
The fraction 65/15 can be simplified. Both the numerator and denominator are divisible by 5:
65 ÷ 5 = 13 15 ÷ 5 = 3
Therefore, 65/15 simplifies to 13/3.
Converting Back to a Mixed Number
Finally, convert the improper fraction back to a mixed number:
- Divide the numerator by the denominator: 13 ÷ 3 = 4 with a remainder of 1.
- The quotient becomes the whole number: 4
- The remainder becomes the numerator: 1
- Keep the same denominator: 3
The final answer is 4 1/3.
Conclusion
By converting mixed numbers to improper fractions, multiplying them, and simplifying the result, we found that 1 2/3 x 2 3/5 equals 4 1/3. Remember to always simplify your answer to its lowest terms.