What is the product of −2 2/3 𝑎𝑛𝑑 2 1/5 

To find the product of \(-2 \dfrac{2}{3}\) and \(2 \dfrac{1}{5}\), follow these steps:

1. **Convert the mixed numbers to improper fractions:**

   - For \(-2 \dfrac{2}{3}\), multiply the whole number by the denominator and add the numerator:
     \[
     -2 \dfrac{2}{3} = -\dfrac{(3 \times 2) + 2}{3} = -\dfrac{6 + 2}{3} = -\dfrac{8}{3}
     \]
   
   - For \(2 \dfrac{1}{5}\), multiply the whole number by the denominator and add the numerator:
     \[
     2 \dfrac{1}{5} = \dfrac{(5 \times 2) + 1}{5} = \dfrac{10 + 1}{5} = \dfrac{11}{5}
     \]

2. **Multiply the improper fractions:**
   \[
   \left( -\dfrac{8}{3} \right) \times \left( \dfrac{11}{5} \right) = -\dfrac{8 \times 11}{3 \times 5} = -\dfrac{88}{15}
   \]

3. **Convert the result back to a mixed number:**

   \[
   -\dfrac{88}{15} = -5 \dfrac{13}{15}
   \]

Thus, the product of \(-2 \dfrac{2}{3}\) and \(2 \dfrac{1}{5}\) is \(-5 \dfrac{13}{15}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you multiply fractions with mixed numbers?
2. How do you simplify improper fractions?
3. How can you convert mixed numbers into improper fractions?
4. How do you multiply negative and positive fractions?
5. What are some common mistakes when multiplying mixed numbers?

**Tip:** Always convert mixed numbers to improper fractions before performing multiplication!

What is the product of −2 2/3 and 2 1/5?

Learn how to find the product of −2 2/3 and 2 1/5 by converting mixed numbers into improper fractions and multiplying them. This detailed solution is ideal for students in Grades 6-8, covering multiplication of mixed numbers, fractions, and negative numbers.

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