Multiply or divide as indicated. Write answers in lowest terms as needed. $2\frac{2}{3}\cdot 1\frac{3}{5}$

Verified step by step guidance

1. First, convert the mixed numbers to improper fractions. For 2(2/3), multiply the whole number 2 by the denominator 3 and add the numerator 2: \(2 \times 3 + 2 = 8\), so \(2(2/3) = \frac{8}{3}\). For 1(3/5), multiply the whole number 1 by the denominator 5 and add the numerator 3: \(1 \times 5 + 3 = 8\), so \(1(3/5) = \frac{8}{5}\).
2. Rewrite the multiplication problem using the improper fractions: \(\frac{8}{3} \times \frac{8}{5}\).
3. Multiply the numerators together and the denominators together: Numerator = \(8 \times 8\), Denominator = \(3 \times 5\), so the product is \(\frac{8 \times 8}{3 \times 5}\).
4. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it to reduce the fraction to lowest terms.
5. If needed, convert the simplified improper fraction back to a mixed number by dividing the numerator by the denominator to find the whole number part and the remainder as the new numerator.

Key Concepts

Multiplication of Mixed Numbers

To multiply mixed numbers, first convert them into improper fractions. This involves multiplying the whole number by the denominator and adding the numerator. Once converted, multiply the numerators together and the denominators together.

Simplifying Fractions

After performing multiplication, simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD). This reduces the fraction to its lowest terms, making the answer clearer and more concise.

Converting Improper Fractions to Mixed Numbers

If the product is an improper fraction, convert it back to a mixed number by dividing the numerator by the denominator. The quotient becomes the whole number part, and the remainder over the denominator forms the fractional part.