Find each product or quotient where possible. See Example 2. 2𝝅/( 2⁄3) (Leave 𝝅 in the answer.)

Verified step by step guidance

1. Identify the expression to be evaluated, which is the product of \(2\pi\) and \(\frac{2}{3}\).
2. Recall that when multiplying a constant by a fraction, you multiply the constant by the numerator and then divide by the denominator.
3. Write the multiplication explicitly as \(2\pi \times \frac{2}{3} = \frac{2 \times 2\pi}{3}\).
4. Simplify the numerator by multiplying the constants: \(2 \times 2\pi = 4\pi\).
5. Express the final product as \(\frac{4\pi}{3}\), leaving \(\pi\) in the answer as requested.

Key Concepts

Multiplication and Division of Fractions

Understanding how to multiply and divide fractions is essential, as the problem involves multiplying or dividing expressions like 2π and 2/3. Multiplying fractions involves multiplying numerators and denominators directly, while division requires multiplying by the reciprocal of the divisor.

Handling Constants like π in Expressions

π is an irrational constant often left in symbolic form in answers. When multiplying or dividing expressions involving π, treat it as a constant factor, simplifying numerical coefficients separately while keeping π intact in the final expression.

Simplifying Algebraic Expressions

After performing multiplication or division, simplifying the resulting expression by reducing fractions or combining like terms is necessary. This ensures the answer is in its simplest form, making it easier to interpret and use in further calculations.