Simplify each expression. See Example 8.-2⁄3 (12w) (7z)

Verified step by step guidance

1. First, rewrite the expression clearly: \(-\frac{2}{3} \times (12w) \times (7z)\).
2. Next, group the numerical coefficients together and the variables together: \(\left(-\frac{2}{3} \times 12 \times 7\right) \times (w \times z)\).
3. Multiply the numerical coefficients step-by-step: first multiply \(-\frac{2}{3}\) by 12, then multiply the result by 7.
4. After simplifying the numerical part, combine the variables \(w\) and \(z\) by writing them as \(wz\).
5. Finally, write the simplified numerical coefficient multiplied by \(wz\) to express the fully simplified expression.

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed to ensure consistent results. Multiplication and division are performed from left to right before addition and subtraction. In this expression, multiplication of constants and variables should be done carefully following this order.

Multiplication of Constants and Variables

When multiplying constants and variables, multiply the numerical coefficients separately and then combine the variables by writing them together. For example, multiplying -2/3, 12, and 7 involves multiplying the numbers first, then attaching the variables w and z as factors.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor. In this problem, simplifying the fraction -2/3 multiplied by whole numbers helps to reduce the expression to a simpler form before combining with variables.