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

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Identify the expression to simplify: \(-\frac{2}{3} \times (12w) \times (7z)\).

First, multiply the numerical coefficients together: \(-\frac{2}{3} \times 12 \times 7\).

Calculate the product of the constants step-by-step: multiply \(12\) and \(7\) to get \(84\), then multiply \(-\frac{2}{3}\) by \(84\).

Simplify the multiplication of the fraction and the integer: \(-\frac{2}{3} \times 84\) by dividing \(84\) by \(3\) first, then multiply by \(-2\).

Finally, write the simplified numerical coefficient together with the variables \(w\) and \(z\) to express the fully simplified product.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Multiplication of Fractions and Whole Numbers

When multiplying a fraction by whole numbers or variables, multiply the numerators together and the denominators together. For example, multiplying -2/3 by 12 involves multiplying -2 by 12 and then dividing by 3.

Multiplication of Variables

Variables can be multiplied together by simply writing them side by side. For instance, multiplying w and z results in wz, which represents the product of the two variables.

Simplification of Algebraic Expressions

Simplifying expressions involves combining like terms and reducing numerical coefficients. After multiplying numbers and variables, reduce the fraction or product to its simplest form for a clearer, more concise expression.

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