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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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.

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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.

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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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