Question
20. The equation \( 4 \times 7=(4 \times 3)+ \) \( (4 \times 4) \) is an example of what property?
Ask by Ryan Bright. in the United States
Jan 22,2025
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La ecuación \( 4 \times 7 = (4 \times 3) + (4 \times 4) \) ilustra la **propiedad distributiva**.
Solution
La ecuación \( 4 \times 7 = (4 \times 3) + (4 \times 4) \) es un ejemplo de la **propiedad distributiva**.
**Propiedad Distributiva**: Esta propiedad establece que multiplicar una suma por un número es lo mismo que multiplicar cada sumando por ese número y luego sumar los resultados. Matemáticamente, se expresa como:
\[ a \times (b + c) = (a \times b) + (a \times c) \]
En tu ejemplo:
\[ 4 \times 7 = 4 \times (3 + 4) = (4 \times 3) + (4 \times 4) = 12 + 16 = 28 \]
Esta propiedad es fundamental en álgebra y facilita la simplificación de expresiones algebraicas.
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Simplify this solution Mind Expander
This equation illustrates the Distributive Property of multiplication over addition. Specifically, it shows how distributing the factor 4 across the sum of 3 and 4 yields the same result as multiplying 4 by their total, which emphasizes the flexibility of rearranging terms in multiplication. Understanding the Distributive Property is vital for simplifying expressions in algebra. It's particularly handy when dealing with polynomials or fractions, allowing you to break down complex problems into more manageable parts, preventing common mistakes like overlooking additive relationships or miscalculating values within operations.
