Name the property of real numbers illustrated by the equation 2·(8·7)=(2·8)·7 answers are. Distributive property ,associative property multiplication, Communicative property multiplication, Associative property addition
assoc prop of mult.
Also, it's commutative, not communicative!
The property of real numbers illustrated by the equation 2·(8·7)=(2·8)·7 is the Associative Property of Multiplication.
To understand this property, let's break down the equation step by step:
1. 2·(8·7): In this expression, we have two pairs of parentheses. Within the inner parentheses, we have the product of 8 and 7, which is 56. Then, the outer parentheses multiply 2 by the result of 8·7, giving us 2·56.
2. (2·8)·7: Similarly, in this expression, we have two pairs of parentheses. Within the first parentheses, we have the product of 2 and 8, which is 16. Then, we multiply the result of 2·8 by 7, resulting in 16·7.
So, both sides of the equation simplify to 2·56 and 16·7, respectively. Both of these calculations give us the same value, 112.
The Associative Property of Multiplication states that when we have a series of multiplications involving three or more real numbers, the grouping of the numbers does not affect the final product. In this case, we group (8·7) first and then multiply it by 2, or we group (2·8) first and then multiply it by 7. Both ways result in the same product, demonstrating the Associative Property of Multiplication.