MATH SOLVE

7 months ago

Q:
# Which pair of expressions is equivalent using the Associative Property of Multiplication? (3 points) 5(3a ⋅ 4) = 15a ⋅ 20 5(3a ⋅ 4) = (3a ⋅ 4) ⋅ 5 5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4 5(3a ⋅ 4) = 5 ⋅ 3a ⋅ 4 6

Accepted Solution

A:

Answer:5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4Step-by-step explanation:The Associative Property is applied to two types of operations: addition and multiplication. This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.In this sense, the associative property for the sum is mathematically given by:[tex](x+y)+z=x+(y+z)[/tex]and for the multiplication by:[tex](xy)z=x(yz)[/tex]Now, let:[tex]x=5\\y=3a\\z=4[/tex]Using the Associative Property of Multiplication:[tex](xy)z=x(yz)\\\\Replacing\hspace{3}the\hspace{3}values\\\\(5\cdot 3a)\cdot4=5(3a\cdot 4)[/tex]Therefore the equivalent expressions are:5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4