Question
Which equation uses the associative property?
A - 1r=r1r=r1r=r
B - rs=srrs=srrs=sr
C - r(st)=(rs)tr\left(st\right)=\left(rs\right)tr(st)=(rs)t
D- r(s+t)=rs+rtr\left(s+t\right)=rs+rtr(s+t)=rs+rt
A - 1r=r1r=r1r=r
B - rs=srrs=srrs=sr
C - r(st)=(rs)tr\left(st\right)=\left(rs\right)tr(st)=(rs)t
D- r(s+t)=rs+rtr\left(s+t\right)=rs+rtr(s+t)=rs+rt
Answers
GPT-4o mini
The associative property refers to the way in which the elements of an operation can be regrouped without changing the result. This property applies to addition (for example, \((a + b) + c = a + (b + c)\)) and multiplication (for example, \((a \cdot b) \cdot c = a \cdot (b \cdot c)\)).
Looking at the provided options:
A - \(1r = r1 = r\): This demonstrates the concept of identity, not the associative property.
B - \(rs = srr = srr = sr\): This isn't a clear demonstration of the associative property.
C - \(r(st) = (rs)t\): This equation shows the associative property of multiplication. It explicitly reorganizes the grouping of the elements.
D - \(r(s + t) = rs + rt\): This equation demonstrates the distributive property, not the associative property.
Therefore, the correct option that uses the associative property is:
**C - \( r(st) = (rs)t \)**.
Looking at the provided options:
A - \(1r = r1 = r\): This demonstrates the concept of identity, not the associative property.
B - \(rs = srr = srr = sr\): This isn't a clear demonstration of the associative property.
C - \(r(st) = (rs)t\): This equation shows the associative property of multiplication. It explicitly reorganizes the grouping of the elements.
D - \(r(s + t) = rs + rt\): This equation demonstrates the distributive property, not the associative property.
Therefore, the correct option that uses the associative property is:
**C - \( r(st) = (rs)t \)**.