Which one is associative?
6(3) + 6(7) = 6(10)
or
1/2(8*9)=4*9
looks like (b) to me
(a) is distributive
thanks.
To determine which equation is associative, we need to compare the operations being performed in each equation.
The first equation is 6(3) + 6(7) = 6(10). Here, the operation being performed is multiplication (denoted by the symbol '*'), and the multiplication is being followed by addition (denoted by the symbol '+').
The second equation is 1/2(8*9) = 4*9. Similarly, the operation being performed is multiplication.
To test for associativity, we need to check if changing the grouping of the operations within each equation gives the same result. In other words, we need to determine if it matters which numbers are multiplied first and which numbers are added together.
Let's consider the first equation: 6(3) + 6(7) = 6(10). If we simplify the left side of the equation first by performing the multiplications first, we get: 18 + 42 = 60. If we simplify the right side by performing the multiplication first, we get: 60 = 60. The result is the same, so this equation is associative.
Now let's consider the second equation: 1/2(8*9) = 4*9. If we simplify the left side of the equation first by performing the multiplication first, we get: 1/2(72) = 36. If we simplify the right side by performing the multiplication first, we get: 4*9 = 36. Again, the result is the same, so this equation is also associative.
Therefore, both equations are associative.