Name the property that is illustrated in each equation

h + (y+4.1) = (h+y) + 4.1

t*1.5=1.5t

s*p=p*s

(0+z) + 8 = (z+0) + 8

The associative property says that if we're adding a bunch of numbers together, the parentheses do not affect the order in which we add. that means:

a + (b + c) is the same as (a + b) + c

therefore:

h + (y + 4.1) = (h + y) + 4.1

this is illustrating that property, specifically in regards to addition. so the answer is the associative property of addition.

the commutative property, on the other hand, states that order itself doesn't affect the answer when we're adding a bunch of numbers together. this means that:

a + b + c = c + b + a = a + c + b and so on and so forth.

so when we have the following equation:

t * 1.5 = 1.5 * t

this is demonstrating the commutative property of multiplication.

s * p = p * s

guess what! this is really the same question as before. all we're doing is flipping the two numbers (variables) around, showing that order does not matter. thus, the answer is yet again the commutative property of multiplication.

(0 + z) + 8 = (z + 0) + 8

this one might look like the associative property, but the associative property involves moving the parentheses around or getting rid of them altogether to show that the parentheses don't matter to the final answer. In this one, all that is happening is the 0 and z are being flipped inside the parentheses, illustrating the commutative property of addition.