Answer:
see attached
Explanation:
You want the expressions in the correct sequence to prove ...
z + z + z + z = 4z
Multiplication identity
The multiplicative identity property tells you z × 1 = z. Anything multiplied by 1 is unchanged. This lets us replace z in the original expression by z·1 in every case.
Distributive property
The distributive property tells you that multiplication distributes over addition. This means ...
z ·1 + z · 1 + z · 1 + z · 1 = z · (1 + 1 + 1 + 1)
Addition
The properties of addition and the set of integers tell us that ...
1 + 1 + 1 + 1 = 4
so we can replace the indicated sum by its value:
z · (1 + 1 + 1 + 1) = z · 4
Commutative property
The commutative property of multiplication says a product is the same if the operands are in a different order:
z · 4 = 4·z = 4z
This is the last step in showing z + z + z + z = 4z.
The correct order of tiles is shown in the attachment.
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