4. Complete the following: a. The commutative property i. $$ a+b= $$ b. The associative property o i. $$ (a+b)+c= $$ a c. The distributive property of i. $$ a(b+c)= $$ d. 0 (zero) is the identity elem e. 1 (one) is the identity eleme

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Let's complete each of the properties step by step:

a. **The commutative property** states that the order in which two numbers are added or multiplied does not change the result.

i. $$ a + b = b + a $$

b. **The associative property** states that the way in which numbers are grouped when adding or multiplying does not change the result.

i. $$ (a + b) + c = a + (b + c) $$

c. **The distributive property** states that multiplying a number by a sum is the same as doing each multiplication separately.

i. $$ a(b + c) = ab + ac $$

d. **0 (zero) is the identity element for addition**, meaning that adding zero to any number does not change the number.

i. $$ a + 0 = a $$

e. **1 (one) is the identity element for multiplication**, meaning that multiplying any number by one does not change the number.

i. $$ a \cdot 1 = a $$

These properties are fundamental in arithmetic and algebra, helping to simplify expressions and solve equations.
a. **Commutative Property**: i. $$ a + b = b + a $$ b. **Associative Property**: i. $$ (a + b) + c = a + (b + c) $$ c. **Distributive Property**: i. $$ a(b + c) = ab + ac $$ d. **Identity Element for Addition**: i. $$ a + 0 = a $$ e. **Identity Element for Multiplication**: i. $$ a \cdot 1 = a $$

4. Complete the following: a. The commutative property i. \( a+b= \) b. The associative property o i. \( (a+b)+c= \) a c. The distributive property of i. \( a(b+c)= \) d. 0 (zero) is the identity elem e. 1 (one) is the identity eleme

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