Adding zero to any number does not change the value of the number. It remains the same.

Subtracting zero from any number does not change the value of the number. It remains the same.

Multiplying any number by zero always results in zero. This is because zero represents the absence of quantity, so multiplying any number by zero means there is no quantity to multiply.

Division by zero is undefined. This is because dividing a number by zero means trying to find how many times zero goes into that number, which is impossible. Therefore, division by zero is undefined.

When adding two numbers, if one of the numbers is zero, the sum is simply the other number. This is because adding zero does not change the value of the other number.

When subtracting two numbers, if one of the numbers is zero, the difference is simply the other number. This is because subtracting zero does not change the value of the other number.

When multiplying two numbers, if one of the numbers is zero, the product is always zero. This is because multiplying any number by zero results in zero.

Division by zero is undefined. Therefore, if one of the numbers in a division operation is zero, the quotient is undefined.

The identity element for addition is zero. This is because adding zero to any number does not change the value of the number.

The identity element for multiplication is one. This is because multiplying any number by one does not change the value of the number.

The additive inverse of a number is the number that, when added to the original number, results in zero. This is also known as the opposite of the number.

The multiplicative inverse of a number is the number that, when multiplied by the original number, results in one. This is also known as the reciprocal of the number.

The commutative property states that the order of addition does not affect the sum. This means that adding the numbers in any order will result in the same sum.

The commutative property states that the order of multiplication does not affect the product. This means that multiplying the numbers in any order will result in the same product.

The distributive property states that multiplication distributes over addition. This means that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the products.