## Understand Division

As in the cases of addition and multiplication, certain properties hold for division. The Property of One for Multiplication (also called the Identity Property of Multiplication) states that for any number n, n × 1 = n. This property is applied to division in the following forms.

For any number n, n ÷ 1 = n.

For any number n, n ≠ 0, n ÷ n = 1.

The Zero Property of Multiplication states that for any number n, n × 0 = 0. Because multiplication and division are inverse operations, the statement implies that

For any number n, n ≠ 0, 0 ÷ n = 0.

The condition n ≠ 0 is essential in the above statements because neither n ÷ 0 nor 0 ÷ 0 are defined.

**Division With Remainders**

When you divide a group of objects into smaller equal groups, there may be some objects left over. For instance, when you divide 18 by 7, the result is seven groups of 2 with 4 left over. The 4 left over is the remainder in the division problem.

The answer to the division in the example is usually written 2 R4. When the result of the division is checked using multiplication, the remainder must be added to the product of the divisor and the quotient. The resulting sum should equal the dividend in the original problem.

**Teaching Model 8.2:** Divide With Remainders