How to Explain Predictability of Patterns in Division
- 1). Describe the connection between division and multiplication. In multiplication, you multiply two numbers to determine the product. For example, 2 x 3 = 6. In division, the dividend is divided by the divisor to determine the quotient. For example, 6 / 3 = 2. Therefore, the product of multiplication is the dividend of the division problem.
- 2). Practice division problems for which the dividend and the divisor are the same. Whenever the dividend and the divisor have the same value, the quotient is always 1. For example, 6 / 6 = 1 and 4 / 4 = 1.
- 3). State the rules for using zero as a dividend or as a divisor. If the dividend is zero, then the quotient is zero. For example, 0 / 2 = 0. If the divisor is zero, then the problem is undefined. For example, 2 / 0 is undefined.
- 4). Do problems that show how adding a zero to the dividend can affect the value of the quotient. For example, 3 / 3 =1, 30 / 3 = 10, and 300 / 3 = 100. When a zero is added to the dividend and the value of the divisor is the same, a zero also is added to the quotient.
- 5). Do problems that show how adding a zero to the divisor affects the quotient. For example, 300 / 3 = 100, 300 / 30 = 10, and 300 / 300 = 1. When a zero is added to the divisor and the value of the dividend is the same, then a zero is removed from the quotient.
- 6). Relate the patterns of multiplication to those in division. For example, the five times tables alternate between a product with a zero as the last digit and a five as the last digit, such as: 5 x 2 = 10 and 5 x 3 = 15. If you use the products as dividends and one of the other numbers as divisors, then you will receive five as the quotient. For example, 10 / 2 = 5 and 15 / 3 = 5.
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