## Divide by One-Digit Divisors

The division algorithm for whole numbers is based on the base-ten numeration system. Proficiency in division requires proficiency in multiplication and subtraction. In discussing division, the use of correct vocabulary is essential.

Example: Divide 59 by 8

Since division problems with zeros in the quotient cause some students difficulty, extra practice with such computations should be provided. Point out to students that when dividing money, the decimal point in the quotient is placed directly above the decimal point in the dividend.

**Finding the Mean**

One application of division is finding the mean, or average, of a set of numbers. The mean is found by adding the numbers and then dividing the sum by the number of addends. The mean tells what each number would be if the sum remained the same and the individual numbers were equal.

Example: Find the mean for 9, 19, 44, 8, 25, 4, 27, and 32.

Divide the sum by the number of addends:

168 ÷ 8 = 21

The mean is only one measure of central tendency of a set of data. Other measures of central tendency are discussed elsewhere.

**Dividing by Multiples of 10**

Patterns can be used when dividing by multiples of 10.

630 ÷ 7 = 90

6,300 ÷ 7 = 900

63,000 ÷ 7 = 9,000

630,000 ÷ 7 = 90,000

630 ÷ 70 = 9

6,300 ÷ 700 = 9

63,000 ÷ 7,000 = 9

630,000 ÷ 70,000 = 9

Think: (63 ÷ 7) × 10

Think: (63 ÷ 7) × 100

Think: (63 ÷ 7) × 1,000

Think: (63 ÷ 7) × 10,000

Think: (63 ÷ 7) × (10 ÷ 10)

Think: (63 ÷ 7) × (100 ÷100)

Think: (63 ÷ 7) × (1,000 ÷ 1,000)

Think: (63 ÷ 7) × (10,000 ÷ 10,000)

**Teaching Model 4.4:** Divisibility