Business Arithmetic

WRITTEN EXERCISES

1. State how we may divide by 48, by 56, by 72, by 81. In this manner divide each of the following:

In estimating the value of short cuts account should be taken not only of the saving of time but of the compactness of the form in which the work may be written out. This is specially important when the operation is a part of a larger piece of work. Long division in the usual form is particularly to be avoided on this account. (See § 61.)

87. Dividing by 25, 50, 125. Since 25 = 100, or one fourth of 100, it follows that a number may be divided by 25 by dividing it by 100 and then multiplying by 4. Similarly to divide by 50, divide by 100 and multiply by 2.

Thus, 7900 ÷ 25

4 X 79

316 and 19400 ÷ 50 = 2 X 194 = 388.

Since 125 is one eighth of 1000, a number may be divided by 125 by dividing by 1000 and then multiplying by 8.

For further short cuts in multiplication and division, see Chapter XIV after common and decimal fractions have been studied.

WRITTEN EXERCISES

Find the quotient and remainder in each of the following:

88. Quotients to the Nearest Integer. In many problems it is required to get the quotient to the nearest integer, neglecting the remainder.

Example 1. Divide 845921 by 389, finding the quotient to its nearest integer.

On dividing we find a quotient of 2174 and a remainder of 235.

Since the remainder is more than one half the divisor, 1 is added to the last figure in the quotient and the remainder is neglected. Hence, 2175 is the required quotient.

Example 2. Divide 562190 by 874, finding the quotient to the nearest integer.

On dividing we find a quotient of 644 and a remainder of 334.

Since the remainder is less than one half the divisor, it is neglected and 644 is the required quotient.

When the remainder is exactly equal to one half the divisor, it is customary to add 1 to the quotient.

89. Finding Averages. It is frequently required to find the average of several numbers. Thus, the average attendance in a school is found, for a week, a month, or even a year.

Rule. To find the average of several numbers, divide their sum by the number of numbers.

Example. In a certain school the attendance for the five school days of a week was 897, 882, 904, 906, 898. Find the average for the week.

Adding and dividing by 5, the quotient is 897 and the remainder 2. If it is required to get the average attendance to the nearest integer, 897 is the required result.

ORAL EXERCISES

1. What is meant by the average of a given set of numbers? 2. How would you find the average weight of the boys in a class?

WRITTEN EXERCISES

In the following find the quotients to the nearest integer:

Find the average to the nearest integer of each of the following sets of numbers.

10. 891, 736, 1078, 459, 1280, 936, 1006, 998. 11. 1980, 376, 2490, 549, 2180, 396, 1470, 456. 12. 98, 396, 475, 3891, 1280, 4370, 1520, 274. 13. 670, 94, 52, 74, 31, 47, 24, 391, 84, 3, 40.

DRILL IN DIVISION

Divide and test by casting out 9's. See § 82.

In the following write down the quotients and remainders.

Find the quotients in the following as in § 86.

GENERAL DRILL IN DIVISION

In finding the quotients and remainders in the following, use short

CHAPTER VI

DRILL IN FUNDAMENTAL OPERATIONS

90. Necessity for Continued Drill. - The practical business man must be ready at all times to perform the operations of addition, subtraction, multiplication, and division with considerable speed and practically absolute accuracy. To acquire such skill it is necessary to practice on these operations at short intervals extended over a long period of time. For this reason drills on the fundamental operations will be given at the ends of the chapters throughout this book.