1. Add the following, both horizontally and vertically:

2. The cost of instruction in the high schools of a certain city was as follows:

Find the total cost of high school instruction for each of the three years, the cost of each kind of school for the three-year period, and the total amount paid during the three years.

3. For one week a butcher's sales in pounds were as follows:

Find the total sale for each day, the total sale of each kind of

meat for the week, and the total of all kinds for the week.

DRILL IN ADDITION AND SUBTRACTION

Subtract the following horizontally:

16. From 3864 subtract the sum of 486, 982, 1400, 230, 145. 17. From 10978 subtract the sum of 1265, 1342, 819, 600, 540, 135. 18. From 21764 subtract the sum of 8041, 1365, 6008, 569, 2901, 56. 19. From 30671 subtract the sum of 15076, 8270, 867, 241, 1009. 20. From 95204 subtract the sum of 20045, 7069, 8329, 5004, 6025. 21. From 70026 subtract the sum of 19206, 10718, 19201, 1856.

DRILL IN MULTIPLICATION

Write the product in each of the following examples. See § 49.

Use short cuts wherever you can in the following:

75. Taking an Inventory. At certain stated times a merchant counts the number of articles of each kind which he has in stock and thus finds approximately the value of the goods in the store. This process is called taking an inventory.

PROBLEMS

For each of the following partial inventories, copy data on a suitable blank, extend, and find the total values.

PROBLEMS

1. The table below gives the total number of freight trains and the total amount of freight hauled on a certain road in the years indicated. Find the average number of tons of freight per train for each of the years named. Also find the average load per train for this whole period.

Suggestion. To find the average load per train for the period, find the total number of trains and the total amount of freight carried.

2. The attendance at a certain school for the twenty school days of a month was: 1874, 1892, 1924, 1914, 1903, 1917, 1893, 1897, 1898, 1898, 1902, 1904, 1907, 1899, 1897, 1904, 1914, 1891, 1907, 1894. Find the average attendance for this month.

3. The following table gives the number of acres in corn and the total yield for the states named as given by a recent census. Find to the nearest bushel the average yield in each state. Also find the average for all these states.

Suggestion. To find the average for all these states find first the total number of acres and the total yield.

CHAPTER VII

DIVISIBILITY OF NUMBERS, FACTORS, MULTIPLES

This chapter serves as an introduction to the chapters on fractions, since dealing with fractions requires a knowledge of the divisibility of numbers, and of the factors and multiples of numbers.

76. Integers. The numbers obtained by ordinary counting, beginning with 1, are called integers. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are all the integers from 1 to 10 inclusive.

77. Odd and Even Integers. Every second integer, beginning with 2, is called an even integer. Zero is also regarded as an even integer. Thus, 0, 2, 4, 6, 8, 10, integers from 0 to 20 inclusive.

12, 14, 16, 18, 20 are all the even

All integers which are not even are called odd integers.

We frequently say odd or even numbers, instead of odd and even integers. 78. Factors. If a given integer is the product of two or more integers, these are said to be factors of the given integer.

Thus, 2 and 3 are factors of 6, as are also 1 and 6.

A number (integer) which

79. Prime and Composite Numbers. has no factors except itself and 1 is called a prime number. integers which are not prime are called composite numbers.

All

Thus, 1, 2, 3, 5, 7, 11 are prime numbers, while 4, 6, 8, 9, 10 are composite. 80. Prime Factors. A prime number which is a factor of an

other number is called a prime factor of that number. Thus, 1, 2, 3 are prime factors of 6, and also of 12.

ORAL EXERCISES

1. Give all prime numbers from 1 to 50.

2. Give all prime factors of the numbers: 6, 8, 10, 15, 18, 20. 3. Give all composite factors of 12, 16, 24, 36.