USING WHAT YOU HAVE LEARNED

1. A wagon dealer pays $1680 for 12 wagons. At this rate, how much do 3 wagons cost? How much do 9 wagons cost? 2. At the rate of $2040 for 16 acres of land, how much will a man have to pay for 8 acres? for 32 acres? for 100 acres? 3. If a stock dealer buys some cattle for $22,100, paying $68 a head, how many head of cattle does he buy?

4. If a jobber sells during the year $164,822 worth of shoes at $122 a case, how many cases does he sell?

5. If a dealer sells $246,897 worth of linseed oil during year at $63 a barrel, how many barrels does he sell?

6. If a factory sells 7368 ready-made suits of a certain grade for $184,200, what is the price per suit?

7. If a state pays $4,651,596 for constructing 942 mi. of model road, what is the average cost per mile?

8. If it costs $10,473,204 to construct 574 mi. of railroad, what is the average cost per mile?

9. If a company employs 16,018 men on the same schedule of wages, and the pay roll for these men is $28,031,500 a year, find the annual wages of each man.

10. If a company employs 3840 men on the same schedule of wages, and the pay roll for these men is $6,336,000 a year, find the monthly wages of each man.

11. A shop has 1328 men on its pay roll, all receiving the same wages. For 6 da. this pay roll amounts to $43,824. How much does each man receive on the average a day?

12. In a certain savings bank 116,180 persons have deposited $39,827,991. Find to the nearest cent the average deposit of each person.

FINDING PRICES, WAGES, AND COST

1. Under a certain contract a boss carpenter paid 27 men $2193.75 for 13 da. work, all the men receiving the same wages. Find the daily wages of each.

2. A dealer sold 3 sets of furniture each week for 4 wk. and received $825. The sets were all sold at the same price per set. Find the price at which each set was sold.

3. A merchant bought 1 doz. suits of clothes and found they were in such demand that he bought 2 doz. more of the same kind, the prices being the same. He paid $1157.40 for all the suits. How much did he pay per suit?

4. A manufacturer has 240 men on his pay roll, the wages of all being the same. He pays them $6900 in 5 da. Find the daily wage per man.

5. In a certain school of 43 pupils the teacher's salary is $1100 a year. The cost of fuel is $164.80; of books and other school supplies, $148.75; of repairs and improvements, $86.29. Find the total cost per pupil for the year.

6. In a certain city a man's gas bill for a certain month is $4.25. He uses 5000 cu. ft. of gas in that month. Find how much he has to pay per 1000 cu. ft.

7. The clerks in a certain store bought 17 Government Savings Stamps in a certain month, paying $71.91 for the lot. What was the price of each stamp?

8. The men in a certain railroad shop paid $3299.40 for 39 Treasury Savings Certificates. How much did they pay for each certificate?

9. A wholesale dealer paid $40,150 for 7300 pairs of shoes. If he sold the shoes for $6.25 a pair, how much more did he receive for them than he paid?

USING WHAT YOU HAVE LEARNED

1. If 27 acres of land are worth $2227.50, what is the average value per acre? How much are 4 acres worth?

2. If a dealer pays $413.42 for 14 suits of ready-made clothes, how much does he pay per suit? At the same rate, how much would he pay for 7 suits? for 28 suits? for 21 suits?

3. A man pays $1430 for the rent of an apartment in the city for 11 mo. At this rate, how much does he pay for 5 mo. ? for 7 mo.? for 3 mo.? for 8 mo. ?

4. A man bought 7 M ft. of lumber at $48.50 per M. He sold half the lumber at $8.75 per C, and the other half at $47.50 per M. How much did he gain?

The teacher should explain that 7 M means 7000, and $8.75 per C means $8.75 per hundred feet. Lumber is usually sold by the M; that is, by the 1000 feet. The method of measuring lumber is considered later in the course.

5. At an athletic meet 860 spectators bought tickets at 45¢ each, and 1240 at 25¢ each. What is the average amount paid per spectator?

In all such cases give the result to the nearest cent.

6. An owner made a net profit of $865 on one house, $540 on a second, $690 on a third, and lost $275 on a fourth. What was his average profit per house?

Net profit means the profit after all expenses have been paid.

7. At 60 lb. to the bushel, how many bushels in 28,750 lb. of wheat, and how many pounds over?

8. An experiment station reports that the corn raised on an acre of good land should contain 147 lb. of fat. How many acres would be needed to produce 5586 lb. of fat?

The chief ingredients in corn are protein, carbohydrates, and fat

II. COMMON FRACTIONS

MEANING OF FRACTIONS

All work oral

1. Which is the greater, of an apple or of the same apple? 2. Which is the greater, 2 or 3?or? 3 or 4? or ? 3. Which number is the greatest, 2, 3, or 4? Which fraction is the greatest,,, or ? Which fraction is the least?

4. In the figures here shown, what fractional part of figure A is shaded? What part of figure B is shaded? What part of figure C is shaded?

5. From figure A we see

A

B

C

that is equal to how many sixths? From figure B we see that

is equal to how many sixths?

6. In the figures here shown, X is what part as large as Y? X is what part as large as Z?

7. Each of these small rectangles is what part of the large rectangle? Each of these shaded triangles is what part of the

large rectangle? What part of the

rectangle is of of it? What part is of of it? How much is

This page is typical of the work with objects that should introduce this review of fractions.

The definitions on page 44 should not be learned verbatim, but the teacher should be certain that the pupils can use the terms correctly.

Fraction. A number which shows how many equal parts of anything are taken is called a fraction.

Explain that shows that 3 of the 4 equal parts are taken.

Denominator. The number in a fraction which shows into how many equal parts anything has been divided is called the denominator of the fraction.

Numerator. The number in a fraction which shows how many equal parts of anything have been taken is called the numerator of the fraction.

In this figure, B contains three of the four equal parts of a sphere; that is, B is of a sphere, 4 being the denominator and 3 the numerator.

A

B

с

Terms. The numerator and the denominator together are called the terms of the fraction.

Common Fraction. A fraction like, in which both terms are expressed, is called a common fraction.

The teacher should explain that we write of a dollar thus, $0.25; and that in the case of $0.25 both terms of the fraction are not expressed.

Unit Fraction. A fraction like, in which the numerator is 1, is called a unit fraction.

Proper and Improper Fractions. A fraction like, with the numerator less than the denominator, is called a proper fraction. A fraction like or, in which the numerator equals or exceeds the denominator, is called an improper fraction.

Integer. A number like 7, that is, a number expressed without fractions, is called an integer.

Mixed Number. A number like 2, composed of an integer and a fraction taken together, is called a mixed number.