20. A grocer sold 7 barrels of flour for $38.43. How much did he receive per barrel?

21. In making the voyage from Southampton to New York, an ocean steamer consumes 2375 tons of coal in 5 days. What is the average amount consumed per day?

22. A special train made the distance from Chicago to New York in 16 hours. The distance by the route taken was 960 miles. What was the average speed per hour?

23. Two trains leave Chicago at the same time. One travels east at the rate of 48 miles an hour and the other travels west at the rate of 39 miles an hour. How far apart are they in 4 hours?

24. Two trains start at the same time, one from New York and the other from Chicago. They travel towards each other on the same line, the former at the rate of 53 miles an hour and the latter at the rate of 48 miles an hour. The distance between New York and Chicago being 980 miles by this route, how far apart are the trains in 4 hours?

25. A farmer sowed 68 acres to clover, using 13 pounds of seed to the acre. How many pounds did he use in all? If the crop averaged 4 tons to the acre, how many tons did

the farmer cut in all ?

26. A coal dealer buys coal at $2.87 a ton. He pays $0.67 a ton for railway transportation and $0.78 a ton for delivery, and sells the coal for $5.25 a ton. How much profit does he make per ton?

27. A watering trough holds 118 gallons. It is cracked so that water leaks out at the rate of 24 gallons an hour, but water flows in through a feed pipe at the rate of 83 gallons an hour. If the trough is empty when the water is turned on, how long will it take to fill the trough?

EXERCISE 26

WRITTEN REVIEW QUESTIONS

1. Define units and give three illustrations.

2. Define numbers and give examples of two kinds. 3. What do you mean by integers, and what other names can you give to them?

4. What are abstract numbers? concrete numbers?

5. Distinguish between notation and numeration.

6. What are the two kinds of notation known to you? Why are they so called?

7. What do you mean by numerals? by digits?

8. What is meant by the place value of a figure ?

9. What is the difference between orders and periods in writing numbers? Illustrate each.

10. How are periods indicated in the writing of numbers? Illustrate in two ways.

11. In writing United States money, how are the dollars separated from the cents? Illustrate.

12. What are the characters used in writing Arabic numbers, and those used in writing Roman numbers? Write four hundred forty-nine in each system.

13. What name is given to numbers that are to be added? What is the name of the result?

14. What is meant by like numbers? Illustrate by three pairs of like numbers.

15. How do you check the work in addition?

16. What names are given to the three numbers used in subtraction? Illustrate.

17. How do you check the work in subtraction?

18. What do you mean by multiplication? Show that it is a short process of addition.

19. What names are given to the three numbers used in multiplication? Illustrate.

20. What are factors? Illustrate.

21. May the multiplicand be abstract? May it be concrete? Illustrate both cases.

22. What is the effect of changing the order of the addends? also of the factors of a number? Illustrate by the cases of 4 + 7 + 9, and 4 × 7 × 9.

23. What is meant by a power of a number? by the square of a number? by the cube of a number? Illustrate.

24. What is the short way of multiplying an integer by 100? of multiplying United States money by 100?

25. What do you mean by division? In what way does division differ from multiplication?

26. Name the terms used in division and give an example showing the use of each.

27. If the dividend and divisor are concrete, what else may be said of their nature? What is the nature of the quotient? Illustrate.

28. May the dividend be concrete and the divisor abstract? Illustrate.

29. What is the short process of dividing an integer by 10? Illustrate by dividing 4750 by 10.

30. What is the effect on the quotient of multiplying the dividend or dividing the divisor? Illustrate each case.

31. What is the effect on the quotient of dividing the dividend or multiplying the divisor? Illustrate each case.

CHAPTER VI

DECIMAL FRACTIONS

66. Meaning of Decimals. We have already seen that $2.25 means $2 + 25 cents, which is the same as $2,25 or $24.

In the same way, 2.25 miles means 225 miles, or 24 miles; 1.50 means 15%, or 11; 1.75 means 175, or 1; 1.5 means 15, or 11; 2.125 means 2,125, or 21; and 0.125 means 125, or }. (See § 65.)

That is, 0.5 or .5 is a fraction whose denominator is not written, it being understood to be 10 from the fact that 5 occupies the first place to the right of the decimal point. We therefore have the following:

0.5 means, for the 5 extends to the 10th's place; 0.25 means, for the 25 extends to the 100th's place; 0.125 means, for the 125 extends to the 1000th's place. The names of the places are, in part, as follows:

1 3 4 5

2 7 6 5

This number is read "one thousand three hundred forty-five and two thousand seven hundred sixty-five ten-thousandths." The orders beyond ten-thousandths are hundred-thousandths, millionths, tenmillionths, and so on.

67. Decimal Fractions. A fraction whose denominator is not written, but is some power of 10, is called a decimal fraction, or more often simply a decimal.

Thus 0.25, which has the same value as 2, is a decimal fraction. An integer and a decimal together form a mixed decimal; for example, 2.25.

68. Decimal Point. The period written at the left of the tenths is called the decimal point.

For example, 0.7 = 1; 0.08 = 18ʊ, or 2; 0.005 = 10‰0, or zoo. It was not necessary to write a zero at the left of the decimal point in the above cases, for 0.5 means the same as .5. The zero is often written there to call attention more quickly to the decimal point.

69. Reading Decimals. We read a decimal precisely as if it were a whole number, and then give it the name of the lowest decimal place.

It is best to pronounce the word and at the decimal point only. Thus 100.023 is read " one hundred and twenty-three thousandths," while 0.123 is read "one hundred twenty-three thousandths."

Read aloud as dollars and decimals of a dollar :

33. $1.25.

34. $25.05.

35. $26.70.

36. $125.50.