107. MISCELLANEOUS EXAMPLES. 1. What is the cost of 5 yd. of cloth at $3.375 a yard?

2. What is the cost of 3.2 gal. of coal oil at $.50 a gallon?

3. At $.975 a bushel, how much wheat can be bought for $12.285?

4. A man having 160 and thirteen thousandths acres of land, sold 55 and twenty-seven thousandths acres: how much had he left?

5. If 3.5 cords of wood cost $23.14, what is the cost of one cord?

6. At $18.40 a ton, how much hay can be bought for $2.76?

7. How much corn at $.375 a bushel can be bought for $.125?

8. What is the cost of 1 bushel of wheat, if 4.5 bushels cost $8.46?

9. Reduce to a decimal fraction.

10. At $1.20 a yd., how much cloth can be bought for $100.35?

11. Reduce .456875 to a common fraction.

12. What decimal part of 90 is 17?

13. At $12 an acre, how much land can be bought for $11.25?

14. What cost 12.375 gal. of wine at $3.44 a gallon?

15. If I give 2.12 bu. of corn for 1 day's work, how much should I give for 14.5 days' work? How much would it be worth at $.84 a bushel?

16. A merchant sold 12.5 lb. of coffee at $.40 a pound, 6.25 lb. of tea at $2.12 a pound, 2.75 lb. of

candles at $.26 a pound, and .375 gal. of oil at $2.00 a gallon; he received in exchange butter at $.40 a pound: how many pounds did he receive?

17. A had 42 gallons of a mixture of alcohol and water; .15 of the whole was water: what was the cost of the alcohol at $3.42 a gallon?

18. What is the cost of 63.75 lb. of paper at $.27 a pound?

19. If 1.375 lb. of sugar cost $.33, what is the cost of 17.3265 lb.?

20. What is the cost of 415.625 lb. of copper at $.48 a pound?

21. How many yards of cambric .55 yd. wide, will it take to line a cloak, made of 6 yd. of cloth 1.2 yd. wide?

22. A field contains an acre; its width is 7.25 rd.: what is its length?

23. Express as a decimal 1 of 51⁄2 yd.

24. Seven and two-tenths times the quantity of sugar A has, would cost $29.70 at $.25 a pound: how many pounds has A?

26. The product of two numbers is 6.23; one of the numbers is 124.6: what is the other number?

QUESTIONS FOR REVIEW.

What is a decimal fraction? Is its denominator expressed? How is it indicated? Into what is the unit, divided in decimal fractions? How many units of one order make a unit of the next higher order? How are decimal fractions written? How is the decimal separated from the whole number?

What is the first place at the right of units? The second place? The third? What the rule for numeration of decimals? For notation? How are mixed decimal numbers read? Upon what does the value of each figure depend?

What effect upon the value of a figure does removing it one place further from units have? Removing it one place nearer units? If a decimal fraction occupies one place, what is its denominator? If two places? Three? What is the denominator of any decimal fraction?

Proof?

What the rule for addition of decimals? For the subtraction of decimals? Proof? If there are fewer decimal places in the minuend than the subtrahend, how proceed? Does annexing ciphers to a decimal alter its value? Why not? What the rule for multiplication of decimals? Proof? For division of decimals? Proof? If the divisor has more decimals than the dividend, how proceed? How proceed where there is a remainder after division? In pointing, how regard the ciphers? How reduce a common fraction to a decimal? How proceed when the division can not be exactly performed? How reduce a decimal to a common fraction?

What is a fraction? What is a unit? What is meant by onehalf? One-third? Two-thirds? One-fourth? What is the denominator of a fraction? The numerator?

In the fraction, what is the numerator? What are the terms of a fraction?

The denominator? How many kinds of frac

tions are there? What is a common fraction? How are common fractions expressed? How read? How written?

What is a proper fraction? An improper fraction? A simple fraction? A compound fraction? A complex fraction? A mixed number? What is reduction of fractions?

Upon what does the value of one of the parts of a fraction depend? Upon what does the value of the fraction depend? What is the value of a proper fraction? An improper fraction? Upon what three principles do the operations in fractions depend? When is a fraction in its lowest terms?

Give the rule for reducing fractions to their lowest terms. For reducing an improper fraction to a whole or mixed number. A whole or mixed number to an improper fraction.

THE METRICAL SYSTEM

OF WEIGHTS AND MEASURES.

108. The Metrical System is so called because the Meter is the base, and the principal and invariable unit, upon which the system is founded.

This system was first employed by the French; and, hence, is frequently called the French System of Weights and Measures. Great confusion formerly existed in the weights and measures of France. Each province had its particular measures, which caused great embarrassment in commerce.

Government vainly endeavored to establish a uniformity, and to regulate all measures by those used in Paris.

In 1790, the French Assembly proclaimed the necessity of a complete reform, and invited other governments to join them in establishing a simple system, to be common to all nations.

The coöperation of other nations could not at the time be secured, and a commission, nominated by the Academy of Sciences, and composed of eminent scholars, was instructed to prepare a general system of measures.

The new system was adopted, and declared obligatory after Nov. 2, 1801. But its introduction was gradual. It had to struggle against the local customs, and, for a time, only increased the confusion by adding the new measures to the old.

In 1837, the Assembly enacted a law, rendering the exclusive use of the new system obligatory after Jan. 1, 1841; and imposed penalties against the further use of the old system.

It has since been adopted by Spain, Belgium, and Portugal, to the exclusion of all other weights and measures; and is in general or partial use in nearly all the states of Europe and America, and by scientific men throughout the world.

In 1864, the British Parliament passed an act allowing the metrical system to be used throughout the Empire; and in

1866, Congress authorized its use in the United States, and pro vided for its introduction into post-offices for the weighing of letters and papers.

The metrical system, like Federal Money, is founded on the decimal system of notation.

After the principal unit of each denomination is determined and named, the names of the higher denominations are formed by prefixing the. Greek numerals, deka (10), hecto (100), kilo (1000), and myria (10000), to the name of the unit.

The names of the lower denominations are formed, in like manner, by prefixing the Latin numerals, deci (.1), centi (.01), and milli (.001).

MEASURES OF LENGTH.

109. The Meter is the unit for measure of lengths, and is very nearly one ten-millionth (rooooooo) part of the quadrant extending through Paris from the equator to the pole.

NOTE. The meter is equal to 39.37 inches, nearly, or a little less than 1.1 yards. It is also nearly 3 feet, 3 inches, and 3 eighths of an inch, which may be remembered as the rule of the three threes. Five meters are about one rod.

TABLE.

10 Meters, marked M. =1 Dekameter, marked D. M.