20. A laborer gave 12 days' work for 48 bushels of potatoes, worth 50 cents a bushel. What were his daily earnings?

21. A grocer sold 24 boxes of soap, each containing 55 pounds, at 10 cents a pound, and received as pay 88 barrels of apples, each containing 3 bushels. How much were the apples worth a bushel?

22. Sold 20 pounds of butter at 27 cents a pound, which exactly paid for 15 pounds of coffee. What was the price of the coffee a pound?

23. A farmer exchanged 240 bushels of corn, worth $.75 a bushel, for an equal number of bushels of barley, worth $1 a bushel, and oats, worth $.50 a bushel. How many bushels of each did he receive?

24. A farmer bought two kinds of cloth, one kind at $.75 a yard, and the other at $.90, buying twice as many yards of the first kind as of the second. He paid for the cloth, 132 pounds of butter at 40 cents a pound. How many yards of each kind of cloth did he buy?

25. A merchant bought 6 loads of oats, each load containing 22 bags, and each bag 2 bushels, worth 56 cents a bushel. He gave in payment 8 boxes of tea, each containing 24 pounds. What was the tea worth a pound?

26. How many bushels of oats at $.60 a bushel, will pay for 12 tons of coal at $7.20 a ton?

27. How many chests of tea, each containing 63 pounds, worth 87 cents a pound, must be given for 21 bags of coffee, each weighing 28 pounds, worth 37 cents a pound?

28. How many days' work, at $1.25 a day, will pay for 75 bushels of corn, at $.80 a bushel?

184. 1. If any unit, as an apple, or a yard, be divided into 2 equal parts, what is each part named? One-half. 2. If the unit be divided into 3 equal parts, what name is given to 1 of the parts? To 2 of the parts?

3. If the unit be divided into 5 equal parts, what is each part named? What name is given to 3 of the parts?

4. How many halves are there in a unit? How many thirds? Fourths? Fifths? Sixths? Sevenths?

5. If a mile be divided into 4 equal parts, what part of the whole mile is 1 of the parts? 3 of the parts?

6. What is 1 of 5 equal parts of a unit called? What are 2 of 6 equal parts called?. 4 of 10 equal parts ?

7. What is meant by 1 sixth of a unit? By 3 fourths? 8. What are 3 of the 7 equal parts of a week called? 9. Which is the smaller, one-third or one-fourth? Onefifth or one-third ?

10. Which is the greater, one-fourth or one-sixth ?

185. PRINCIPLES.-1. The LESS the NUMBER of equal parts into which a unit is divided, the GREATER is the VALUE of each part.

2. The GREATER the NUMBER of equal parts into which a unit is divided, the LESS is the VALUE of each part.

DEFINITIONS.

186. A Fraction is one or more of the equal parts of a unit. Thus, 1 half and 2 thirds are fractions.

187. A Fractional Unit is one of the equal parts into which any unit is divided. Thus, 1 fourth and 1 fifth are fractional units of fourths and fifths.

Fractional units take their name and their value from the number of parts into which the integral unit is divided.

188. A fraction is usually expressed by two numbers, called the Numerator and the Denominator, one written over the other with a line between them. A fraction written in this form is sometimes called a Common Fraction. Thus,

One-third is written | Nine-tenths

66

66

66

is written

Three-fourths

Five-sixths

Seven-eighths

Thirty-six forty-ninths " 38

189. The Denominator of a fraction shows the number of equal parts into which the unit is divided, and also indicates the name of these parts. It is written below the line.

Thus, in the fraction, 8 is the denominator and shows that the unit is divided into eight equal parts, named eighths.

190. The Numerator of a fraction shows the number of equal parts taken to form the fraction. It is written above the line.

Thus, in , 7 is the numerator, and shows that 7 of the 8 equal parts are taken, or expressed by the fraction

191. The Terms of a fraction are its numerator and denominator. Thus, 6 and 7 are the terms of the fraction 4.

Express by figures,

1. Five-ninths.

2. Seven twenty-fifths. 3. Nine-eighteenths.

6. Twenty-six forty-eighths.

7. Twenty-seven two-hundredths. Forty-three ninety-ninths.

8.

4. Twelve twentieths. 9. Sixteen one-hundred-eighths. 5. Eight thirty-sixths. [10. Fifty-five eighty-ninths.

9

32 960

20

8. 14; 4; 13; 10; 14; 3; 104.

192. Fractions are Proper or Improper.

193. A Proper Fraction is a fraction whose numerator is less than its denominator. Its value is less than a unit. Thus, t, §, and are proper fractions.

194. An Improper Fraction is a fraction whose numerator equals or exceeds its denominator. Its value is equal to, or greater than a unit. Thus, &, 4o, and 1 are improper fractions.

195. A Mixed Number is an integer and a fraction united. Thus, 125 is equivalent to 12+§.

196. The Reciprocal of a number is 1 divided by that number. Thus, the reciprocal of 9 is 1÷9=1; of 16, it is 1÷÷16, etc.

197. The Reciprocal of a Fraction is 1 divided by that fraction, or it is the fraction inverted. Thus, the reciprocal of is 1÷÷2=4; of √, it is 12.

198. The Value of a fraction is the quotient of its numerator divided by its denominator. Thus, 12=4.