7. How many bushels of oats, worth of a dollar per bushel, will pay for of a barrel of flour, worth 9 dollars a barrel? Ans. 15.

8. If of an acre of land sell for 21 dollars, what will an acre sell for at the same rate? Ans. $49.

9. When potatoes are worth of a dollar a bushel, and corn of a dollar a bushel, how many bushels of potatoes are equal in value to 16 bushels of corn? Ans. 221. 10. If a man can chop 23 cords of wood in a day, in how many days can he chop 22 cords?

OPERATION.

22 =

22

4

11) 88

Ans. 8 days.

ANALYSIS. We reduce the mixed number to an improper fraction, and then divide the integer in the same manner as by a proper fraction.

11. Divide 75 by 134.

12. Divide 149 by 241.

Ans. 519.

Ans. 6.

13. A farmer distributed 15 bushels of corn among some poor persons, giving them 13 bushels apiece; among how many persons did he divide it?

14. Divide § of 320 by § of 91.

Ans. 255.

15. Bought of 7 cords of wood for of $32; how much did 1 cord cost?

Ans. $3.

16. A father divided 183 acres of land equally among his sons, giving them 45 acres apiece; how many sons had he?

Ans. 4.

CASE III.

142. To divide a fraction by a fraction.

1. How many pounds of tea can be bought for 1 of a dol lar, at of a dollar a pound?

How divide by a mixed number? Case III is what?

tained in 11 3 times as many times as 1, or 3 times 1, which is i times, which is the number of pounds that could be bought at of a dollar per pound; but is contained but as many times as }, and divided by 2 gives, equal to 1 times, or the number of pounds that can be bought at of a dollar per pound.

We see in the operation that we have multiplied the dividend by the denominator of the divisor, and divided the result by the numerator of the divisor, which is in accordance with 140 for dividing a fraction. Hence, by inverting the terms of the divisor, the two fractions will stand in such relation to each other that we can multiply together the two upper numbers for the numerator of the quotient, and the two lower numbers for the denominator, as shown in the operation. For division of fractions, we have this general

RULE. I. Reduce integers and mixed numbers to improper fractions.

II. Invert the terms of the divisor, and proceed as in multiplication.

NOTES. 1. The dividend and divisor may be reduced to a common denominator, and the numerator of the dividend be divided by the nuerator of the divisor; this will give the same result as the rule. 2. Apply cancellation where practicable.

Rule, first step. Second. What other method is mentioned ?

pressing divis

ion of fractions; it is sometimes called a complex fraction, and the process of performing the division is called reducing a complex fraction to a simple one.

We simply reduce the upper number or dividend to an improper fraction, and the lower number, or divisor, to an improper fraction, and then divide as before.

20. If a horse eat of a bushel of oats in a day, in how

many days will he eat 5 bushels?

Ans. 14.

21. If a man spend 13 dollars per month for tobacco, in what time will he spend 10 dollars?

Ans. 6 months.

What is a complex fraction?

22. How many times will 48 gallons of camphene fill a vessel that holds of of 1 gallon? Ans. 10. 23. If 14 acres of meadow land produce 32 tons of hay, how many tons will 5 acres produce? Ans. 113. 24. If 2 yards of silk cost $34, how much less than $17 will 9 yards cost? Ans. $28. 25. If of a yard of cloth cost of a dollar, how much will 1 yard cost?

26. A man, having $10, gave of his money for clover seed at $3 a bushel; how much did he buy? Ans. 2 bush. 27. How many tons of hay can be purchased for $119, at $93 per ton? Ans. 12.

PROMISCUOUS EXAMPLES.

9 6

1. Reduce,, §, and to equivalent fractions whose denominators shall be 24. Ans. 1,3, 24, 24. 2. Change to an equivalent fraction having 91 for its denominator Ans. .

3. Find the least common denominator of, 13, of 1, 2, of of 1.

4. Add 4, 7, of 14, 3, and 1.

5. Find the difference between of 67 and 8 of 45.

Ans. 1138.

6. The less of two numbers is 4756, and their difference is 1283; what is the greater number?

Ans. 48856

7. What is the difference between the continued products of

9. What number multiplied by g will produce 1825} ?

Ans. 30431.

10. A farmer had of his sheep in one pasture, in another, and the remainder, which were 77, in a third pasture; how many sheep had he? Ans. 140.

11. What will 7 cords of wood cost at of 9 dollars per Ans. $2412.

cord?

12. At of a dollar per bushel, how many bushels of apples can be bought for 57 dollars?

that

13. Paid $1837 § for 7350 bushels of oats; how much was per bushel? Ans. of a dollar. 14. If 235 acres of land cost $4725g, how much will 628 acres cost? Ans. $12601. 15. A man, owning of an iron foundery, sold of his share for $5402; what was the value of the foundery? Ans. $4055ğ. 1 of 83 is % of 7 of what number?

16. 14 less

14,7

Ans. 27.

17. A merchant bought 4 cords of wood at $34 per cord, and paid for it in cloth at § of a dollar per yard; how many yards were required to pay for the wood?

18. How many yards of cloth, of a yard wide, will line 20 yards, 1 yards wide? Ans. 34. 19. If the dividend be 3, and the quotient, what is the divisor?

20. If the sum of two fractions be §, and one of them be 20, what is the other? Ans. Fo 21. If the smaller of two fractions be 4, and their difference, what is the greater? Ans. 3. 22. If 3 pounds of sugar cost 33 cents, how much must be paid for 65 pounds?

23. If 324 bushels of barley can be had for 259 bushels of corn, how much barley can be had for 2000 bushels of corn? Ans. 2500 bushels.

24. A certain sum of money is to be divided among 5 persons; A is to have †, B, C, D, and E the remainder, which is 20 dollars; what is the whole sum to be divided?

Ans. $50.

25. What number, diminished by the difference between and of itself, leaves a remainder of 34?

Ans. 40.

26. If of a farm be valued at $1728, what is the value of the whole?