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lasses cost 4s. 2d. 2 qrs., what lasses cost £210 8s. 4d. what

will 1000 gallons cost?

51. If one pound of tea cost 8s. 5d. 2qrs. what will 108 lbs. cost?

53. If one quintal of fish cost 23s. 9d., what will 345 quintals cost?

is it per gallon?

52. If 108 pounds of tea cost £45 13s. 6d., what will one pound cost?

54. If 345 quintals of fish cost £409 13s. 9d., what was it per quintal?

SUPPLEMENT TO COMPOUND NUMBERS.

1. What is the weight of two pieces of gold, one weighing 1 lb. 0 oz. 6 pwt. 4 grs.; the other, 2lbs. 3 oz. 8 pwt. 16 grs? Answer, 3 lbs. 3 oz. 14 pwt. 20 grs. 2. A man has one wedge of gold, weighing 25 lbs. 3 oz. 12 pwt., and another weighing 1 lb. 11 oz. 12 pwt. 7 grs. What is the weight of the two?

Answer, 27 lbs. 3 oz. 4 pwt. 7 grs. 3. A silver-smith had a quantity of silver, weighing 21 lbs. 9 oz. After refining it by melting, it weighed 15 lbs. 10 oz. 11 pwt. 19 grs. What was lost by melting?

Answer, 5 lbs. 10 oz. 8 pwt. 5 grs.

4. What is the sum and difference of 3 lbs. 10 oz., and 2 lbs. 11 oz. 7 pwt. 4 grs.

Answer, {

Sum:

71

6 lbs. 9 oz. 7 pwt. 4 grs. Difference: 10 oz. 12 pwt. 20 grs. 5. What will 13 lbs. of coffee cost at 1s. 2d. 3 qrs. per

Answer, 15s. 11d. 3 qrs.

pound? 6. What will 47 yds. of cloth cost at 17s. 9d. per yard? Answer, £41 14s. 3d.

7. How much will 10 cwt. of lead cost, at 7d. per lb. ? Answer, £32 13s. 4d. 8. What is the value of 7 cwt. of sugar, at 43d. per lb. ? Answer, £15 10s. 4d. 9. What is the weight of 4 hogsheads of sugar, each weighing 7 cwt. 3 qrs. 19 lbs. ?

Answer, 31 cwt. 2 qrs. 20 lbs. 10. Bought 12 doz. large silver spoons, each weighing 3 oz. 5 pwt.; two doz. tea-spoons, each weighing 15 pwt. 14 grs.; three silver cups, each weighing 9 oz. 7 pwt. ; two silver tankards, each 21 oz. 15 pwt.; 6 silver porrin

gers, each 11 oz. 18 pwt. What is the weight of the whole? Answer, 18 lbs. 4 oz. 3 pwt. 11. If 6 ells cost £5 17s. 6d. what will one ell cost?

?

Answer, 19s. 7d. 12. What must a man spend per month, to spend £17 14s. 6d. in a year Answer, £1 9s. 6d. 13. If 8 cwt. of cocoa cost £15 17s. 4d., what is it per pound. Answer, 4d. 1 qr. 14. If 132 bush. of oats cost £20 12s. 6d. what is the cost of 1 bushel ? Answer, 3s. 1d. 2 qr. 15. If 147 bushels of corn cost £47 12s. 5d., what does

it cost per bushel ?

16. If one acre produce 152

will a square rod produce?

Answer, 6s. 5d. 3 qr. bushels of oats, how much Ans. 3 pks. 6 qts. 1 pt.

17. How much wood in 11 piles, each containing 120 cords, 7 cord-feet, 11 solid feet?

Answer, 1330 cords, 4 cord-feet, 9 solid ft. 18. Multiply £36 12s. 6d. by 9; divide the product by 6; multiply the quotient by 4; divide the product by 12, and give the result.

19. If it take a printer 297h. 59m. 24sec. to set 108 pages, how long will it take him to set one page? Answer, 2h. 45m. 33sec. 20. A person wishes to draw a pipe of wine into bottles, containing a quart, 2 quarts, 1 pint, pint, of each an equal number; how many must he have?

When it is required to find how many times several quantities, each an equal number, may be had in a given quantity—

RULE. Reduce the given quantity to the lowest denomination mentioned for a dividend, and each of the other quantities to the same denomination, and add them together for a divisor. The quotient will be the answer. 1 quart = 8 gills. 2 quarts 16 gills. 1 pint 6 gills.

pint

=

= 2 gills.

The 1 pipe reduced to gills equals 4032 gills, and 403232-126 bottles, the Answer.

32 gills.

21. How many bushels, half bushels, and peck baskets, of each an equal number, will it take to contain 100 bushels? Answer, 57, and 8 qts. over.

QUESTIONS. 10. What is the Rule for the 20th example?

22. There are four fields, one containing 10 acres, 2 roods; another 9 acres; another 11 acres, 3 roods; another, 6 acres, 3 roods, 30 rods. How many shares, of 65 rods each? Answer, 94. 23. A man left $1043,28 to be divided as follows: His wife is to have two thirds; of the other, his sister is to have, and the remainder is to be divided between two nephews and nine distant relatives. To one nephew, he gives 3 shares-to the other, 2-to each of the relatives 1 share each. What is the share of each respectively?

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24. What will 156 acres of land cost at £5 6s. 9d. 2qr. per acre?

Answer, £832 19s. 6d. 25. A values a piece of land at $120, B at $100, C at What is the average judgment?

$110.

A 1

$120

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The average is found by dividing the sum of the several judgments by the number of judges.

$110 Answer.

26. Two gentlemen wished to exchange vehicles. One was a gig, the other was a waggon; but not being able to agree as to the conditions, referred the matter to A, B and C, who decided as follows. A said the owner of the gig should pay the owner of the waggon $20, and B. said he should pay $15; but C said the owner of the waggon should pay the owner of the gig $10. What is the average judgment? Answer,-the owner of the gig must pay $81.

In cases where the judgment of the referees is part on one side of the question, and part on the other, subtract one side from the other, and divide the remainder by the number of referees, and the quotient will be the answer.

27. A and B wish to agree upon the difference. and E, and agree to abide

H

exchange watches, but cannot They refer the matter to C, D by their decision. C gives his

opinion that A should give B $3. D thinks the difference in B's favor is $4; but E takes the other side of justice, and says B should pay A at least $1. What is the average judgment? Answer, A must pay $2.

FRACTIONS.

FRACTIONS are parts of a unit, or of a whole number. If a unit, or any particular thing, be divided into parts, these parts are called fractions. If a thing be divided into two equal parts, these parts are called halves; if into three equal parts, they are called thirds; if into four, fourths, or quarters, &c.

The dividing figure generally gives name to the parts into which a thing is divided. If the divisor be 2, the quotient will be one half of the dividend; if the divisor be 3, the quotient will be one third; if the divisor be 4, the quotient will be one fourth, &c.

Fractions are expressed by two figures, written one above the other, with a line drawn between them. The figure below the line (which is the same as the dividend in Division) shows into how many parts the integer, or whole number, is divided, and is therefore called the denominator. The figure above the line denotes the number of parts contained in the fraction, and is thence called the numerator. Thus (one half)—the figure above the line shows that one of those parts is contained in the fraction; 2, the 4 shows that the whole number is divided into four parts; and the 3, that three of these parts are contained in the fraction. If. $100 be divided into 5 parts, one of those parts will be 120 dolls; two of those parts, =40 dolls. three parts, 60 dolls. ; four parts, 480 dolls. ; and five parts, §=100 dollars.

Fractions are of two kinds-Vulgar, or common; and Decimal. They differ in the form of expression and mode of operation.

QUESTIONS. 1. What are Fractions? 2. If a thing be divided into two equal parts, what are these parts called? 3. Into four equal parts? 4. To what does the dividing figure give name? 5. How are fractions expressed? 6. What is the figure below the line called? 7. What is the figure above the line called? 8. and what does it show? 9. What does the denominator show in the fraction ? 10. The numerator? 11. Fractions are of how many kinds, and what are they? 12. In what do they differ?

In Decimal Fractions, the unit, or integer, is divided into 10, 100, 1000, &c., equal parts; or the denominator is always 1, with as many ciphers annexed as the numerator has places.

In Vulgar Fractions the integer may be divided into any number of parts, and the denominator being always expressed, may be any thing but 1, with or without a cipher or ciphers annexed.

Vulgar Fractions are either proper, improper, compound or mixed.

1. A proper Fraction is one whose numerator is less than the denominator; as 2, 3, 4, &c.

2. An improper Fraction is one whose numerator is equal to, or greater than the denominator; as, %, §, &c. 3. A compound Fraction is a fraction of a fraction; as of of 4, &c.

4. A mixed number is a whole number and fraction written together, as 23, 149, &c.

5. A common divisor, or common measure of two or more numbers, is a number which will divide each of them without a remainder-4 is the common measure of 12.

6. The greatest common divisor of two or more numbers, is the greatest number which will divide those numbers without a remainder. Thus, 12 is the greatest common

measure of 1.

7. Two or more fractions are said to have a common denominator, when the denominator of each is the same.

8. A common multiple of two or more numbers, is a number which may be divided by each of those numbers without a remainder.

9. The least common multiple of two or more numbers, is the least number, which may be divided by those numbers without a remainder. Thus, 8 is the least common multiple of 8, 4 and 2.

10. A perfect number is equal to the sum of all its aliquot parts. Thus, 6 is equal to 3×2×1=6.

QUESTIONS. 13. How is the unit divided in Decimal Fractions? 14. What is always the denominator? 15. In Vulgar Fractions, how is the integer divided? 16. What may the denominator be? 17. How are Vulgar Fractions divided? 18. What is a proper fraction? 19. An improper fraction? 20. A compound fraction? 21. A mixed number? 22. What is a common divisor, or common measure of two numbers? 23. The greatest common divisor? 24. When are fractions said to have a common denominator? 25. What is meant by a common multiple of two or more numbers? 26. The least common multiple? 27. What is a perfect number? 28. What is meant by the terms of a fraction?

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