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114. If 1 hogshead [63 gal.] of molasses cost $26, what is the cost of 1 gallon ?
115. What is the cost of 7 hhd. 6įgal. molasses, at 114 cents per gallon ?
116. What is the cost of 25 yards 3] quarters of ribbon, at 191 cents per yard ?
117. If 54 cords of wood cost $26], what is the cost of 1 cord ?
118. What is the value of 16 s tons of hay, at 11 dollars per ton?
119. What is the value of 1 lb. 6 oz. 12 dwt. of silver, at 204 cents per pennyweight?
120. If 16 yards of broad-cloth cost $86.24, what is the cost of 1 yard ?
121. At 5s. 31d. per yard, what is the cost of 783 yards of cambric, in pounds, shillings, and pence?
122. If 4923 yards of cloth cost £68 4s. 10d., what is the cost of 1 yard ?
123. If 183 yards of cotton cost 12 s. 9 d., what is the cost of 1 yard?
124. What is the value of 57682lb. of coffee at 10% pence per pound ?
125. At what price per pound must I sell 432 1 pounds of coffee, in order to receive £27 3s. for the whole ?
126. If £4437 be equally divided among 76 men, what will each man receive ?
127. If of a yard of cloth cost $3, what is the price of 1 yard ?' Or, $3:4=?
128. If 712 barrels of apples cost $ 21į, what is the cost of 1 barrel of the apples ?
129. If 47 gallons of molasses cost $25, what is the cost of 1 quart?
130. If ik hogshead of wine cost $250 }, what is the cost of 1 quart?
131. Bought 5 yards of silk, at $24 per yard; 151 yards of ribbon, at 12 cents per yard; 17 pairs of gloves, at 684 cents per pair; and 161 yards of lace, at $35 per yard. What is the whole cost?
132. Bought 64 pounds of tea, at 87 } cents per pound; 15 1 pounds of sugar, at 112 cents per pound; 131 pounds. of coffee at 12 cents per pound; and 162 gallons of molasses, at of a dollar per gallon. What is the whole cost?
133. Bought 91 barrels of cider, at $2} per barrel; 8 barrels of apples, at $ 15 per barrel; 16 boxes of raisins, at $ 2.62 per box; 23. pounds of almonds, at 14cents per pound. What is the whole cost ?
134. Bought 358 1 bushels of wheat, at of a dollar per bushel; 420 bushels of rye, at 96 } cents per bushel; 1461 bushels of corn, at z of a dollar per bushel; and 651. bushels of oats, at 23 z cents per bushel. What is the whole cost?
135. A purchased of B, 75ā tons of iron at $ 9.611 per ton. What quantity of coffee, at 12 cents per pound, must A sell B, to cancel the price of the iron?
136. C purchased of D, 1397 hogsheads of molasses, at 15 cents per gallon; and D, at the same time, purchased of C, 8964 tons of iron, at $9} per ton. How inuch was the balance, and to whom was it due ?
137. What is the sum of 11, 12, ý, 24, 1, ii, ii, $, §, 7, 46, 37, and To of ?
138. Suppose jo of 6 of 14 to be a minuend, and of of of a subtrahend; what is the remainder?
139. What is the product of į of of of 100, multiplied by of ã of of of 75 ?
140. What is the quotient of of į of 18, divided by } of já of of of ?
141. Suppose the sum of two fractions to be, and one of the fractions to be ; what is the other ? (See PROBLEM I, page 20.)
142. Suppose the greater of two fractions to be i, and their difference to be 23 ; what is the smaller fraction ? (See PROB. II, page 20.)
143. Suppose the smaller of two fractions to be 4, and their difference to be ; what is the greater fraction ? (See PROB. II1, page 21.)
144. What are the two fractions, whose sum is 93, and whose difference is ? (See PROB. IV, page 21.)
145. If 43. be the product of two factors, one of which · is 'í , what is the other ? (See PROB. v, page 21.).
146. Suppose , to be a dividend, and a quotient; what is the divisor? (See PROB. Vi, page 21.)
147. What must be that dividend, whose divisor is 25 and whose quotient is ž? (See PROB. Vii, page 22.)
148. Suppose the product of three factors to be he's one of those factors being á, and another iz ; what is the the third factor? (See Prob. VIII, page 22.)
149. A merchant owning 1 of a ship, sold of what he owned. What part of the whole ship did he sell ?
150. A merchant owning ji of a ship, sold of what he owned. What part of the ship did he still own ? '
151. If I buy of of a ship, and sell of what I bought, what part of the ship shall í have left?
The kind of fractions, which have been treated in this article, are called Vulgar fractions, or Common fracions, in distinction from another kind, called Decimal fractions, or simply Decimals.
DECIMAL FRACTIONS. A DECIMAL FRACTION is a fraction whose denominator is 10, or 100, or 1000, &c. The denominator of a decimal fraction is never written: the numerator is written with a point prefixed to it, and the denominator is understood to be a unit, with as many ciphers annexed as the numerator has places of figures. Thus, .5 is Bo, .26 is 106,
.907 is 100%;
When a whole number and decimal fraction are written together, the decimal point is placed between them. Thus, 68.2 is 631 , 4.37 is 4107.
In the notation of whole numbers, any figure, wherever it may stand, expresses a quantity to as great as it would express if it were written one place further to the left: and so it is in the notation of decimal fractions—the same system is continued below the place of units. The first place to the right of units is the place of tenths; the second,
of hundredths; the third, of thousandths; the fourth, of ten-thousandths; and so on.
Ciphers placed on the right hand of decimal figures, do not alter the value of the decimal; because, the figures still remain unchanged in their distance from the unit's place. For instance, .5, .50, and .500 are all of equal value, — they are each equal to 1. But every cipher that is placed on the left of a decimal, renders its value ten times smaller, by removing the figures one place further from the unit's place. Thus, if we prefix one cipher to .5, it becomes .05 ; if we prefix two ciphers, it becomes .005 (166]; and so on.
TO READ DECIMAL FRACTIONS— Enumerate and read the figures as they would be read if they were whole numbers, and conclude by pronouncing the name of the lowest denomination. 1. Read the several numbers in the following columns.
.2008 4.008 24.09 .064 .00006 6.37002 630.1174 .0003 .03795 .99999 6 .972479
.5237 .130009 5.0001 28.797 2. Write in decimals the following mixed numbers.
1810 21250 331% Stobbo 24766 326 13 812000 47 100000 3810c 71 do · 97 1060 612560 6510000 . 191346o 6102506 551060%600
2 51 10000
1000 12 51 10000
ADDITION OF DECIMALS.,
3. Add the following numbers into one sum. 151.7 +70.602+4.06+807.2659.
151.7 1 In arranging decimals for addition, 70.602 we place tenths under tenths, hun
4.06 dredths under hundredths, &c. We 807.2659 then begin with the lowest denomi1033.6279
nation, and proceed to add the columns as in whole numbers.
4. What is the sum of 256.94 +9121.7 +8.3065 ?
5. Add together.6517 + 19.2+ 2.8009 +51.0007 + .00009+22.206+4.732. .
In Federal Money, the dollar is the unit; that is, dol. lars are whole numbers; dimes are tenths, cents are hundredths, and mills are thousandths.
6. Add together $18.25, $4.09, $2.40, $231.075, $ 64.207, $ 50.258, $10.09 and 25 cts.
7. Write the following sums of money in the form of decimals, and add them together. $1 and 1 cent, 37 cents, $25 and 7 dimes, 65 cents, $15, 9 dimes, 8 mills, 4 cents and 3 mills, i of a mill, $ 7 and 8 cents, t of a mill, 364 cents, 10 eagles and 25 dollars, and 7 cents.
SUBTRACTION OF DECIMALS. 8. Subtract 4.16482 from 19.375. 19.375 .. . After placing tenths under tenths, 4.16482 1 &c., we subtract as in whole num
The blank places over the 2
I and 8 are viewed as ciphers. 9. Subtract 592.64 from 617.23169. 10. Subtract 48.06 from 260.3. 11. Subtract .89275 from 12690.2. 12. Subtract .281036 from 51. 13. What is the difference between 1 and .1? 14. What is the difference between 24.367 and 13 ? 15. What is the difference between .136 and .1295 ?
16. Write 8 dollars and 7 cents in decimal form, and subtract therefrom, 48 cents and 1 mill.
17. Subtract 9 dimes and 6 mills from 15 dollars. '
MULTIPLICATION OF DECIMALS. Multiplying by any fraction, is taking a certain part of the multiplicand for the product; consequently, multiply. ing one fraction by another, must produce a fraction smaller than either of the factors. For example, 4 X
=100; or, decimally, .4%.3=.12. Hence observe, · that the number of decimal figures in any product, must
thalosi or, dether of the other,