BiLLs of PARCELs. Boston, July 18, 1826 Henry Fairdealer, Bought of Thomas Richman, 35 yards of sheeting, at 18 cents per yard. 9 “ {{ cambrick, “ 53 “ (4. ** 11 “ {{ linen, “ 42 “ 46 << 3. 4. & 4 muslin, 4% 71 44 4. << 5 silk handkerchiefs “ 92 “a piece, Received Payment, - $22,42. - Thomas Richman. JNote 4.—When the price of one unit of any quantity, is dollars and cents, we multiply it as a simple number, and point off the two right hand figures of the product, which will be cents, and those to the left, dollars. The operations in dollars and cents, will be illustrated in Decimal Fractions. New-York, July 18, 1826. John Clerk, Bought of Charles Honesty, 9 yards of Broadcloth, at $7,33 per yard, 5 “ Cassimere, “ 1,75 & 4 11 “ Camblet, “ ,78 4. 6 “ Holland, “ .30. “ 3 Waistcoat patterns, “ 1,42 14 46 Loaf {{ {{ ,23 44 Received payment by his note of the above date, $81,78 For Benjamin Tradeall, SECTION III. SUBTRACTION OF SIMPLE NUMBERS. Subtracting is taking one number from another; or taking a part from the whole. In the preceding section, the principles of adding numbers together, have been explained; in this, we shall illustrate the methods of separating them. When two or more numbers are put together, so that they may all be expressed by one number or sum, we add numbers; but when we take away a part of a number, or take one number from another, we subtract numbers. When we say, 2 put with 4, makes 6, we add 2 to the 4 ; but when we say, 2 taken from 4, and 2 remains, we subtract the 2 from 4. Subtraction is evidently the reverse of Addition. -s000eDEFINITIONS, .4 minuend is a number from which another number is to be taken ; or, a number from which a part is to be taken, of course, it must always be as large or larger than the other numbers, for we cannot take from one number, another larger than itself. A subtrahend is a number which is to be taken from another. .A remainder is a number which is left after one number is taken from another; or, it is the difference between two numbers. A remainder may equal, or be greater than the subtrahend, but never can equal the minuend. [2 taken from 5, leaves 3. Here 5 is the minuend, 2 the subtrahend, and 3 the remainder.] Let the pupil answer the following questions: What is the difference between 2 and 6 Be tween 5 and 7 ? Between 4 and 82 Between 1 and 8 * Between 2 and 87 Between 1 and 97 Be tween 2 and 97 Between 4 and 92 Between 7 and 8 * Between 3 and 82 Between 3 and 97 Between 3 and 102 Between 4 and 10 ” Between 5 and 102 Between 5 and 11 ? Between 6 and 11 ? Between 6 and 13? Between 13 and 7 ? Between I4 and 97 Between 15 and 11 ? Between 16 and 19 2 Between 17 and 21 ? How many more are 11 than 9° 19 than 152 21 than 37 29 than 24 2 28 than 232 31 than 292 Rule 1.-State the question or example by setting the subtrahend, or less number, under the larger, so that every figure may stand directly under one of its own local name; that is, units under units, tens under tens, &c. 2. Commence subtracting at the right hand, and proceed regularly to the left, setting underneath the difference between every figure of the subtrahend and that which stands directly above it in the minuend. Question 1. What is the difference between 68 and 452 Operation. TMinuend, 6 8 Illustration.—In this quesSubtrahend, 4 5 tion, 3 is the difference be- tween the 5 and 8, and the 2, Remainder, 2 3 or 2 tens, is the difference between the 4 and the 6, or 40 and 60; therefore 20 and 3, or 23, is the difference between 68 and 45. The same answer may be obtained by separating the numbers. Operation. 6 0--8=6 8 Explanation.—Here I sepa4 0–H5=4 5 rate the 8 from the 68, and the 5 from the 45. I then 2 0-H.3=2 3 subtract the 5 from the 8, and the 40 from the 60, and add the remainders together, which gives the same answer as before. 2. Required the difference between 98 and 87? - - Rem. 11. 3. How many more are 679 than 521 ? Ans. 158. 4. George has 63 marbles, and James has 52; how many has George more than James? . Ans. 11. 5. A boy went to a store with seventy-nine cents, and spent thirty-eight of them ; how many had he left 2 Ans. 41. 6. Henry had 11 apples, and gave 8 of them to Thomas; how many had he left 2 Ans. 3. 7. William said he had 35 cents; John said he had 24; how many more had William than John 7 Ans. 11. 8. A merchant sells 137 pounds of sugar from a hogshead which contains 548 pounds; how many pounds remain? Ans. 411. 9. A man gave 13 dollars to one son, and 37 to another; how many had one more than the other ? Ans. 24. 10. A man gave 5 dollars for a hat, and 19 dollars for a greatcoat; how much less did his hat cost him than his greatcoat 2 - Ans. $14. 11. What is the difference between six thousand, five hundred and thirty-nine, and four thousand, one hundred and eleven 2 Ans. 2428. 12. One man has on hand 965 dollars, another, 623 dollars less; how many dollars has the latter? Ans. $342. 13. Take 40 from 145, and what will remain? Operation. 1 4 5 - Explanation.—In this question, 4 0 there being no units in the right hand place of the subtrahend, the 1 0 5. 5 must be brought down. The number of tens in the less number, is *. to that in the larger; consequently, there is no difference, and the tens' place in the remainder must be supplied with a cipher. As there is no figure in hundreds' place in the less number, the hundred in the larger will not be lessened? 14. If you take 160 from 2375, how many will remain Ans. 2215. 15. A. merchant bought 1621 boxes of lemons; after selling eleven hundred, how many had he left? Ams. 521. 16. If a merchant buy twelve hundred and seventy-nine dollars worth of riband, and sell it for thirteen hundred and eighty-nine dollars, what does he gain } Ans. $110. Vote 1.--The gain must evidently be the difference between what he gave and what he received. RULE 2.--When the under figure is larger than the one above it, suppose 10 to be added to the upper figure, and subtract the under figure from the sum ; then add 1 to the next left hand place in the. subtrahend. 17. What is the difference between 115 and 2032? Operation. - from 12 leaves 7. In the second column, 1, or 1 ten, added to 1, makes 2, and 2 taken from 3 leaves 1. In the third column, the 1 being more than the cipher, we suppose 10 placed where the cipher is, and take 1 from it, which leaves 9. Although there is no figure under the fourth place in the minuend, because we added 10 into the third place, we must suppose 1 to be set under the 2, and subtracted from it. 18. If the greater of two numbers be 1661, and the less 446, what is the difference 2 Ans. 1215. 19. A man has in his possession $4092, but he owes $1519; how much is he worth 2 Ans. $2573. 20. By the census of 1820, Boston contained |