Ans. 3156. 2478. 1933. 2035. 307. (30.) What is the sum of 678, 947, 652, 879? (31.) What is the sum of 704, 685, 770, 319? (32.) What is the sum of 648, 309, 214, 762 ? (33.) What is the sum of 218, 917, 653, 247? (34.) What is the sum of 414, 702, 315, 876? (35.) In 5 canal-boats, the 1st is loaded with 27649 pounds; the 2d with 31074 pounds; the 3d with 34640 pounds; the 4th with 33071 pounds; the 5th with 30720 pounds. Required the number of pounds in the 5 boats. Ans. 157154 pounds. (36.) The collector in this place received of A. 421 dollars; of B. 670 dollars; of C. 429 dollars; of D. 50 dollars; of E. 540 dollars; of F. 601 dollars. Required the whole Ans. 2711 dollars. amount ? (37.) There are 60 seconds in one minute; how many seconds are there in 5 minutes? Ans. 300 seconds. (38.) A country merchant purchased in New York 2741 pounds of coffee, 478 pounds of loaf-sugar, 47 pounds of black tea, 321 pounds of green tea, 250 pounds of iron, 229 pounds of cut-nails, 640 pounds of salt; required the number of pounds. Ans. 4706 pounds. (39.) One half of a farm is worth 15678 dollars; how. much is the whole farm worth? Ans. 31356 dollars. (40.) If you should commence a journey and travel 7 days, the first day 32 miles, and then increase 1 mile every day, how many miles would you travel in the 7 days? . Ans. 245 miles. (41.) A gentleman near Cincinnati (Ohio), who owns an extensive plantation, raised in one season 4780 bushels of wheat, 2070 bushels of rye, 7892 bushels of corn, 3879 bushels of oats, 1500 bushels of turnips, 2798 bushels of potatoes, 640 bushels of buckwheat, 5 bushels of cloverseed, and 7 bushels of flaxseed; how many bushels did the plantation produce in one year? Ans. 23571 bushels. (42.) Add together 6079, 30, 4789, 607, 52, 8496. Ans. 20053. (43.) Add together 31, 47, 608, 9742, 39, 78965. Ans. 89432. (44.) Add together 7, 92, 87, 640, 5617, 87954. Ans. 94397. (45.) Add together 96145, 3045, 281, 79, 84, 9. Ans. 99643. (46.) A. has six hundred and forty-eight sheep; B. has nine hundred and eighty-seven; C. has fourteen hundred and ninety-one; D. has two thousand: how many sheep in all four of the flocks? Ans. 5126 sheep. (47.) A merchant purchased of D. 642 barrels of flour, for which he paid 4792 dollars; of G. 783 barrels, for which he paid 5380 dollars: how many barrels of flour did he purchase, and how much did he pay Ans. 1425 barrels, and paid 10172 dollars. 1. SUBTRACTION is the second primary rule in Arithmetic, and is the reverse of Addition. 2. It teaches to take a less number from a greater of the same name or kind, and to show their difference, or remainder. 3. There must always be two given numbers in subtraction. 4. The larger number is called the minuend, and the less the subtrahend. 5. The difference between those two numbers is called the remainder.. 6. The sign (-) which is called minus or less, when placed between two numbers, signifies that the number on the right is to be subtracted from the number on the left. 7. Thus 10-5=5 remainder; that is, 5 subtracted from 10 will leave 5, and this is the difference, or remainder. 8. If you have 10 dollars, and should pay a debt of 5 dollars, you would have 5 remaining, because 5+5=10. REVIEW. 1. Which is the second primary rule? What is it the reverse of? 2. What does it teach? 3. How many numbers must be given? 4. What are they called? 5. What is the difference called? 6. What is the sign, and what does it signify? 7. Explain this operation. 8. If you take 5 from 10, why would 5 remain? 234567 2-2-0 4-4=0] 6-6=0 8-8=0|10-10=0| To read the table, say 1 from 2 and 1 remains; 1 from 5 and 4 remain. Exercises. If 3 be taken from 8, how many will be left? 2 from 7? 7 from 9? 5 from 9? 4 from 9? 2 from 9? 6 from 9? 8 from 9? 2 from 8? 4 from 8? 3 from 8? 6 from 8? 7 from 8? 1 from 7? 4 from 7? 3 from 7? 5 from 7? 7 from 10? 9 from 11? 7 from 12? 5 from 12? 4 from 11? 6 from 12? 7 from 13? 8 from 14? 9 from 13? 10 from 14? 9 from 15? 11 from 16? 8 from 16? 9 from 15? 9 from 20? 11 from 20? 12 from 18? 11 from 19? 13 from 15? 11 from 17? 12 from 15? 11 from 13? 7 from 19? Take 7 from 12 and 2 from the remainder. RULE I. 1. Write down the greatest number first, then write the less number directly under it, observing to place units under units, tens under tens, &c.; draw a line underneath. 2. Begin with the units, or right-hand figure, and subtract that figure from the figure over it, and set down the difference. 3. When the figure in the lower number is more than the one above it, subtract from 10, and the difference between that figure and 10 must be added to the figure in the upper number; then set down that figure. 4. When you subtract from 10, carry 1, and add it to the next left-hand figure. 5. Proceed in this manner with all the figures, and the number thus obtained will be the difference between the two given numbers. RULE II. 1. After stating the sum as above directed, then, if either of the lower figures be greater than the upper one, conceive 10 to be added, or add 10 to the upper figure; then take the lower figure from it, and set down the remainder. 2. When 10 is thus added to the upper figure, there must be 1 added to the next lower figure. PROOF. Add the remainder, or difference, to the less number, and their sum will be equal to the greater number. REVIEW. 2. 1. How will you write numbers in Subtraction? Where do you begin to subtract? 3. When the figure in the lower number is more than the one above it, how will you proceed? 4. When you subtract from 10, or borrow, what must be done? 5. What next? RULE 2: 1. How can you subtract by this rule? 2. When 10 is added to the upper figure, what must be done? Proof. Take 13 from 24, and 3 from the remainder. (1.) 8407 minuend. 7325 subtrahend. 1082 remainder. S407 proof. Examples. Explanation.-Begin in the place of units with 5, and say 5 from 7 and 2 remain, which set down; then 2 from 0 you can not, but 2 from 10 and 8 will remain, set this down; now there is 1 to carry to the next figure on the left, 3, which added to it will make 4; then 4 from 4 and 0 remain; then 7 from 8 and 1 remain. This last number, 1082, is the difference in value between the two numbers above the line, minuend and subtrahend: because if we add this remainder, or difference, to the subtrahend, the number subtracted from the minuend, it will produce that number; therefore, draw a line under the remainder and add it to the subtrahend. Thus 2 and 5 are 7, 8 and 2 are 10, set down 0, and carry 1 to 0 is 1, and 3 are 4, 1 and 7 are 8=8407 proof: the same as the minuend. |