Section 4. MULTIPLICATION. TABLE OF PYTHAGORAS. 1 2 3 41 5 6 7 8 9 10 11 12 13| 2 4 6 8 24 3 6 9 6 12 18 24 30| 36 42 14| 15| 16| 17| 10 12 14 16 18 20 22 26 28 30 32 34 12 15| 18| 21| 24 27 30 33 36 39 42 45 48 51 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105|110|115|120| 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138|144 56| 63| 70| 77 84 91| 98|105|112|119|126|133|140|147|154|161|168 72 80 88 96|104|112|120|128|136|144|152|160|168|176|184|192| 81| 90 99|108|117|126|135 144|153|162|171|180|189|198|207|216 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 11 22 33 44 55 66 77 88 99|110|121 132 143 154 165 176 187 | 198 209 220 231 242 253 264 12 24 36 48 60 72 84 96 108 120 132 144 156 168|180|192|204|216|228|240|252|264|276|288| 13 26 39 52 65 78| 91|104|117 130 143|156|169 182 195 208 221 234 247 260 273 286 299 312 14 28 42 56 70 84 98|112|126 140 154 168|182|196|210|224 238 252 266 280 294 308 322 336 15 30 45 60| 75 90|105|120 135 150 165 180 195 210 225 240 255|270|285 300 315 330|345|360| 16 32 48 64 80 96 112|128|144|160 176|192|208|224|240 256 272 288|304|320 336 352 368 384 17 31 51 68 85102 119 136 153 170 187|204|221|238|255 272 2891506 323 340 357 374 391 408 18 36 54 72| 90|108|126|144|162 180|198|216|234|252|270|283 306|324|342|360 378|396|414|432| 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285|304|323|342 361|3S0|399|418|437|456| 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 21 421 63 841105|126|147|168|189 210 231 252 273 294 315 336 357 378 399 420|441|462|483|504| 22 44 66 88|110|132|154|176|198|220|242|264|286|308|330|352|374|396|418|440 462 484|506528 23 46 69 92115|138 161|184|207|230 253 276 299 322|345|368|391|414 437 460 483 506 529 552 24 48 72 961120|144|168|192|216 240 264 288 312 336 360 384 408 432 456|480 504 528 5521576 MENTAL OPERATIONS. 1. What cost three bushels of wheat at three dollars per bushel ? 2. What cost 5 barrels of flour at 6 dollars per barrel? 3. What cost 6 bushels of beans at 2 dollars per bushel? 4. What cost 5 quarts of cherries at 7 cents per quart? 5. What will 7 gallons of vinegar cost at 12 cents per quart? 6. What cost 9 acres of land at 10 dollars per acre? 7. If a pint of currants cost 4 cents, what cost 9 quarts? 8. If, in 1 penny, there are 4 farthings, how many in 9 pence ? In 7 pence? In 8 pence? In 4 pence? In 3 pence ? 9. If 12 pence make a shilling, how many pence in 3 shillings? In 5 shillings? In 7 shillings? In 9 shillings? 10. If 4 pecks make a bushel, how many pecks in 2 bushels? In 3 bushels? In 4 bushels? In 6 bushels ? In 7 bushels? In 9 bushels ? 11. If 12 inches make 1 foot, how many inches in 3 feet? In 4 feet? In 5 feet? In 7 feet? In 8 feet? In 9 feet? In 10 feet? In 12 feet? 12. If there be 9 feet in a square yard, how many feet in 4 yards? In 5 yards? In 6 yards? In 8 yards? In 9 yards? In 12 yards? 13. What cost 3 yards of cloth at 5 dollars per yard? 4 yards? 5 yards? 6 yards? 7 yards? 8 yards? 9 yards? 10 yards? 11 yards? 12 yards? 20 yards? 14. If 1 pound of iron cost 7 cents, what cost 2 pounds? 3 pounds? 5 pounds? 6 pounds? 7 pounds? 8 pounds? 9 pounds? 12 pounds? 15. If 1 pound of raisins cost 6 cents, what cost 4 pounds? 5 pounds? 6 pounds? 7 pounds? 8 pounds? 9 pounds? 10 pounds? 12 pounds? 16. In 1 acre there are 4 roods, how many roods in 2 acres? In 3 acres? In 4 acres? In 5 acres? In 6 acres? In 9 acres? 17. A good pair of boots is worth 5 dollars; what must I give for 5 pair? For 6 pair? For 7 pair? For 8 pair? 18. A cord of good walnut wood may be obtained for 8 dollars; what must I give for 4 cords? For 6 cords? For 9 cords? 19. A gallon of molasses is worth 25 cents, what is the value of 2 gallons? Of 3 gallons? Of 4 gallons? Of 5 gallons? Of 6 gallons? 20. What cost 4 quarts of milk at 5 cents a quart? and 8 gallons of vinegar at 10 cents a gallon? 21. If a man earn 7 dollars a week, how much will he earn in 3 weeks? In 4 weeks? In 5 weeks? In 6 weeks? In 7 weeks? In 9 weeks? 22. If one thousand feet of boards cost 12 dollars, what' cost 4 thousand? 5 thousand? 6 thousand? 7 thousand? 12 thousand ? 23. In 1 pound there are 20 shillings, how many shillings in 3 pounds? In 4 pounds? In 6 pounds? In 9 pounds? 24. If 3 pair of shoes buy 1 pair of boots, how many pair of shoes will it take to buy 7 pair of boots ? 25. If 5 bushels of apples buy 1 barrel of flour, how many bushels of apples are equal in value to 12 barrels of flour? The foregoing questions having been performed, it will be perceived, that' MULTIPLICATION is a compendious way of performing Addition, and that it consists of three parts; the multiplicand, or number to be multiplied; the multiplier, or number to multiply by; and the result, which is called the product. The pupil, having thoroughly committed the multiplication Table, will notice the following RULE. Place the larger number uppermost, and then set the multiplier under it, so that units may be under units, &c., and multiply by the multiplier, beginning at the unit's place and carry for tens as in addition. When the multiplier consists of more places than one, multiply each figure in the multiplicand by every figure in the multiplier, beginning with the units, and placing the first figure of each product directly under its multiplier, then add all their several products together in the same order, as they stand, and their sum will be the true product required. When there are ciphers between the significant figures of the multipliers, omit them, and multiply by the significant figures only. If there be ciphers at the right hand of the multiplier or multiplicand, they may be neglected in the operation, but their number must be affixed to the product. PROOF. Multiplication may be proved by division, or by multiplying the multiplier by the multiplicand, as in 12th and 13th questions, or by casting out the 9's, thus; cast the 9's from the multiplicand and place the remainder at the right hand of a cross, then cast the 9's from the multiplier and set the remainder at the left hand of the cross, then cast the 9's from the product, and set the remainder at the top of the cross. Multiply the numbers together on each side of the cross, and cast the 9's from their product, and if the remainder be like the number at the top of the cross, it may be presumed the work is right. See question 14. 25. Multiply 46700 by 60103. 26. Multiply 83000 by 10007. 27. Multiply 40009 by 40009. 2806810100. 830581000. 1600720081. 28. What cost 14 barrels of apples at 3 dollars per barrel? Ans. 42 dollars. 29. What cost 17 tons of hay at 18 dollars per ton? Ans. 306 dollars. 30. What cost 47 cords of wood at 7 dollars per cord? Ans. 329 dollars. 31. What cost 47 hogsheads of molasses at 13 dollars per hogshead? Ans. 611 dollars. 32. What cost 97 oxen at 29 dollars each? Ans. 2813 dollars. |