Section 4.

MULTIPLICATION.

TABLE OF PYTHAGORAS.

1 2

3

4

5 6

7 8

21

41

6

8

10

12

14

3

6

9

12

15

18

21

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 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| 6 12 18 24 30 36 42 48 54 60 66 78 84| 90 | 96| 102|108|114|120|126|132 138|144 7 14 21 28 35 42 49 56 84 91 98|105|112|119 126|133|140|147|154|161|168 8 16 24 32 40 48 56 64 96 104|112|120|128|136|144|152 160 168|176|184|192 9 18 27 36 45 54 63 72 90 | 99 108 117 126|135|144 153 162 171|180|189|198|207|216| 10 20 30 40 50 60 70 80 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 84 96 108 120 132 144|156|168|180|192|204|216|228|240|252|264 276 288 78 91|104|117 130|143 156|169|182|195|208|221|234 247 260 273|286|299|312 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 34 51 68 85 102|119 136 153 170 187|204|221|238|255|272 289|306|323|340|357 374 391 408 18 36 54 72| 90|108|126|144|162|180|198|216|234|252|270|288|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|380|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 42 63 84 105 126 147 168 189|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|506 528 23 46 69 92|115|138 161|184|207|230|253|276|299|322|345|368|391|414|437|460|483 506 529 552 24 48 72 96 120 144 168|192|216|240|264|288|312|336|360|384|408|432 456|480|504|528 552|576

13 26 39 52 65

14 28 42 56| 70

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 one 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 one 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 one 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 one 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.

B*

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. question 14.

QUESTIONS FOR THE SLATE.

See

26. Multiply 83000 by 10007. 27. Multiply 40009 by 40009.

830581000.

1600720081.

28. What cost 14 barrels of apples at 3 dollars per barrel ?

29. What cost 17 tons of hay at

Ans. 42 dollars. 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.

Ans. 2813 dollars.

32. What cost 97 oxen at 29 dollars each ?