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21 41 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
3 6 9 12 15 181 21 24 27 30 33 36 39| 42| 45 48 51 511 571 60 63 66 69 72
41 8 12 16 20 24 28 32 361 401 44 43 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 72|7884 90 96 102|108 114 120126|132|138|144
71 14 21 29 35 42 40 36! 631 701 77 841 911 98|105/112 119|126|133 140|147|154/161|168
8 16 24 32 40 48 56 641 72 80 381 96 104|112|120128|136|144 152|160|168|176|184|192
9| 181 271 36| 451 511 631 721 81 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|160170|150|190/200 210220/230|240
11 22 33 44 55 66 77| 88 99|110|121132|143|154 165 176|187|198|209|220 231242 253

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14| 28 42 561 70 841 98|112|126/140|154|168|182|196/210/224|238|252 266|250294308322 336
15! 301 45 60 75 90 105 120135|150|165|180195/ 210|225/240/255270/285 300|315/330 345|360
16 32 48 64 80 96/112|128|144|160|176/192/208221|240 256 272 288|304|320336|352|368,384
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TABLE OF PYTHAGORAS.

MULTIPLICATION.

Section 4.

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, foc., 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 I’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.

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Answers. 17. Multiply 767853 by 9.

6910677. 18. Multiply 876538765 by 8.

7012310120. 19. Multiply 7654328 by 7.

53580296. 20. Multiply 4976387 by 5.

24881935. 21. Multiply 8765448 by 12.

105185376. 22. Multiply 4567839 by 11.

50246229. 23. Multiply 68759 by 5678.

390413602. 24. Multiply 78113 by 70005.

5468300565. 25. Multiply 46700 by 60103.

2806810100. 26. Multiply 83000 by 10007.

830581000. 27. Multiply 40009 by 40009.

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.

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