1 times 8 is 4 are 20 8 4. times 8 are 32 94 times 9 are 36 7 times 10 4 times 10 are 40 7 times 10 are 70 11 4 times 11 are 44 7 times 11 are 77 12 4 times 12 are 48 7 times 12 are 84 05 times 0 are 08 times 0 are 2 5 times I are 58 times 1 are 4 5 times 65 times 85 times 0 8 7 times 8 are 56 9 are 63 2 are 10 8 times 2 are 16 3 are 24 8 times 4 are 32 60 3 times 0 are 06 times 0 are 3 times 1 are 3 6 times 3 times 2 are 6 6 times 3 times 3 are 96 times 3 times 4 are 12 6 times 3 times 5 are 15 6 times 3 times 6 are 18 6 times 3 times 7 are 21 6 times 3 times 8 are 24 6 times 3 times 9 are 27 6 times 3 times 10 are 30 3 times 11 are 33 2 are 4 are 36 5 are 45 6 are 54 7 are 63 8 are 72 9 are 81 6 times 10 are 60 9 times 10 are 90 6 times 11 are 66 9 times 11 are 99 3 times 12 are 36 6 times 12 are 72 9 times 12 are 108 10 times 0 are 10 times 1 are 10 times 2 are 10 times. 3 are 10 times. 4 are 10 times 5 are 10 times 6 are 10 times 7 are 011 times 0 are 1011 times 1 are 2011 times 2 are 3011 times 3 are 4011 times 4 are 50 11 times 5 are 6011 times 6 are 7011 times 7 are 80 11 times 8 are 012 times 0 are 0 1112 times 1 are 12 22 12 times 2 are 24 33 12 times 3 are 36 44 12 times 4 are 48 55 12 times 5 are 60 66 12 times 6 are 72 77 12 times, 7 are 84 90 11 times 9 are 8812 times 8 are 96 9912 times 9 are 108 10 times 8 are 10 times 9 are 10 times 10 are 100 11 times 10 are 110 12 times 10 are 120 10 times 11 are 11011 times 11 are 121 12 times 11 are 132 10 times 12 are 120 11 times 12 are 132 12 times 12 are 144 QUESTIONS SHOWING THE USE OF THE TABLE. 9x 8 how many ? many ? 7x 8 how = 1x6x 9= = how many ? 1x9x12 how many? 5×2×11= how many? 7x1×12= how many ? 9x1x 9= how many? 11x1x 7 how many? 12x1x 5 how many? 1x2x 3= how many? 1x4x 5 how many ? 2×6× 5 how many? 3x4x 9 how many? 4×3×11= how many? 5×2× 9 how many? 6×2× 5= how many 1. What is the cost of 7 pounds of butter at 12 cents a pound? ? = 2. What is the cost of 12 pounds of tea at 6 shillings 'a pound? 3. What is the cost of 12 pounds of coffee at 9 cents a pound? 4. What is the cost of 11 yards of cloth at 6 dollars a yard? 5. What is the cost of 9 books, at 11 cents each? 6. What is the cost of 12 pencils at 8 cents apiece? 7. What is the cost of 10 pairs of shoes at 2 dollars a pair? 8. What is the cost of 12 pairs of stockings at 3 shillings a pair? 9. What is the cost of 11 hens at 12 cents apiece? 10. What is the cost of 12 inkstands at 12 cents apiece? 11. What is the cost of 9 pairs of shoes at 10 shillings a pair? 12. What is the cost of 9 chairs at 6 dollars apiece? 13. What is the cost of 7 yards of cloth at 8 dollars a yard? 14. What is the cost of 9 handkerchiefs at 7 shillings apiece? 15. How many dollars must I pay for 9 yards of cloth at 8 dollars a yard ? 16. If 5 bushels of wheat make one barrel of flour, how many bushels will it take to make 8 barrels ? 17. There are nine rows of apple-trees in a field, and 11 apple-trees in each row: how many apple-trees are there in the field? 18. If I can earn 5 dollars in one month, how much can I earn in 3 months? In 4? In 5? In 9? In 11? In 12? 19. If a father gathers 12 bushels of corn in a day, and his son 8, how much would each gather in 3 days? In 5? In 7? In 9? In 10? In 12? 20. A man hires a horse and sleigh; he pays 12 cents a mile for the horse, and 7 cents for the sleigh: after riding 12 miles how much must he pay for them both? 21. If a man eats 11 ounces of bread in a day, and his wife 9, how much will each eat in 11 days? How much will they both eat in that time? 22. Jane bought 12 yards of riband at 8 cents a yard, and Mary 11 yards at 7 cents a yard: how much did each pay, and how much was paid by both of them? 23. A merchant bought 7 pieces of cloth, each containing 12 yards; and 9 other pieces, each containing 11 yards; how many yards in each lot, and how many yards in all ? 24. What is the product of 3 tens multiplied by 5? Of 6 tens multiplied by 2? 25. What is the product of one unit of the third order multiplied by 2? By 3? By 4? 26. A man buys 12 sheep at 3 dollars apiece, and sells them at 2 dollars apiece: how much does he lose? 27. John bought 6 tops at 8 cents apiece, 3 knives at 30 cents each, and 11 quills at a penny a piece: what did he pay for all? 28. A merchant bought 8 packages of penknives, each package containing 12 knives; 9 other packages, each containing 11 knives, and 7 other packages, each containing 5 knives: how many knives in each package, and how many in all of them? EXAMPLES ILLUSTRATING PRINCIPLES. 22. Let it be required to multiply 4 by 3, and also to multiply 5 by 3. From these examples we see, that the product of 4 multiplied by 3 is 12, the number which arises from adding three 4's together; and that the product of 5 by 3 is equal to 15, the number which arises from adding three 5's together. We see from the above examples, that any product may be found by setting down the multiplicand as many times as there are units in the multiplier, and adding all the numbers together. MULTIPLICATION is therefore a short method of addition. 22. How may any product be found? How then may multiplication be considered? 23. Let it be required to multiply 236 by 4, It is required to take 236, 4 times. Now 236 is made up of 6 units, 3 tens, and 2 hundreds, and the units of each order must be taken 4 times. First, set down the 236; then write the 4 under the units' place and draw a line beneath it. Next, multiply the 6 by 4: the product is 24 units; set them down. Then multiply the 3 tens by 4: the product is 12 tens; set down the 2 in the tens' place, leaving the 1 to the left, in the place of hundreds. Next multiply the 2 by 4: the product OPERATION. 236 4 24 units. 12 tens. 8 hundreds, 944 Product. OPERATION. 236 8, which being hundreds, is set down under the 1. The sum of these numbers, 944, is the entire product. The product can also be found thus: say 4 times 6 are 24: set down the 4, and then say, 4 times 3 are 12 and 2 to carry are 14: set down the 4, and then say, 4 times 2 are 8 and 1 to carry are 9. Set down the 9, and the product is 944 as before. 4 944 Hence, we see that, if units of any order be multiplied by simple units, the unit of the product will be of the same order as that expressed by the figure of the multiplicand. 24. Let it be required to multiply 506 by 302. In this example, we say, 2 times 6 are 12; then set down the 2, and say, 2 times 0 are 0 and 1 to carry make 1. Then say, 2 times 5 are 10. Then beginning with the 0, we say, 0 times 6 is 0: set down the 0. Then say, OPERATION. 506 .302 1012 000 1518 152812 0 times 0 is 0, and 0 times 5 is 0. 23. If the number 236 be multiplied by 4, how many times is it to be taken? How many times is each order of units to be taken? If units of any order be multiplied by simple units, what is the order of the units of the product? |