Hence, to multiply a whole number by 10, we annex one cipher to the multiplicand; to multiply by 100, we annex two ciphers; to multiply by 1,000, we annex three ciphers; and so on. Thus, 75 x 10 = 750; 34 × 100 = 3,400; 87 x 1000 87,000. If the significant figure of the multiplier followed by ciphers is greater than 1, we first multiply by the significant figure or figures, and then annex the ciphers. Multiply 317 by 300. EXPLANATION. We multiply 317 by 3, which gives 951, and to this we annex two ciphers, as shown in the illustration. ILLUSTRATION. 317 300 95100 Multiply 406 by 400. 9. 516 by 800. 10. 217 by 2000. 4. 4,175 by 80. 5. 874 yds. by 300. 6. $841 by 70. 13. 927 by 1200. 7. 8,888 by 3,700. 14. 561 by 2,050. If both factors terminate in ciphers, multiply the significant figures, and to the result annex as many ciphers as there are at the right of both factors. Multiply 8900 by 9000. EXPLANATION.-Here we multiply 89 by 9, which gives 801, and to the result we annex five ciphers as shown in the illustration. ILLUSTRATION. 8900 9000 80100000 One cipher annexed to a number moves each digit how many places to the left? This is the same as multiplying by what number? How do you multiply by 10? How by 100? How by 1,000? When the multiplier is a significant figure followed by one or more ciphers how do you multiply? 64. A composite number is one that can be separated into other integral factors than itself and one. Thus, 6 is a composite number, because it can be separated into the factors 2 and 3. NOTE.-Scholars should be carefully taught to distinguish between factors of a number and parts of a number. Any number is the sum of its parts, but the product of its factors. EXERCISES FOR ORAL WORK. Separate into two factors each of the following numbers: . (1.) (2.) (3.) (4) (5.) (6.) (7.) (8.) (9.) (10.)` 10, 15, 21, 14, 22, 25, 26, 32, 40, 42. Separate into three factors each of the following numbers: (11.) (12.) (13.) (14.) (15.) (16.) (17.) (18.) (19.) (20.) 8, 12, 16, 24, 27, 30, 36, 48, 56, 45. To multiply by a composite number, we may multiply by each of its factors in succession. Thus, to multiply 118 by 24, we may multiply 118 by 6, which gives 708, and then multiply the result by 4, which gives 2,832; this is the required product. In the same manner multiply the following EXAMPLES. 21. Multiply 78 by 48, (6 × 8). 28. Multiply 15 × 18 by 16 × 12. The product of more than two factors is called a Continued Product. Thus, in example 27, the number 1,680 is the continued product of 8, 5, 7, and 6. What is a composite number? How do you multiply by the factors of a composite number? What is a continued product? 65. 1. What will 7 hundred pounds of sugar cost at $9 a hundred? $9 × 7 = how many dollars? 2. 4 quarters make 1 yard; how many quarters in 8 yards? 4 times 8 equals how many? 3. If a man earn $7 a week, how much will he earn in 10 weeks? How much in 12 weeks? 4. How many yards of cloth in 7 pieces, each piece containing 10 yards? How many in 8 pieces? 5. What will 5 barrels of flour cost at $8 a barrel ? FOR WRITTEN WORK. 6. What will 38 barrels of flour cost at $13 a barrel ? Ans. $494. 7. What is the cost of 675 lbs. of cheese at 14 cents a pound? At 12 cents a pound? At 11 cents a pound? 8. A farmer sold 211 bushels of potatoes at 74 cents a bushel; how much did he receive? 9. What is the cost of 786 quarts of milk at 9 cents a quart? What at 10 cents a quart? 10. If $1 will buy 21 tickets, how much will $37 buy? FOR ORAL WORK. 66. 1. In one yard there are 3 feet; how many feet in 12 yards? In 9 yards? In 7 yards? In 11 yards? 2. How many feet in 6 yards and 2 feet? In 7 yards and 2 feet? In 6 yards and 1 foot? 3. If one quarter of a yard of beaver cloth costs $2, what will 1 yard cost? What will 2 yards cost? 4. If 4 bushels of wheat make one barrel of flour, how many bushels will be required to make 9 barrels ? 5. A gentleman bought 10 yards of silk at $2 a yard, and 6 pairs of stockings at 50 cts. a pair; how much should he pay for the goods? 6. If $1 will FOR WRITTEN WORK. buy 4 lbs. of butter, how many pounds will $82 buy? How many lbs. will $37 buy? 7. If $1 will buy 8 lbs. of sugar, how many pounds will $17 buy? How many will $13 buy? 8. There are 3,600 seconds in 1 hour; how many seconds are there in 24 hours, or 1 day? 9. How many seconds are there in two days? 10. If a chest of tea contains 64 lbs. and each pound is worth 70 cents, what will be the value of 18 chests? 11. A drover bought 74 head of cattle at $82 a head, and sold the lot for $7,500; how much did he make? FOR ORAL WORK. 67. 1. 10 decimeters make 1 meter; how many decimeters make 6 meters? 2. 10 centimeters make one decimeter; how many centimeters in 8 decimeters? 3. 10 millimeters make one centimeter; how many millimeters make 9 centimeters? 4. On a chess-board there are eight rows of squares and eight squares in each row; how many squares are there on the board? 5. Two men start from the same place and travel in opposite directions; one travels 2 miles an hour, the other travels 3 miles an hour; how far apart will they be at the end of 5 hours? 6. Two men start from the same place and travel the same way; one travels 2 miles an hour and the other 3 miles an hour; how far apart will they be at the end. of 8 hours? 7. Bought 3 meters of linen at $2 a meter, 7 meters of silk at $3 a meter, 5 meters of ribbon for $4, some crape for $2, and gave the merchant 4 ten-dollar bills; how much change should I receive back? FOR WRITTEN WORK. 8. A farmer has 3 flocks of sheep, numbering respectively 50, 60, and 75 head, and each sheep yields 4 lbs. of |