24. Name all the products of which 12 is a factor to 144. 25. What cost 9 six-cent books? 12? 8? 26. What will 12 dozen eggs cost at a cent apiece? 27. How many days in a 9 weeks' vacation? 28. How many corners have 11 squares? 29. I pay 7 cents daily for milk. for a week? What is my milk bill 30. How many inches in 8 feet? In 9? In 11? 31. How many feet in 12 yards of ribbon ? 32. What cost 7 lbs. at 5 cents a pound, and 5 quarts at 4 cents a quart? 33. What numbers multiplied make 36? 56? 81? 96? 34. What factors produce 48? 72? 121? 63? 49? 35. At $8 a barrel, how many times $8 will 9 barrels of flour cost? 36. How many are 9 x $8? 8x $9? 3×2×2? 2 ×3×2? 2×2×3? 58. Principles of Multiplication. 1. The multiplier is always considered an abstract number. 2. The product and the multiplicand are always like numbers. 3. The product is the same whatever the order of the factors. WRITTEN EXERCISES. 37. Find the product of 274 multiplied by 7. We ones, we multiply: 7 times 4 ones are 28 ones, or 2 tens 8 ones. write the 8 ones beneath in the place of ones, and reserve the 2 tens. 7 times 7 tens are 49 tens, and 49 tens plus the 2 tens reserved are 51 tens, or 5 hundreds 1 ten. We write the 1 ten beneath in tens' place, and reserve the 5 hundreds. 7 times 2 hundreds are 14 hundreds, and 14 hundreds plus 5 hundreds reserved are 19 hundreds, or 1 thousand and 9 hundreds. We write the 9 hundreds beneath in hundreds' place, and the 1 thousand in thousands' place. The product is 1 thousand 9 hundreds 1 ten 8 ones, or 1918. 5 times 2 tenths are 10 tenths, and 10 tenths plus the 2 tenths reserved are 12 tenths, or 1 one and 2 tenths. We write the 2 tenths beneath in tenths' place, and reserve the 1 one. 5 times 4 ones are 20 ones, and 20 ones plus the 1 one reserved are 21 ones, or 2 tens and 1 one. We write the 1 one beneath in ones' place, and reserve the 2 tens; and so on. The multiplier being an integer, the product has as many decimal places as the multiplicand. ORAL EXERCISES. 55. How much will 12 coats cost at $9 each ? 56. When plows are $ 11 each, what will eight cost? 57. If 7 men can do a piece of work in 9 days, in what time will 1 man do the same work? 58. If a vessel sails at the rate of 12 miles an hour, how far will it sail in 12 hours? 59. What will 11 barrels of flour cost at $10 each? 60. How many horses will consume in one day as many bushels of oats as 11 horses consume in 12 days? 73. Give the product of the following numbers multiplied by 12; by 11; by 5; by 4. 9, 11, 3, 5, 12, 8, 2, 7, 10, 6, 4. 74. Multiply the numbers of the preceding exercise by 8; by 9; by 7; by 6, and add 3 to each product. 75. How many are 6 times 24 ? Solution. - 24 is 20+4; 6 times 20 are 120; 6 times 4 are 24; hence 6 times 20+ 4, or 24, are 120 + 24, or 144. 76. At 26 cents a yard, how many cents will 7 yards of cloth cost? 77. At the rate of 23 miles an hour, how many miles will a train of cars move in 8 hours? 78. What will 9 suits of clothes cost at $30 a suit? 79. What will 5 sewing-machines cost at $ 50 each? WRITTEN EXERCISES. 80. What is the product of 534 and 242 ? tial product; multiplying by the 4 tens, we have 2136 tens for the second partial product, which we write so that its right-hand figure shall come in the tens' column; multiplying by the 2 hundreds, we have 1068 hundreds for the third partial product, which we write so that units of the same order shall come in the same column; adding the three partial products, we have 129228 as the product required. To prove the work, since the product is the same whatever the order of the factors, we multiply the 242by the 534, and have, as before, 129228. 703 NOTE. In solution of Ex. 88, there being 0 tens in the multiplier, we pass to the hundreds of the multiplier. 59. Rule for Multiplication. Write the multiplier under the multiplicand, with a line beneath. Beginning at the right, multiply each figure of the multiplicand by each figure of the multiplier successively, placing the right-hand figure of each partial product under the figure of the multiplier that produced it. Add the partial products, and from the right of the result point off as many decimal places as are found in both factors. 60. PROOF. See if the same result is obtained by multiplying the multiplier by the multiplicand. Multiply: 89. 347 by 769. 90. 826 by 243. 91. 90.4 by 85. 92. $32.13 by 91. 97. $198.06 by 805. 98. 45.32 by 907. 99. 982.4 by 3004. 100. $60.51 by 768. 101. 87.35 by 94. 102. $ 80.42 by 832. 103. 30.69 by 907. 104. $817.42 by 358. 119. On board of a steamer there are 163 barrels of sugar, each weighing 295 pounds. What is the weight of the whole ? 120. The factors of a product are 1468 and 87; what is the product? 121. The factors of a product are 681, 507, and 12; what is the product? 122. The multiplicand is 804.51, and the multiplier 63; what is the product? 123. What number 914 08 × 64? 124. At $82.50 an acre, what is the value of 25 acres of land? |