EXPLANATION. - The ciphers at the right of the partial products may be omitted, the significant figures occupying their proper places without the ciphers. 264 142 528 1056 264 37488 Thus, in multiplying by 4 tens, the lowest order in the product is tens; hence the first figure of the product is written under tens, and the rest in their proper order. In multiplying by hundreds, the lowest order of units in the product is hundreds; hence the first figure of the product is written under hundreds, and the rest in their proper order. RULE. Write the multiplier under the multiplicand, with units under units, tens under tens, etc. Multiply each figure of the multiplicand by each significant figure of the multiplier successively, beginning with units. Place the right-hand figure of each product under the figure of the multiplier used to obtain it, and add the partial products. Review the work, or multiply the multiplier by PROOF. the multiplicand. correct. If the results agree, the work is probably When there is a cipher in the multiplier, multiply by the significant figures only, taking care to place the first figure in the product under the figure of the multiplier used to obtain it. 80. B sold 17 firkins of butter, each firkin containing 56 M pounds, at $.38 a pound. How much did he receive for it? 81. The earth moves in its orbit 19 miles in a second; how far does it move in 60 seconds, or 1 minute? How far in 60 minutes, or 1 hour? 82. Two steamers start from the same place and sail in opposite directions, one at the rate of 18 miles an hour, and the other at the rate of 15 miles an hour. How far will they be apart in 39 hours? 83. Two ships are 7483 miles apart, and are sailing towards each other, one at the rate of 46, the other at the rate of 53 miles a day. How far will they be apart at the end of 73 days? Finding 84. I bought 156 barrels of flour for $1015. 32 barrels of it worthless, I sold the remainder at $9 a barrel. Did I gain or lose, and how much? 85. In an orchard there are 117 rows of trees, and each row contains 69 trees. How many trees are there in the orchard? 86. A freight train consists of 26 cars; each car contains 82 barrels of flour, and each barrel of flour weighs 196 pounds. How many pounds of flour in the entire cargo? 87. Mr. Burns earns $37.60 a week. His expenses are $19.50 a week. How much can he save in 26 weeks? 88. It requires 1972 pickets to fence one side of a square lot. How many pickets will be required to fence 17 lots of the same size and shape? 89. I sold from my farm 270 bushels of wheat at $.98 per bushel, 300 bushels of corn at $.55 per bushel, 175 bushels of oats at $.35 per bushel, and 60 bushels of potatoes at $.45 per bushel. What was the value of the crops sold from the farm? STAND. AR. - -5 90. A lady bought at a store 12 yards of silk at 87 cents a yard, 36 yards of ribbon at 15 cents a yard, and 17 yards of muslin at 8 cents a yard. She gave the clerk a 20dollar bill to pay for it. How much change should she receive? 91. A has $65, B has three times as much as A, and C has as much as both, lacking $25. How much have they all? 92. I bought 80 tons of coal at $3.25 a ton, and paid freight amounting to $13.75. I sold 55 tons for $3.80 a ton, and the balance for $3.95 a ton. How much did I make on the coal? 93. Mr. Hughes sold a farm of 160 acres at $97.50 per acre, and received in payment a note for $3765.27, and the rest in cash. How much cash did he receive? 94. A dealer bought 700 bushels of wheat at $.95 a, bushel. He sold 256 bushels at $1.10 a bushel, 44 bushels at $1.15 a bushel, and the remainder for $394. How much did he gain on the entire sale? 95. A speculator bought 640 acres of land at $20 an acre. He sold at one time 350 acres at $25 an acre; at another time 150 acres at $28 an acre. What must he receive for the remainder to gain $4500 on the purchase? 96. A farmer who raised 1160 bushels of oats kept 75 bushels for seed, and enough to winter 12 horses, allowing 45 bushels to each horse, and sold the remainder. How many bushels did he sell? 97. A cloth merchant sold three lots of cassimeres, the first containing 19 pieces of 28 yards each, at $1.75 per yard; the second containing 14 pieces of 27 yards each, at $1.87 per yard; and the third containing 40 pieces averaging 25 yards each, at $1.95 per yard. What was the value of the whole ? DIVISION. 73. 1. How many groups of 2 pencils each can be formed from 6 pencils? How many 2's are there in 6? 2. How many groups containing 3 marbles each can be formed from 9 marbles? How many 3's are there in 9? 3. How many 3's are there in 6? How many 4's in 8? many times is 3 contained in 6? 2 in 6? 4 in 8? How 4. How many cents will each child have when 12 cents are divided equally among 4 children? How many 4's in 12? 5. If 16 cents are divided equally among 8 children, how much will each have? 6. What have you been doing with the above numbers? 7. How many are five 6's? How many 6's in 30? 8. How many are seven 4's? How many 4's in 28? How many 3's in 20? 9. How many are six 3's and 2? 10. How many 5's are there in 22? four 5's and 2? How many are 74. The process of finding how many times one number is contained in another is called Division; or, Division is the process of separating & number into equal parts. 75. The number to be divided is called the Dividend. 76. The number by which we divide is called the Divisor. |