64. A man earned $144 in 12 weeks. What was that a week? 65. How many 10's in 100? How many 100's in 1000? 66. In 65 how many tens and what over? In 235 how many hundreds and what over? 67. How many times 20 in 100? (204) in (1004)? How many times (100 × 2)? How many times (20 × 2) in 72. A General Principle of Division. Dividing or multiplying both dividend and divisor by the same number does not alter the quotient. with these 10 tens the 5 ones of the dividend, we have 105 ones. 12 is in 105, 8 times. We write the 8 ones above the ones of the dividend. Writing 8 times 12 are 96, which taken from the 105 of the dividend leaves 9, and indicating its division by the divisor, we have theas a part of the quotient, we have as the quotient 98. 69. Divide 9876 by 21. 70. Divide 3276 by 14. 71. Divide 31278 by 23. 72. Divide 106.97 by 19. 73. Divide 26.575 by 25. 74. Divide 1868.5 by 37. 73. Rule for Division. Write the divisor at the left of the dividend with a curve between them. Find how many times the divisor is contained in the few est left-hand figures of the dividend that will contain it, and write the result under or over the right-hand figure of the dividend used, as the first quotient figure. Multiply the divisor by this quotient, subtract the product from the partial dividend used, and to the remainder annex the next dividend figure for a second partial dividend. Divide and proceed as before, until all the dividend figures have been used. If there is a final remainder, write it with the divisor under it, as a part of the quotient. NOTE 1. - The division is called Short Division when only the divisor, dividend, and quotient are written; and Long Division when each process of the solution is written. In short division the quotient is usually written below the dividend, and in long division over, or at the right of, the dividend. NOTE 2. When the divisor is an integer, and the quotient is written under 'or over the dividend, the decimal point in the quotient must be placed immediately under or over the point in the dividend. 74. PROOF. Multiply the quotient by the divisor, and to the product add the remainder, if any. The result should be the dividend. 75. Divide 182.72 by 45, and prove the work. 76. Find the quotient of $114.48 divided by 36. 77. Find one twenty-eighth of $ 896.56. 85. 1298763 ÷ 873 87. 88. = = ? 86. of 63450 78. Divide 347692 by 351. 79. Divide 8468.31 by 793. 80. Divide 947684 by 982. 81. Divide 3287.64 by 735. 82. Divide 6798.341 by 1234. 89. 83. Divide $8392.476 by 987. 90. 84. Divide 3004760 by 5942. 91. 92. What is the price of one sleigh if 85 cost $10625? 93. How many horses at $225 each will $5400 buy? 94. If $671178.90 is the valuation of a hamlet having 98. inhabitants, what is the average valuation to an inhabitant? 95. If the distance across the Atlantic Ocean is 3000 miles, in how many days will a ship, sailing 115 miles a day, make that distance? 96. What number multiplied by 512 gives a product of 1763.68 ? 97. What number multiplied by 2135 gives a product of 6419945? 98. Divide 49300 by 432. 100. $5711.04 ÷ 108 = 99. Divide 700074 by 2047. 101. $50000 ÷ 365 = ? 102. Divide 489 by 25 to hundredths. 19.56 25) 489.00 25 225 14.0 12.5 1.50 1.50 ? Solution. 489 489.00. Dividing the 489.00 by 25, we obtain as the result required 19.56. If the division had not terminated, we could have denoted this by placing the sign + after the hundredths in the quotient to indicate the incompleteness. 103. Divide 2722.5 by 44 to hundredths. 107. If as many persons die in thirty-three years as are equal to the entire population, how many persons die annually, to the nearest unit, on an average, out of every million? The divisor a number of tens, hundreds, etc. 108. Divide 1467 by 10; by 100; by 1000. or to find 1 tenth of a number, it is only necessary to move each figure of it one place to the right. This is done by moving the decimal point one place to the left, giving 146 as the quotient. In the same way two removals of the point to the left divides by 100, three removals by 1000, and so on. That is, 75. To divide by 10, 100, 1000, etc., Move the decimal point of the dividend as many places to the left as there are ciphers in the divisor. Or, if the exact remainder is required, we may indicate the division by 10, by marking off one place, and have as a quotient 582, and a remainder of 4 ones. Dividing 582 by 16, we have for a quotient 36, and a remainder 6 tens. Uniting the two remainders, we have as the true remainder 64. 110. There are 1000 mills in a dollar; how many dollars are there in 19650 mills? 111. Divide 3962 by 100; by 1000. 112. Divide 9108 by 200 to hundredths. 113. Divide 12386 by 90, and find the true remainder. 114. Divide 5886990 by 5400 to hundredths. 115. In the State of Alabama 1437272 acres have produced 51000 bales of cotton. What was that to an acre? 116. If light moves at the rate of 186000 miles in a second, how long is it in passing from the sun to the earth, a distance of 92000000 miles? MISCELLANEOUS EXERCISES. 133. A farmer obtained $7665 for the apples from his orchard at $3 a barrel. How many barrels did he have? 134. Two men start from the same place and travel in opposite directions, one at the rate of 25 miles a day, and the other at the rate of 31 miles a day. When 5656 miles apart how many days had they traveled? 135. A cargo of 25 tons of coal was bought by the long ton of 2240 pounds, and sold by the short ton of 2000 pounds. How many short tons was the gain? 136. A farmer bought 75 acres of land at $34 an acre, and 85 acres at $20.40 an acre. What was the average cost of the whole an acre? |