SUBTRACTION OF DECIMALS. 60. Illustrative Example. From 16.5 miles take 3.875 miles. WRITTEN WORK. 16.5 The numbers are written as before, so that units of the same order shall be expressed in the same column. Beginning with the units of the lowest order to subtract: 5 from 10, 5; 7 from 9, 2; 8 from 14, 6; etc. Ans. 12.625 miles. 98. From 3.667 take 1.145. 100. Subtract 0.095 from 1. 99. From 32.05 take 17.125. 101. Subtract 2.083 from 10. 102. Find the difference between 16 and 16 thousandths. Subtract the following in lines and in columns: 61. From the preceding examples may be derived the following Rule for Subtraction. (1) Write the minuend and underneath write the subtrahend, so that units of the same order shall be expressed in the same column. Draw a line beneath. (2) Begin with the units of the lowest order to subtract, and proceed to the highest, writing each remainder under the line in its proper place. (3) If any term of the minuend is less than the corresponding term of the subtrahend, add ten to it and then subtract; but consider that the next term of the minuend has been diminished by one. Proof. Add the remainder to the subtrahend: the sum should equal the minuend. 62. Forms of Examples in Subtraction. 111. From 9460 take 5466; from the remainder take 1284. 112. From ten thousand one hundred subtract four thousand fifteen; from the remainder subtract 397. 113. How many more is 3685 than 1857 ? 114. What number added to 1763 will make 1822? 115. The sum of two numbers is 745; the greater one is 569. What is the smaller one? 116. Find the difference between 202,020 and twenty thousand two hundred two. 117. A minuend being 1828 inches, a subtrahend 934 inches, what is the remainder? 118. 2789 plus what number equals 4280? 120. A minuend being 5280 feet, and a remainder 2789 feet, find the subtrahend. 121. After a certain number had been taken out of 500, there remained 184. What was the number taken out? 122. From 980 take 98; from the remainder take 98, and so continue till nothing remains. How many 98's are subtracted? 123. 17.24 less 9.16 equals what? 125. Subtract 1 tenth from 10. 126. Take 426 thousandths from 1. 127. $35.60 added to what will make $500 ? 128. If 91 and 7 hundredths is the minuend and 13.102 the remainder, what is the subtrahend? 129. Mr. Lee bought a farm for $3650.80, and sold it for $4525. How much did he gain? 130. Mr. Fitz bought a house for $975. After spending it $46.30, he sold it for $862.50. How much did he upon lose? Examples for Oral or Written Work. 63. a. In July, during 17 days the wind blew from the southwest, during 6 from the west; for the other days, the winds were variable. How many days were they variable? b. Mr. Wood had 38 tomato plants, and sold 12 to one man and 8 to another. How many had he left? c. Alvin had 27 peaches and 25 pears. He gave 9 peaches to Bennie and 8 pears to John. How many peaches had he left? How many pears? d. Having 80 miles to travel, I rode 20 miles in the morning, 15 in the afternoon, and 12 in the evening. How many miles of the journey remained? e. Harry was to be away from home 63 days. After 25 days had passed, how many more days had he to remain away? f. If James buys a knife for 35 cents and loses 12 cents by selling it, for how much does he sell it? g. Nellie's cash account for a week was as follows: On hand, 20 cents; allowance, 25 cents; earned, 15 cents; spent, 13 cents. What was the balance of her account? h. If you have 23 cents, how many more cents must you get to buy a sled worth 62 cents? i. A man bought a horse for $75 and sold him for $54. How much money did he lose? j. Out of 50 butterflies observed by a boy, all but 17 alighted upon objects approaching their own color. How many alighted on such protecting surfaces? How many more did alight on such surfaces than did not? k. A caterer bargained to pay for a set of fixtures $90 in board. The board for four successive months was $12, $10, $15, and $11. What still remained due? h. The roadway over the Natural Bridge in Virginia is 122 feet high from the creek below, and 40 feet above the top of the arch. What is the distance from the top of the arch to the creek below? m. The first Sunday school in New England was established in 1793. How many years is it since then? n. Franklin was born in 1706 and died in 1790. What was his age at the time of his death? o. In 1830 the population of the United States was 13 millions; in 1890 it was 63 millions. How many millions did the population increase in that time? p. If sound travels 4768 feet a second in salt water, and 4714 feet a second in fresh water, how many more feet a second does it travel in salt water than in fresh ? How much money would be left, and what might the coins be, if a dollar were given in payment for q. A hat, 25; a slate, 15; ink, 8¢? r. A dictionary, 67; a dozen pencils, 18¢? s. A microscope, 25¢; a case to put it in, 13¢? t. 50 one-cent letter stamps; paper, 74; envelopes, 84 ? u. A collar, 134; tie, 184; a handkerchief, 19¢? v. "Robinson Crusoe," 274; "Grandfather's Chair," 364; "Black Beauty," 24¢? 64. Examples for Written Work. 131. The first savings bank was established in 1778 at Hamburg; the first established in New England was in 1816. What time elapsed between? 132. The year's earnings of a family were $1925. If their expenses were $1136, how much was saved? 133. A and B together invested $ 5740 in business. If B put in $2575, how much did A put in? 134. The earnings of a coöperative bank for the second six months after its establishment were $1874.53, which was $576.34 more than the earnings for the first six months. What were the earnings for the first six months? 135. The Amazon River is 3750 miles long; the Mississippi is 4300 miles long. What is the difference in their lengths? 136. The sailing distance from New York to Queenstown is 2890 miles. When a steamer has run 1368 miles on her course from New York, how far has she still to go? 137. Iron melts at a temperature of 3980 degrees Fahrenheit, and gold at 2590 degrees. How much higher temperature is required to melt iron than gold? 138. In one week a grain elevator received 984,560 bushels of grain; of this 769,386 bushels were delivered. How much remained in the elevator? 139. A pound of lead, avoirdupois weight, equals 7000 grains; a pound of gold, troy weight, equals 5760 grains. How many more grains are there in a pound of lead than in a pound of gold? 140. What is the difference in value between a half eagle ($5) of United States money and a pound of English money valued at $4.8665? 141. On the 1st of January I had $216.35 in a bank; on the 3d I drew out $31.50, and on the 4th, $62.75. How much remained in the bank? 142. A man having $918 kept $ 381 and bought with the remainder a horse and carriage, paying for the horse $387. How much did he pay for the carriage? 143. Two vessels sailing towards each other are 108 miles apart. If one sails 35.4 miles and the other 47.7 miles, how far apart will they be? 144. The depth of rainfall for the summer months was found to be 15.5 inches; for June and July it was 9.875 inches. What was the depth of rainfall in August? 145. The several items of an account amount to $1968.24; of this amount $1174.68 has been paid. Find the balance. |