may then be considered 3 ten-thousands 3 thousands 9 hundreds 9 tens and 10 ones. Taking from the changed minuend the 2 ten-thousands 1 thousand 3 hundreds 4 tens 5 ones of the subtrahend, we have as the difference required, 12655. Subtract: 97. 5544 from 40000. 100. 97 from 10000. 103. 67.055 from 73.607. 104. 19.55 from 831.50. 105. 444.5 from 10060. 106. 921.56 from 1000. 107. $13.63 from $500.20. 108. $127 from $1963.75. 109. What is the value of 83956-78415? 110. What is the value of 60440 - 33457 ? 111. What is the value of 109800 - 98799? 112. From one hundred nine take one, and nine hundredths? 113. America was discovered in 1492; how many years from that date to 1881 ? 114. A man began business with $1760, and after two years had $2500.75. How much had he gained? 115. The number of regular soldiers furnished by the several States in the war of the Revolution was 231771; of these a single State furnished 67907. How many were furnished by other States? 116. A merchant bought goods to the amount of $7563.56, and sold them for $11630.50. How much did he gain? 117. The Atlantic slope contains 967576 square miles, and the Mississippi valley 1237111 square miles. How much does the latter exceed the former? 118. The population of New York City in 1870 was 942192, and in 1880 was 1209561. How much was the gain? 119. The product of gold in a certain year was from Nevada $19546516, and from California $17760679. How much greater was the product from Nevada than from California? MISCELLANEOUS EXERCISES. 120. A man owing $ 767.50 paid one time $ 190, at another $131, and at a third $ 155.25. How much did he then owe? 121. James Dow's real estate is valued at $3769, and his personal estate at $2648.75. He owes Job Smith $1728 and Abraham Tyler $ 1161.93. How much is he worth when these debts are paid? 122. Modern notation in arithmetic was introduced from Arabia into Europe in the year 991, algebra from the same country in 431 years later, and decimal fractions were invented in 1602. Required the number of years from each to 1882. 123. Sydney has $178.50, Albert $75.75 more than Sydney, and Charles has as much as Sydney and Albert less $ 80.93. How much more has Charles than Sydney? 124. What is the value of 1645 + 635 + 416 — 1314? 125. Two vessels 4563 miles apart start to meet each other. When one of them has made 1575 miles of the distance and the other 1658 miles, how far are they apart? 126. A man whose property was $50675 gave his son Edwin $ 8555.50, his son Robert $7000, his daughter Mary $ 9563.75, his wife $ 20000, and a public library the remainder. How much was given the public library? 127. The population, in 1880, of Philadelphia was 847542; of Boston, 362535; and of Providence, 104760. How much greater was the population of Philadelphia than that of Boston and Providence? 128. A man who had $1250 in a savings bank took out $51.75 at one time, $ 84.93 at another, and $267 at another. He then put in $ 185. How much then had he in the bank? QUESTIONS. 41. What is subtraction? 42. What is the difference? 43. The minuend? 44. The subtrahend? 45. The sign of subtraction? 46. What are principles of subtraction? 47. How do you subtract? If any order of the minuend has less units than the same order of the subtrahend, what is done? 48. What is the proof of subtraction? MULTIPLICATION. 49. 1. If a man can earn 8 dollars in a week, how many dollars can he earn in 4 weeks? How many dollars are 4 times 8 dollars? 2. What will 5 quarts of cherries cost at 10 cents a quart? 3. William has 9 apples and Alfred 7 times as many. How many has Alfred ? 7 times 9 are how many ones? 50. Multiplication is taking one number as many times as there are ones in another. 51. The Multiplicand is the number to be taken or multiplied. 52. The Multiplier is the number that shows how many times the multiplicand is to be taken. 53. The Product is the result of a multiplication; and the factors of a product are the numbers multiplied together to produce it. 54. The Sign of Multiplication is X. It means multiplied by, or times. Thus, 7 × 5 may be read seven multiplied by five, or seven times five. 55. A Concrete Number is a number in which some kind of unit is named. Thus, 2 books, 3 days, $7, are concrete numbers. 56. An Abstract Number is a number in which no particular kind of unit is named. Thus, 2, 5, 7 are abstract numbers. ORAL EXERCISES. 4. How many wings have 8 doves? 5. How much can you earn in 3 days if you earn 10 cents a day? 6. At 9 cents each what will a half-dozen writing-books cost? 7. How many horns have 8 yoke of oxen? 8. How many days in 12 weeks? In 9 weeks? 9. How far can you ride in 7 hours at the rate of 8 miles an hour? 10. How many desks in a school-room having 8 rows with 7 desks in a row? 11. How many legs have 6 span of horses? 12. At 7 cents each what cost a dozen pencils ? 13. A ten-foot pole is how many inches long? 20. Give the products by 2, from 2 x 2 to 2 x 12. Solution. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. 21 Give the products by 4, from 4 x 0 to 4 x 12. 22. Count by 7's from 0 to 84. 23. Subtract by 9's from 108 to 0. |