REVIEW II.

Addition is the process of combining two or more numbers so as to form a single number. The result obtained by adding two or more numbers is called their sum.

For convenience, numbers to be added are written so that figures expressing the same order shall fall in the same. column.

In adding numbers, first add all the units of the lowest order; then all the units of the next higher order, and so on, reserving from the sum of the numbers of any order the tens of that order, to be added as ones to the next higher order.

Only units of the same kind can be added; so many things of one kind added to so many things of the same kind.

To test the accuracy of the work, add in the inverse order, or by double columns.

The sign is read "plus," and is used to indicate addition. The sign is read "is equal to," and is placed between expressions which are equal.

=

Subtraction is the process of finding the difference between two numbers, or of finding the number that must be added to one of the two numbers in order that their sum shall be equal to the other.

The subtrahend is the number to be subtracted; the minuend is the number from which the subtrahend is to be taken; the difference is the number sought.

The addition of the same number to both the subtrahend and minuend does not affect the difference. Hence, we may add ten to any order of the minuend if we add one to the next higher order of the subtrahend.

For convenience, the figures of the subtrahend are written under those of the minuend so that those of the same order shall fall in the same column. If a decimal extend to the right more places in one than in the other, the missing places are supplied mentally with zeros.

First subtract the number of the lowest order in the subtrahend from that of the same order in the minuend. If the number in any order in the subtrahend be greater than the number in the corresponding order in the minuend, add ten to that number in the minuend before subtracting, and then add one to the number of the next higher order in the subtrahend.

The sign is read "minus," and is used to indicate subtraction.

Only units of the same kind can be subtracted; so many units of one kind subtracted from so many units of the same kind.

To test the accuracy of the work, add the subtrahend and difference together; and if the work be correct, their sum will be equal to the minuend.

Whenever a question arises in which the minuend is smaller than the subtrahend, we may subtract the minuend from the subtrahend, and prefix the minus sign to the result. Such a result is called a minus number.

CHAPTER V.

APPLICATIONS OF ADDITION AND SUBTRACTION.

91. IN a till are $391 in bills, $67.50 in gold, $39.75 in silver, and $2.77 in copper and nickel. How much money is in the till?

92. Starting out with $315.75 in one wallet and $54.37 in another, I pay the grocer $127.38; the butcher, $64.17; the shoemaker, $21.40; the landlord, $50; the tailor, $35. What ought I to have left?

93. On a bill of $753.43, I pay $517.87. How much do I still owe? If I owe $817.87, and have but $637.50, how much do I lack of being able to pay?

94. If a man was born January 1, 1812, how old was he January 1, 1878? How old December 31, 1857?

95. America was discovered in 1492. How many years after its discovery was each of the following events?

Settlement of Florida, 1565; of Virginia, 1607; of Massachusetts, 1620; of Quebec, 1608; French and Indian War, 1756; Declaration of Independence, 1776; inauguration of Washington, 1789; war with England, 1812; Mexican War, 1846; Civil War, 1861.

96. How many days in common years, and in leap-years, between January 1 and March 1? January 4 and April 4?

February 5 and May 5? February 7 and October 7? January 4 and July 4? March 4 and July 4?

97. The sum of two numbers is 3; their difference, 1. What are the numbers? The sum of two numbers is 5; their difference, 1. Required the numbers. What two numbers added together make 8, if the difference of the numbers is 2? If the difference is 0? if 4? if 6?

98. If the minuend is 9874, and remainder 3185, what is the subtrahend? The subtrahend being 7659, and remainder 675.68, what is the minuend?

99. The smaller of two numbers is 7.95764328; their difference is .00087692. What is the larger number?

100. The larger of two numbers is 7.95764328, and their difference is 7.153485. What is the smaller number?

101. A hired man pumps out of my cistern in one hour 243.75 gallons; in the next hour, 227.5 gallons; in 45 minutes more, an additional 137.75 gallons; and the cistern is empty. How much was in it?

102. From what number must I subtract 5 to leave 7? 8 to leave 9? From what number must I subtract 5.1736 to leave 8.1964? 6.231 to leave 9.6648? 74.213 to leave 25.787?

103. What must be subtracted from 1 to leave .5? to leave .53? to leave .532? to leave .5236? to leave .5235988 ?

104. I start on a journey of 3433 miles. The first day I make 428 miles; the second day, 511 miles; the third,

APPLICATIONS OF ADDITION AND SUBTRACTION.

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497 miles; the fourth, 513. How many miles of my journey remained for me at the close of each day? How many miles had I gone at the close of each day?

105. Subtract 76,343 from the sum of 61,932, 51,387, 5193, 4674, and 8199; then subtract 23,657 from the remainder.

106. J. bought a farm and stock for $7633.90; sold off the stock for $305.75; then sold the farm for $7325. What did he lose?

107. If I gave $4375 for my land, and paid for house, barn, sheds, and fences, $2789.50; also $973.75 for horses, cattle, tools, etc.; what did my farm and stock cost?

If I sold part of the land for $675, and some cattle, etc., for $217.50, what may I estimate as the cost of what I have left?

108. Alfred the Great died at the age of 52, A.D. 901. In what year was he born? William the Conqueror began to reign A.D. 1066, and reigned 21 years. In what year did he die? Socrates was born в.C. 469, and died at the age of 70. In what year did he die? Plato was born B.C. 429, and died at the age of 82. In what year did he die? Demosthenes died at the age of 60, B.C. 322. In what year was he born? The battle of Marathon was fought B.C. 490; 560 years later Jerusalem was destroyed by Titus. In what year was Jerusalem destroyed?

109. John has 158 cents, James has 271 cents; James gives John 56 cents. Which has more than the other, and how many more?