and 200 miners: What is the whole number of men in the army? Ans. 13923. 9. The mail route from Albany to New-York is 144 miles, from New-York to Philadelphia 90 miles, from Philadelphia to Baltimore 98 miles, and from Baltimore to Washington City 38 miles: What is the distance from Albany to Washington? Ans. miles. 10. Suppose a man was born on the 1st of January, 1795: When will he be 85 years old? Ans. In 1880. 11. A man dying leaves his only daughter nine hundred and ninety-nine dollars, and to each of three sons two hundred dollars more than he left the daughter. What was each son's portion, and what the amount of the whole estate? Each son's part Ans. Whole estate dollars. dollars. 12. What was the whole number of inhabitants in the United States in 1840; there being in Maine 501,793; New Hampshire 284,574; Vermont 291,948; Massachusetts 737,699; Rhode Island 108,830; Connecticut 309,978; New-York 2,428,921; New-Jersey 373,306; Pennsylvania 1,724,033; Delaware 78,085; Maryland 469,232, Virginia 1,239,797; North Carolina 753,419; South Carolina 594,398; Georgia 691,392; Alabama 590,756; Mississippi 375,651; Louisiana 352,411; Tennessee 829,210; Kentucky 779,828; Ohio 1,519,467; Indiana 685,866; Illinois 476,183; Missouri 383,702; Arkansas 97,574; Michigan 212,267; Florida 54,477; Wisconsin Territory 30,945; Iowa Territory 43,112; District of Columbia 43,712; Naval Service 6,100 ? Ans. 17,068,666. SUBTRACTION OF SIMPLE NUMBERS. § 16. John has 6 apples and Charles has 4. How many more apples has John than Charles ? Ans. 2. Two is called the difference between the number of apples which John has, and the number of apples which Charles has. SUBTRACTION is finding the difference between two numbers. The larger of the two numbers is called the minuend, the lesser is called the subtrahend, and their difference is called the remainder. Q. What is Subtraction? What is the larger number called? What is the smaller number called? What is the difference called? § 17. James has 8 pears and gives 5 to William : how many has he left? Ans. 3. Q. Which number is the minuend? Which the subtrahend? Which the remainder? § 18. The sign —, is called minus, a term signifying less. When placed between two numbers it denotes that the one on the right is to be taken from the one on the left. Thus, 6-4-2, denotes that 4 is to be taken from 6 Here 6 is the minuend, 4 the subtrahend, and 2 the remainder. When the numbers are small, their difference is apparent, and instead of saying, 6 minus 4 equals 2, we say, 4 from 6 leaves 2. Q. What is the sign of subtraction? What is it called? What does the term signify? When placed between two numbers what does it denote? When the numbers are small how do you read them, as 6-4 ? § 19. The following table should be committed to memory, and read, two from two naught remains; two from three, one remains, &c. When the numbers are small, as in the above examples, 1. James has 27 apples, and gives 14 to John: how 27 Minuend. 14 Subtrahend. The 27 is made up of 7 units and 2 13 2. What are the remainders in the following examples. 3. A farmer has 378 sheep, and sold 256: how many had he left? 378 256 122 We first write the number 378, and then the 256 under it, so that units shall fall under units, tens under tens, and hundreds under hundreds. We then take 6 units from 8, 5 tens from 7 tens, and 2 hundreds from 3 hundreds, leaving for the remainder 122. 4. A merchant has 578 dollars in cash, and pays 475 dollars for goods: how much has he left? Ans. 103 dollars. 5. What are the remainders in the following examples. 6. What is the difference between 4 units and 1 ten We write the ten, and then place the 4 under the units' place. Then we say, 4 from ten leaves 6. 10 4 6 7. What is the difference between 2 tens and 6 units? Here we may say, 6 from 20 leaves 14. 8. What is the difference between 14 and 8? Having written the 8 under the 14, so that units shall stand under units, we see that 8cannot be subtracted from 4, but we can say, 8 from 14 leaves 6. 20 6 14 14 8 6 9. What is the difference between 3 tens and 7 units? What is the difference between 4 tens and 2 tens? What is the difference between 5 tens and 1 ten? 10. What is the difference between 9 tens and 6 units? 11. What is the difference between a unit of the second order and a unit of the first order? 12. What is the difference between a unit of the third order, and a unit of the second order? 13. What is the difference between four units of the third order, and three tens? 90 84 10 1 9 100 10 90 400 30 370 EXAMPLES. OPERATION. 869 Minuend. 327 Subtrahend. 1. From the number 869 subtract 327. We begin at the right hand figure of the lower line, and say, 7 from 9 leaves 2 set down the 2 under the 7. Proceeding to the next column, we say, 2 from 6 leaves 4: set down the 4, and then say, 3 from 8 leaves 5. remainder, or true difference between the numbers. 2. From 654 subtra :t 472. Beginning at the lower figure on the right we say, 2 from 4 leaves 2: set down the 2. At the next step we meet a difficulty; for, we cannot subtract 7 from 5. We avoid this difficulty, thus. Ten units in the second place are equal to one unit of the third place § 8. Therefore, if we add 10 to the 5 and diminish 6 by 1 the value of the upper line will not be changed. the right. 542 Remainder. Thus, 542 is the OPERATION. hundreds. tens Aunits hundreds. 654 5154 472 4 72 182 1 82 The numbers are so written at |