annex a cypher thereto; then the 140 containing the divisor four times, place the 4 in the quotient, and point it (4) off for a decimal; then the decimals in the divisor and quotient will be equal to those in the dividend. To prove the work, add the remainder and all the numbers subtracted together, the amount of which, corresponding with the dividend, proves the work to be correct. 2. Divide ,00000448 by ,0007. Ans. ,0064. Ans. ,009462. Ans. 32,406. Ans. 14,596. Ans. 792,9. Ans. ,91024. Ans. 5794,1. Ans. ,00071047. 10. Divide $1002,2454 $21,06. Ans. $47,59. 11. Divide $43,029312976 $0,47801. 12. Divide 3152,7,7006. 13. Divide 5341,87564,75. Ans. $90,0176. Ans. 4500. Ans. 82,5. Ans. 1000000. 14. Divide one thousand by one thousandth part of one. 15. Divide,2744 by forty-nine hundredths. Ans. Fifty-six hundredths. 16. Divide,7336 by eight tenths. 17. If 59,459 gallons of Madeira wine cost $124,982818, what will one gallon cost? Ans. $2,102. Ans. $5,65. 18. If 69,25 sides of sole leather cost $391,2625, what cost one side ? 19. If 749,59 pieces of India crape cost $31489,601269, what is that a piece? Ans. $42,0091. 20. Sold 155,75 boxes of cotton balls for $297,4825; How much is that a box? Ans. $1,91. Ans. $7,065. 21. Bought 19,5 hundred weight of raisins for $137,7675: What did they cost a hundred weight? 22. If 2198,75 yards of tape cost $41,77625, what is that a yard? Ans. $0,019. 23. Sold 4,5 dozen of silver cups for $59,13: What was the price of one dozen? Ans. $13,14. 24. In 1819, the mail was transported yearly 7574189,25 miles How far was it transported daily at that rate, allowing the year to contain 365,25 days? : Ans. 20737 miles. 25. In 1818, the capitals of the Banks in the State of New-York, amounted to $24000000; allowing threefourths of a million of dollars to each bank, how many banks were there? Ans. 32. FRACTIONS, OR BROKEN NUMBERS. Q. What are Fractions, or Broken Numbers? A. Fractions are expressions for any assignable parts of a unit, or whole number. Q. How are they represented? A. Fractions are represented by two numbers, placed one directly over the other, with a horizontal line drawn between them, thus, one-fourth, one-half, & threefourths, one third, two thirds, three fifths, & five sixths, one seventh, two sevenths, &c. One whole number is equal to 4 quarters, and is also equal to two halves, &c. Q. What name has each of these figures, and what does it show? A. The figure below the line is called the Denominator, and shows into how many parts an unit or integer is divided; the figure above the line is called the Numerator, and shows how many of those parts are signified by the fraction. Illustration. signifies 1 fourth part. 1 half, or 2 fourth parts. ALSO, signifies 1 third part. 4 seventh parts. signifies 5 seventh parts. 4 ninth parts. 5 ninth parts. 8 ninth parts, &c. NOTE. In the above illustration, the fractions,,, †, &c. which would naturally come in with the others, are omitted as not being reduced to their lowest terms. ADDITION OF FRACTIONS. CASE I. RULE. Q. How do you place the numbers to be added, when the given fractions are all quarters ? A. Call one quarter, two quarters, three quarters; then, if there be fractions only, place them in one column, but if there be fractions joined with whole numbers, place them in a column at the right hand of the whole numbers; add them together, and divide their amount by either of the denominators, except that of the , and the quotient will be in whole numbers. EXAMPLES. NOTE.-The method of proceeding in Addition of Fractions illustrated. 1. What is the amount of 3, 4, 1⁄2, together? , and 1, when added NOTE.-To find the amount of the numbers here given to be added, begin with the and say, 3 and 2 are 5, and 1 is 6, and 3 are 9 (quarters,) which divide by 4 (quarters,) and it gives a quotient of 2 (whole numbers) and (one quarter) remains; set down the 1, and carry the 2 and add to the one, which will make 3; set down the 3, and the answer is then three whole numbers, and one quarter The reason of dividing the amount of the fractions (quarters) by either of the denominators (except the 1) is, because 4 quarters are equal to one whole number. 2. What is the amount of 21, 14, 33, and 44? Ans. 12. 3. Find the amount of 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, and ?? Ans. 53. 4. Give the amount of 31, 7, 101, and 19 ? 5. Add 9, 12, 9061, and 40003 together? Ans. 411. Ans. 4918. 6. The number and depth of snows, &c. which fell from Dec. 30th, 1819, to April 7th, 1820, inclusive, were as follows, viz. Dec. 30th, 1819, 1 snow, 9 inches deep; Jan. 11th, 1820, 1 do. 6 in. do.; 17th, 1 do. 6 in. do.; 19th, 1 do. 2 in. do. ; 22d, 1 do. 54 in. do. ; 25th, I do. 0 in. do.; 27th, 1 do. 1 in. do. ; 29th, 1 do. 1 in. do.; 31st, 1 do. 1 in. do.; Feb. 3d, 1 do. 31⁄2 in. do.; 7th, 1 do. 5 in. do. ; 9th, 1 do. 9 in. do. ; 11th, 1 do. 16 in. do. ; 20th, 1 do. 0 in. do.; March 2d, 1 do. 3 in. do.; 4th, 1 do. 2 in. do. 9th, 1 hail, 4 in. do. ; 17th, 1 snow, 3 in. do. April 6th, 1 do. 1 in. do.; 7th, 1 do. 24 in. do. : What was the number, and also the depth of all the snows, &c.? 20 snows, &c. Ans. 821 inches, total depth. ; CASE II. RULE. Q. When the fractions are either greater or less than quarters, how do you proceed? A. Add all the numerators together, and divide their amount by either of the denominators; but in this case, all the denominators belonging to one question must be equal or alike; i. e. all thirds, all fifths, all sixths, &c. EXAMPLES. 1. What is the amount of, 3, 4, 21, 3, and 5% ? Operation. one third.. two thirds. 43 four and two thirds. 21 two and one third. 5 five and two thirds. 141 Amount, or answer. NOTE.-To find the amount of the numbers here given to be added, add up all the numerators, and divide their amount by either of the denominators (3,) which will give a quotient of 3 (whole numbers,) and (one third) will remain; set down the, and carry the 3 and add to the column of units or whole numbers, the amount of which (being 14,) set down, and the answer is 141. 2. What is the amount of,, †, 3, 4, 14}? 3. What is the amount of, 4, 3, 4, §, 4, 4. What is the amount of 94, 4, 54, 4, and 1, 63, 21, and Ans. 294. and a? Ans. 35. 24? Ans. 18. and 4. 4, 7, and 198. Ans. 100. together. Ans. 36. 5. Give the amount of, 4, 1, 1, †, f, 3, ་ 6. Find the amount of 3, 162, §, 541, 73, 7. Add 10, 14, 11, 81, 1, and 8. Give the amount of, 8, 11, 18, 48, 58, and 1328. 26) Ans. 16. |
