Proof. 15 weeks. 2. In 413 days; how many 7 hours and minutes ? 105 days. Ans. 9912h. 594720m. 24 3. In 413280 minutes ; how many hours, days and 420 weeks? 210 Ans. 6888h. 287d. 41w 2520 hours 4. How many hours in 4 60 years, allowing 365 days and 151200 minutes. 6 hours to the year? 60 Ans. 35064h, 6]0)90720010 seconds, 5. How many seconds in 60 years, allowing 365 days 6 610)151200 hours, to the year ? 24)2520(7) 105 Ans. 1893456000s. 24 15 6. From the 2d of March to 120 the 19th of November; how 120 many days? Ans. 262d. 7. From April the 19th to the 20th of January in the next year; how many days? Ans. 276d. NOTE.—In reckoning time, exclu:le the first day and reckon the last. CIRCULAR MEASURE OR MOTION.* 60 Seconds, sec. (") make 1 Minute, min. marked 1 60 Minutes, | Degree, deg. 30 Degrees, 1 Sign, S. 12 Signs, or 360 degrees, 1 Circle of the zodiack. * This measure is used in measuring latitude and longitude, and in computing the revolutions of the earth and other planets round the sun. The great circle of a sphere, containing the 12 signs, through which the sun passes, is called the zodiack. NOTE.-Every circle, great or small, contains 360 degrees. EXAMPLES. Ans. 21600. 12S. DEMONSTRATION. We first 30 multiply by 30, because 30 de 360 degrees. grees make a sign; we next 60 multiply by 60, because 6 minutes make a degree. Ans. 21600 min. 2. In six months the sun passes through 6 signs of the zos diack; how many degrees, minutes, and seconds? Ans. 180deg. 10800min. 648000sec. 3. In 1124304 seconds ? how many signs? Ans. 108. i 2deg. 18min. 24sec. 112 Pounds -- Inake 1 Quintal of fish. 1 Quire. 1 Ream. SUPPLEMENT TO REDUCTION, EXERCISES. 1. In 36 pounds; how many shillings, sixpences and threepences ? Ans. 720 shillings, 1440 sixpences, 2880 threepences. 2. In 19200 half pence; how many pence, shillings, and pounds? Ans. 9600 pence, 800 shil., 40 pounds. 3. In 48 guineas; how many dollars at 8 shillings each? Ans. $168. 4. In 1 mile; how many rods ? Ans. 320rds. 5. In 12244 pints; how many hogsheads ? Ans. 24hhd. 18gal. 2qts. 6. In 25600 rods; how many acres ? Ans. 160 acres. 7. In 684 quarters; how many Ells English? Ans. 136 Ells, 4qrs. NOTE.- When it is required to know how many sorts of coin, and of each an equal number, are contained in a given sum; reduce the several sorts of coin to the lowest denomination mentioned in either, and add them together for a divisor; then reduce your given sum to the same denomination for a dividend, and divide, and the quotient will show how many your dividend contains of each kind. Observe the same directions with regard to weights and measures. 8. In 56 guineas; how many pistoles, pounds, dollars and shillings, and of each an equal number? Ans, 30 of each kind, 38 shillings over, 1 pistole 22s. 56 guineas. 1 pound 20 28 the shillings in a guinea. 1 dollar 8 448 I shilling 1 112 For a divisor 51s. 1568 shillings for a dividend. Div. Dividend. DEM.--The reason of this is 51)1568(30 of each kind. obvious, because our divisor con tains the amount of one coin of 153 each kind, and our quotient shows 38 over. how often this divisor can be sub tracted from the dividend, consequently the quotient shows how often we can have a coin of each kind, because as often as the divisor, which contains a coin of each kind, can be subtracted from the dividend, so often, we must have a coin of each kind. 6. In 312 moidores; how many guineas, pistoles, pounds and dollars, and of each an equal number? Ans. 144 of each. 10. A silversmith received 20lb. of silver, with instructions to make it into spoons of 202.; cups of 3oz.; and teapois of 10 ounces, and of each a like number: what was the number? Ans. 16 of each. 11. A man desirous of racking off a barrel of brandy, in pint bottles, quart bottles, and two quart bottles, and of each an equal number, wishes to knoiy how many bottles he must have of each kind ? Ans. 36. 12. How many times will a ship 132 feet long sail her length in crossing the Atlantick, allowing the distance to be 3000 miles ? Ans. 120000 times. 13. How often will a chariot wheel, 18 feet 4 inches in circumference, turn round in running 22 miles? Ans. 6336 times, 14. A merchant imported from London 46 bales of broadcloth, each containing 24 pieces, and each piece 40 Ells English; how many yards were there? Ans. 55200 yards. 15. The cargo of a ship from the West Indies, consisted of 500 hogsheads of molasses, and 200 pipes of wine; how many gallons in all, and how much was the ship's burden, allowing every pint to weigh 1 pound? Ans. 56700gal. 202 tuns, 10cwt. 16. It is required to divide 10 pounds 13 shillings, between 'a man, woman, and boy; the man must have 9 times as much as the woman, and the woman 7 times as much as the boy; what will be the share of each? , the lings Ans. Slings, the woman's, and the boy's 3 shil . . The b. 1 share. The w. 7 shares. The m. 63 shares. 1 X 7 7 X 9 63 The man's shares. £ S. 7 The woman's shares. 10 13 1 The boy's share. 20 Divisor 71 Shares in all. 213 7 he may draw his one, three times. plain that the giv en sum must be 189 shillings, man's share. divided into 71 parts, because 189 man's share. considering the Proof. boy to have one 21 woman's share. part or share, the 3 boy's share. woman must have 7, because she 210)21|3 must have 7 times £10 13s. equals the given sum. as much as the boy; and for the same reason the man must have 63, because he must have 9 times as much as the woman, whose share is 7, and 9 times 7 are 63. Then when these shares are added, we find they amount to 71, then dividing the given sum by 71, must give the boy's share, because he has but one share in the 71; and we find by dividing, that our quotient is 3 shillings for the boy's share; then the 3s. multiplied by 7 must give the woman's share, because she has seven times as much as the boy; that is, 21s for the woman's share; the man must have 9 times as much as the woman; then multiplying the 21, the woman's share, by 9, must give the man's share, which we find to be 189 shillings; then by adding these shares we find they amount to the given sum, which proves our work, 17. Let 192 dollars be divided among three men, A, B, and C, in such a manner, that as often as A receives $5, B may have $8; and as often as B receives $8, C may have $11; what number of dollars will each receive ? Ans. A $40, B $64, C $88. QUESTIONS ON REDUCTION. What is reduction ? A. Changing one denomination to another. By changing denominations do you alter the value? A. No; because if we change from a superiour to an inferiour denomination, the inforiour must express as many more as shall equal the superiour in value. How many kinds of reduction are there ? A. Two, reduction descending and reduction ascending. What is reduction descending? A. Bringing higher denominations to lower. How is reduction de scending performed? 4. By multiplication. What rule do you observe in multiplying? A. Multiply the highest denomination given by that number which it takes of the next lower to make à unit in that highest, and if the given sum contains any in the next inferiour denomination, add them to the product, and so continue the work tili the given sum is reduced to the denomination required. What is reduction ascending? A. Changing tower denominations into higher. How is it performed ? A. By division; divide the given number by that number which will make a unit in the next higher, and so continue to do, till you have brought it to the denomination required. Suppose you have remainders, what must you call them? A. Of the same name of the dividend that produced them; and they must be brought down in the regular order of the denominations in the quotient or answer, How do you reduce dollars to cents ? A. By multiplying the dollars by 100, and the product will express cents. Why should that reduce dollars to cents ? A. Because we must have 100 limes as many cents as dollars to express the same in value. If your given sum contains dollars and cents, how may you reduce them to cents? A. By taking away the separatrix, and joining the cents to the dollars. Why should that reduce the whole to cents ? A. Because the dollars when united to the cents express hundreds in cents, and the cen's count the, same as before. How do you reduce cents to mills ? A. By multiplying the cents by 10. Why should that reduce cents to mills? A. It is repeating the cents 10 times, and we must have ten times the number of mills, to equal the cents in value. What are the denominations in sterling money?, A. Pounds, shillings, pence, and farthings. How do you reduce pounds to shillings? A. By multiplying the pounds by 20. Why multiply the pounds by 20? A. Because it takes 20 shillings to make a pound, and we must have 20 times the number of shillings to equal our pounds in value. How do you reduce shillings to pence? A. By múltiplying the skillings by 12, because it takes 12 pence to make a shilling, and we must have 12 times as many pence as shillings to equal the shillings in value. How do you reduce pence to farthings ? A. By multiplying the pence by 4, because it takes 4 farthings to make a penny, and we must have 4 times as many farthings as pence to equal our pence in value? How would you reduce pounds to farthings? A. I multiply the pounds by 20, and have shilIings for the product; and then multiply the shillings by 12, and have pence for my product; and lastly, multiply the pence by 4, and the product is farthings. How do you reduce farthings to pounds ? A. Divide the farthings by 4, and the quotient will be pence, because one fourth the number of pence will equal the farthings in value; and then divide the pence by 12, because it takes 12 pence to make a shilling; and lastly, divide the shillings by 20, because it takes 20 shillings to make one pound, and one twentieth the number of pounds will equal the shillings in value. How do you reduce pounds to sixpences? A. Multiply by 20, and then that product by 2. Why multiply by 20 and 2? A. Because 20 shillings make a pound and 2 six-pences make a shilling. How do you reduce grains to pounds Troy? A. Divide by 24, because 24 grains make one pennyweight, and the penny weights divide by 20, because 20 pennyweights make an ounce, |