140. REDUCTION 99 QUESTIONS FOR PRACTICE. English Money. 1. In £65 4s. 6d. 2qr. how 1. In 62618qr. how many many farthings? pounds ? 2. In £1465 14s. 5d. how | 2. In 1407092qr. how many. many farthings ? pounds ? 3. In $47 4s. how many * 3. In 286s. how many dolshillings?" 4. In 29 guineas at 28s. how 14. In 38976qr. how many. many farthings? guineas ? 5. In 40 guineas how many 5. Ia £56 how many guinpounds ? Time. 1. In 4d. 22h. 4m. 20s. how 1 1. In 425060s. how many many seconds ? days? 2. How many minutes in al 2. In 525960m. how many year? years? 3. How many hours in a 3. In 876600h. how many century ? | centuries ? Troy Weight. 1. In 131b. how many grains ? 1 1. In 74880grs. how many 2. In 221b. Goz. 10pwt. how pounds ? many grains ? 1 2 . In 129840gr. how many pounds ? Avoirdupois Weight. 1. In 4 tons how many oun- 1 1. In 143360oz. how many ces? 2. In 7 cwt. 3qr. 10lb. how | 2. In 222720 drams, how inany drams? many cwt. 3. In 1961b, how many oun. 3. In 3136oz. how many ces ? 1 pounds ? Long Measure. 1. In 26 rods how many | 1. In 143 yards how many yards ? rods? 26 As 5d yds. make 1 rod, Here we reduce à 51=5.5 we muliiply the rods by 5.5)143.0(26rd. to a decimal, as be53. To render the mul fore, and divide as tiplication by à more in decimals, (128). easy, we reduce it to de Whenever a fraction cimals, (130) and then 330 occurs, it may be 143.0yd. proceed as in decimals. changed to a decimal, (122) and used as such. 110 130 130 miles ? 2. In 3 miles how mans 2. In 15840ft. how many feet? miles ? 3. In 47m. 5fu. 16rd. 12ft. i 3. In 3020838in. how many hin. how many inches ? miles ? 4. How many inches round | 4. In 1578424320in. how many the earth? | degrees ? Cloth Measure. 1. In 59yds. how many nails? | 1. In 944 nails how many 2. In 362E. E. 2qr. how mal yards ? ny nails? 2. In 7248na. how many E. 3. In 576E. F. how many | Ells ? quarters ? 3. In 1728qr. how many F. Ells ? Square Measure. 1. In 1500 acres how many | 1. In 240000rd. how many rods? acres ? 2. In a township 6m. square 2. In 23040 acres how many how many acres ? 3. In 24 square yards, how 3. In 31104in. how many many inches ? | square yards ? Solid Measure. 1. How many inches in 2| 1. How many cords in 4423. cords of wood ? 68 solid inches? 2. How many inches in 27 | 2. In 1259712in. how many solid yards ? I yards ? Wine Measure. 1. In 178hhd. how many 1 1. In 89712pt. how many pints ? hogsheads ? 2. In 5 pipes how many gills ? ! 2. 20160gi. how many pipes ? Beer Measure. 1. In 8 barrels how many 1 1. In 2304pts. how many bar. pints ? rels ? 2. In 14hhd. how many 2. In 3024 qts. how many quarts ? | hogsheads ? Dry Measure. 1. In 9 quarters how many 1 1. In 4608 pts. how many pints ? quarters ? * 2. Reduce 36bu. 2pk. 6qt. 2. Reduce 2349pt. to bushIpt. to pints. square yards. h 141, 142. REDUCTION 101 Circular Measure. 1. In 6 signs how many min. 1 1. How many signs in 10800 utes ? minutes ? 2. In 47° 23" 15" how many 2. In 170595' how many deseconds ? I grees? REDUCTION OF DECIMALS. 25 141. ). Reduce 4 ounces to the 142. 1. How many ounces decimal of a pound. | are 0.25 of a pound ? 402.= lb. As llb. is Pounds are reduced 16)4.01.25 16oz. 4oz. are 4 .25 to ounces by multipli 16 cation, (139) and 2516. 52 of a pound and 16 multiplied by 16, the reduced to a de 150 ounces in a pound, the 80 cimal (130) is .25 product (122) is 4 oun ces. 80 of a pound. oz. 4.00 2. Reduce 3 inches to 2. How many inches are the decimal of a yard. 10.0833+ of a yard ? 12)3.06.25 3 inches = of Yards are reduced to ft. 24 a foot, and is 0.0833 by multiplying them by 3, 3 and feet to inches by mul-- =0.25ft and 0.25 ----- tiplying by 12. (139) Here 60 ft. are reduced to 0.2499 it will be seen, by compara yards by dividing 12 ing this with the example - at the left hand, that there 3) 0.2500 them by 3 2.9988 is a loss of 12 ten thou-- (140). The sandths of an inch, on ae0.0833 + Ans. sign + de count of the decimal being incom plete, notes that more decimal figures may be had by adding more ci 3. In 0.35 of a day, how phers. many hours and minutes ? To reduce days 3. Reduce 8 hours 24 min./ 0.35 to hours, we multito the decimal of a day. 24 1, and the 60) 24. 24m.=24h.=0. product is 8.4n. and 140 8.4 multiplied by 60 24) 8.40 4h. then 8h. 24 70 gives 24 minutes; m.=8.4h. and then 0.350.=8h. 24 0.35d. min, 8.4h.= h. 8.40 60 The above methods of changing decimals to integers of a different denomination, and the reverse, are called the Reduction of Decimals. 143. To reduce compounds 144. To find the value of a numbers to decimals of the decimal in integers of a lower highest denomination. denomination. RULE.-Divide the lowest | RULE.-Multiply the decidenomination (annexing one mal by that number which it or more cipher, as shall be takes of the next lower denofound necessary) by the num- | mination to make one of the ber which it takes of that to denomination in which the demake one of the next higher cimal is given, and point off as denomination, (126) and write in the multiplication of deci. the quotient as a decimal of mals. (122) Multiply the decithe higher; divide this higher mal part of the product by the denomination by the number number it takes of the next which it takes to make one lower denomination to make still higher, and so continue j one of that, and so on; the to do till it is brought to the several numbers at the left of decimal required. the decimals will be the anI swer. 146, 147, 148. 103 ADDITION. 146. 1. A person gave 21. 178. and 8d. for a load of hay, 11. 6s. 3d. for 5 bush. of wheai, and 10:. 4d. for a load of wood; what did the whole cost ? As we may very evidently add pence to pence, shil1. S. d. lings to shillings, &c. we write down the numbers so 2 17 8 that pence shall stand under pence, shillings under shil. 1 5 3 lings, and so on. We then add the pence, and find their '10 4 sum to be 15d. but as 12dls. 15=ls. 3d. We there. fore write down 3d. under the column of pence, and re4 13 3 Ans. serve the 1s. to he joined with the shillings. We now add together the shillings, which, with the 1s. reserved, 4 13 3 proof. amount to 338.=1l. 13s. we therefore wrile 133. under the column of shillings, and reserve the 1l. to be joined with the pounds. Lastly, we add the pounds, and joining the 11. reserved, write the amount, 11. under the column of pounds; and thus we find the whole cost to be 41. 13s. 3d. The above process is called Compound Addition. COMPOUND ADDITION 147. Is the uniting together of several compound numbers into one sum. (48) RULE. 148. Place the numbers to be added so that those of the same denomination may stand directly under each other. Add the numbers of the lowest denomination, and carry for that number which it takes of that denomination to make 1 of the next higher, writing the excess, if any, at the foot of the column. Proceed with each denomination in the same way till you arrive at the last, whose amount is to be set down as in Simple Addition. PROOF.—The same as in Simple Addition. QUESTIONS FOR PRACTICE. TROY WEIGHT. £ 8. d. gr.. £ S. d. lb. oz. pwt gr 1b. oz. pirt gr. 47 7 6 2 48 10 109 17 3 15 15 14 10 18 20 3 9 4 3 13 16 41 13 2 19 16 13 10 17 0 15 13 9 1 190 61 15 6 10 8 27 10 4 23 |