6. Required the product of 4, 3, and 3. 43 10. Required the product of of 4, and 1⁄2 of 34. Ans. 11. Required the product of 34 and 414. 2 94 24 Ans. 14+ 12. Required the product of 5, 3, of, and 4%. Ans. 2. DIVISION OF VULGAR FRACTIONS. *PREPARE the fractions as before in Multiplication; then divide the numerator by the numerator, and the denominator by the denominator, if they will exactly divide: but if not, then invert the terms of the divisor, and multiply the dividend by it, as in Multiplication. Divison being the reverse of Multiplication, the reason of the Rule is evident. Note, A fraction is best divided by an integer, by dividing the numerator by it; but if it will not exactly divide, then multiply the denominator by it. 12. It is required to divide of by 1⁄2 of 73. Ans. 17T RULE OF THREE IN VULGAR FRACTIONS. MAKE the necessary preparations as before directed; then multiply continually together, the second and third terms, and the first with its parts inverted as in Division, for the answer*. EXAMPLES. 1. If of a yard of velvet cost of a pound sterling; what of a yard cost? will 2. What will 33 oz of silver cost, at 6s 4d an ounce ? Ans. 1/1s 4d. 6 32 3. If of a ship be worth 2731 2s 6d; what are of her worth? Ans. 227/ 12s 1d. 4. What is the purchase of 1230/ bank-stock, at 108 per cent.? Ans. 1336/ is 9d. 5. What is the interest of 273/ 15s for a year, at 34 per cent. ? Ans. 8/17s 114d. 6. If of a ship be worth 73/ 1s 3d, what part of her is 19 worth 250/ 10s? Ans.. 7. What length must be cut off a board that is 7 inches broad, to contain a square foot, or as much as another piece of 12 inches long and 12 broad? Ans. 18 inches. 8. What quantity of shalloon that is of a yard wide, will line 9 yards of cloth, that is 2 yards wide? Ans. 313 yds. *This is only multiplying the 2d and 3d terms together, and dividing the product by the first, as in the Rule of Three in whole numbers. VOL. I. F 9. If 9. If the penny loaf weigh 6 oz, when the price of wheat is 5s the bushel; what ought it to weigh when the wheat is 8s 6d the bushel? Ans. 47 oz. 10. How much in length, of a piece of land that is 11 poles broad, will make an acre of land, or as much as 40 poles in length and 4 in breadth ? Ans. 13 poles. 11. If a courier perform a certain journey in 35 days, travelling 13 hours a day; how long would he be in performing the same, travelling only 11 hours a day? Ans. 40 days. 12. A regiment of soldiers, consisting of 976 men, are to be new cloathed; each coat to contain 2 yards of cloth that is 1 yard wide, and lined with shalloon how many yards of shalloon will line them? yard wide: Ans. 4531 yds 1 qr 29 nails. DECIMAL FRACTIONS. A DECIMAL FRACTION, is that which has for its denominator an unit (1), with as many ciphers annexed as the numerator has places; and it is usually expressed by setting down the numerator only, with a point before it, on the lefthand. Thus, is 4, and 24 is 24, and is '074, and is 00124; where ciphers are prefixed to make up as many places as are ciphers in the denominator, when there is a deficiency of figures. I 24 A mixed number is made up of a whole number with some decimal fraction, the one being separated from the other by a point. Thus, 3.25 is the same as 3, or 125. Ciphers on the right-hand of decimals make no alteration in their value; for 4, or 40, or 400 are decimals having all the same value, each being, or 3. But when they are placed on the left-hand, they decrease the value in a ten-fold proportion: Thus, 4 is, or 4 tenths; but 04 is only, or 4 hundredths, and '004 is only, or 4 thousandths. The 1st place of decimals, counted from the left-hand towards the right, is called the place of primes, or 10ths; the 2d is the place of seconds, or 100ths; the 3d is the place of thirds, or 1000ths; and so on. For, in decimals, as well as in whole numbers, the values of the places increase towards the left-hand, and decrease towards the right, both in the same same tenfold proportion; as in the following Scale or Table of Notation. ADDITION OF DECIMALS. SET the numbers under each other according to the value of their places, like as in whole numbers; in which state the decimal separating points will stand all exactly under each other. Then, beginning at the right-hand, add up all the columns of numbers as in integers; and point off as many places, for decimals, as are in the greatest number of decimal places in any of the lines that are added; or place the point directly below all the other points. EXAMPLES. 1. To add together 290146, and 3146·5, and 2109, and 62417, and 14.16. 29.0146 3146.5 2109. *62417 14.16 5299-29877 the Sum. Ex. 2. What is the sum of 276, 39-213, 72014 9, 417, and 5032? 3. What is the sum of 7530, 16:201, 3.0142, 957.13, 6.72119 and '03014. 4. What is the sum of 312.09, 3.5711, 71956, 71-498, 9739.215, 179, and ⚫0027? SUBTRACTION OF DECIMALS. PLACE the numbers under each other according to the value of their places, as in the last Rule. Then, beginning at the right-hand, subtract as in whole numbers, and point off the decimals as in Addition. EXAMPLES. 1. To find the difference between 91.73 and 2.138. 91.73 Ans. 89.592 the Difference. 2. Find the diff. between 1·9185 and 2·73. Ans. 0·8115. 3. To subtract 4·90142 from 214.81. Ans. 209.90858. MULTIPLICATION OF DECIMALS. * PLACE the factors, and multiply them together the same as if they were whole numbers.-Then point off in the product just as many places of decimals as there are decimals in both the factors. But'if there be not so many figures in the product, then supply the defect by prefixing ciphers. * The Rule will be evident from this example:-Let it be required to multiply 12 by 361; these numbers are equivalent to and; the product of which is 433304332, by the nature of Notation, which consists of as many places as there are ciphers, that is, of as many places as there are in both numbers. And in like manner for any other numbers. |