8. What is the difference between of 5 of a pound, and of a shilling? Ans. 33 100 or 1l 8s 11d. 149 MULTIPLICATION OF VULGAR FRACTIONS. * REDUCE mixed numbers, if there be any, to equivalent fractions; then multiply all the numerators together for a numerator, and all the denominators together for a denominator, which will give the product required. 2. Required the continual product of, 31, 5, and of 3. 3. Required the product of and §. 4. Required the product of and. 5. Required the product of 4, 4, and 11. * Multiplication of any thing by a fraction, implies the taking some part or parts of the thing; it may therefore be truly expressed by a compound fraction; which is resolved by multiplying together the numerators and denominators, Note, A Fraction is best multiplied by an integer, by dividing the denominator by it; but if it will not exactly divide, then multiply the numerator by it. 6. Required Ans. 1. Ans. 23. Ans.. Ans. 20. 6. Required the product of,, and 3 7. Required the product of 7, 3, and 4. 8. Required the product of, and of. 9. Required the product of 6, and 2 of 5. 10. Required the product of of 3, and § of 34. 11. Required the product of 3 and 4. 12. Required the product of 5, 3, 4 of 3, and 41. Ans. 2. Ans. . Ans. 1411. 23 DIVISION OF VULGAR FRACTIONS. * PREPARE the fractions as before in multiplication; then divide the nnmerator 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. : BXAMPLES. 1. Divide 25 by §. = Here 5 = 13, by the first method. 2. Divide by Here 3. It is required to divide * Division 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 4 of 73. Ans. T RULE OF THREE IN VULGAR FRACTIONS. MAKE the necessary preparations as before directed; then multiply continually together, the second and the 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 will of a yard cost? 2. What will 33 oz of silver cost, at 6s 4d an ounce ? Ans. 1l 1s 44d. 32 Ans. 2271 12s 1d. 3. If of a ship be worth 273/ 2s 6d; what are of her worth? 4. What is the purchase of 12301 bank-stock, at 108 per cent.? Ans. 1336 18 9d. 5. What is the interest of 2731 15s for a year, at 31 per cent.? Ans. El 17s 114d. 6. If of a ship be worth 731 18 3d; what part of her is 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. 181 inches. 8. What quantity of shalloon that is of a yard wide, will line 9 yards of cloth, that is 24 yards wide? Ans. 314 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. 10 9. If 9. If the penny loaf weighs 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. 4 oz. 10. How much in length, of a piece of land that is 1111 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. 40815 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 yard wide: how many yards of shalloon will line them? 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 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. 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 335. 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. 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 1, 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 100th 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 ten-fold proportion; as in the following Scale or Table of Notation. 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 29.0146, 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, 7195-6, 71.498, 9739-215, 179, and ⚫0027 ? SUBTRACTION |