6. Add and together. 7. What is the sum of 8. What is the sum of 9. What is the sum of 10. What is the sum of and 24 ? Ans. 140 Ans. 58. Ans. 10 60 of a shilling? of a pound and 11. What is the sum of of a shilling and of a penny ? Ansd or 7d ligg. 12. What is the sum of of a pound, and of a shilling, and of penny? Ans. 1 or 3s id 19 Aus. SUBTRACTION OF VULGAR FRACTIONS. PREPARE the fractions the same as for Addition, when necessary; then subtract the one numerator from the other, and set the remainder over the common denominator, for the difference of the fractions sought. 2. To find the difference between 3 and §. -4=37-38 = 7, the Answer. 3. What 39 Ans. 5 Ans 3. What is the difference between 5 and 7 ? 4. What is the difference between and ? 5. What is the difference between and ? Ans. 19 6. What is the diff. between 53 and 2 of 4? Ans. 7. What is the difference between of a shilling? 156 I 4765. of a pound, and of 191 Ans. 18 or 10s 7d 149.. 8. What is the difference between of 5 of a pound, and of a shilling? Ans. or 11 88 1d. 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. * 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 6. Required the product of, 3, and 3 7. Required the product of 3, 3, and 4 8. Required the product of, and of . 9. Required the product of 6, and of 5. 10. Required the product of of, and of 32 11. Required the product of 32 and 4 12. Required the product of 5, 3, 4 of 3, and 41. 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. EXAMPLES. 1. Divide 25 by. = Here 25 = 13, by the first method. 2. Divide by Here × V = § × {="— 4%. = 3. It is required to divide 1 by 4. Ans.. Ans. 7 Ans 1 Ans. T Ans. Ans. *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. 11. It is required to divide 73 by 95. Ans.. 12. It is required to divide of by 1⁄2 of 73. Ans. 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. will 1. If of a yard of velvet cost of a pound sterling; what of a yard cost? 3 2 5 8 2 B 2. What will 3 oz of silver cost, at 6s 4d an ounce ? Ans. Il 18 4 d. 3. If of a ship be worth 2731 28 6d; what are of her worth? Ans. 227/ 128 ld. 4 What is the purchase of 1230/ bank-stock, at 108 per cent. ? Ans. 1336/ ls 9d. 5. What is the interest of 2731 15s for a year at 3 per cent ? Ans 81 178 111d. 6 If of a ship be worth 737 18 3d; what part of her is worth 250/ 108? 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. 1811 inches. 8 What quantity of shalloon that is of a yard wide, will line 94 yards of cloth. that is 24 yards wide? Ans. 31 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. K 9. If 9. If the penny loaf weight 6 oz, when the price of wheat is 58 the bushel; what ought it to weigh when the Ans. 40%. wheat is 8. 6d the bushel? 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 Ans. 13 poles. poles in length and 4 in breadth? 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 nen, are to be new cloathed; each coat to contain 2 yards of cloth that is yard wide, and lined with shalloon 7 yard wide: how many yards of shalloon will line them? 1 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 leftband Thus, is 4, and 24 is 24, and is 074, and 124 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. 700000 74 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 535, or 325. = 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, 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 For in decimals, as well as thirds, or 1000ths; and so on. in whole numbers, the values of the places increase towards the left-hand, and decrease towards the right, both in the same |