EXAMPLES. 1. To add and together. Here } + $ } like the Answer. 2. To add and together. *+= + 16 = = lyg, the Answer. 3. To add and 7, and 1 of 1 together. +7 + 1 of 1 = $ ++ = + + i=83. 4. To add and together. Ans.! 14. 5. To add and together. 6. Add and together. 7. What is the sum of z and } and ? 8. What is the sum of , and and 2 ? Ans. 578 9. What is the sum of į and of j. and 9. ? 10. What is the sum ol of a pound and of a shilling? Ans. 1350 or 138 100 29. 11. What is the sum of of a shilling and is of a penny ? Ans d or 7d 19. 12. What is the sum of 4 of a pound, and į of a shillingi and is of penny ? Ans. **s or 3s 1d 11,9 Ans 15 Ans. Ans. 1405 Ans. 1066 10089 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. EXAMPLES 1. To find the difference between and Here -== }, the Answer. 2. To find the difference between # and . -= = 3 - 3 = }, the Answer. 3. What Ans š 5 39" 3. What is the difference between and ? 4. What is the difference between iş and it? Aos 5. What is the difference between is and is? Ans. 16 6. What is the diff. between 5 and ļof 47? Ans. 436. 7. What is the difference between of a pound, and of # of a shilling? Ans. Pr's or 10s 70 149. 8. What is the difference between of 53 of a pound, and of a shilling? Ans. 1872 or 12 88 1.d. 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 denomi. nator, which will give the product required. EXAMPLES. 1. Required the product of and. Here 3 x 3 š, the Answer. Orx = = . 2. Required the continual product of z, 31, 5, and of 13 3 13 X 3 39 Here Х X Х Х 47 Ans. 3 4 1 4 5 4 x 2 8 3. Required the product of and 4. Required the product of u and it 5. Required the product of, g, and is. Ans. Ans. 11 Ans.is * 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 5, and 3 7. Required the product of , }, and 4 is 8. Required the product of, and of 9. Required the product of 6, and of 5. 10. Required the product of of }, and of 3 11. Required the product of 34 and 4 . 12. Required the product of 5, į, of , and 47. 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. Ans. 1. Divide by s. Here 25 f == 1, by the first method. 2. Divide by its Here is = * * * =* =* = 4. 3. It is required to divide in by . 4. It is required to divide 76 by 1. 5. It is required to divide by z. 6. It is required to divide & by '*. 7. It is required to divide by 8. It is required to divide by t. Ans. I Ans is. Ansis 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. 9. It is required to divide 1% by 3. 10 It is required to divide y 2. 11. It is required to divide 7 by 9. 12. It is required to divide şof } by 4 of 7}. RULE OF THREE IN VULGAR FRACTIONS. MAKE the necessary preparations as before directed; then muluply 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 is of a yard cost? 3 2 5 8 6 = 68 8d, Answer, 8 5 16 3 3 26 2. What will 3 oz of silver cost, at 68 4d an ounce ? Ans. 11 18 4 d. 3. If ic of a ship be worth 2731 28 64 ; what are of her worth ? Ans. 2271 128 ld. 4 What is the purchase of 12301 bank-stock, at 108 per cent. ? Ans. 13361 18 9d. 5. What is the interest of 2732 158 for a year at 34 per cent ? Ans 81 178 1114. 6 Iff of a ship be worth 732 18 3d; what part of her is worth 2502 108? 7. What length must be cut off a board that is 74 inches broad, to contain a square foot, or as much as another piece of 12 inches long and 12 broad? Ans. 1841 inches, 8: What quantity of shalloon that is of a yard wide, will line 94 yards of cloth. that is 2 yards wide ? Ans. 31 yds. Ans. * This is only multiplying the 2d ard 3d terms together, and dividing the product by the first, as in the Rule of Three in whole numbers. Vol. I. 9. If 9. If the penny loaf weight 6.7 oz, when the price of wheat is 58 the busnel ; what ought it to weigh when the wheat is 8. 6d the bushel ? Ans. 415 02. 10. How much in length, of a piece of land that is ilit poles broad. will make an acre of land, or as much as 40 poles in length and 4 in breadın? Ans. 134 poles. 11. If a courier perform a certain journey in 354 days, travelling 13 hours a day; how long would he be in per forming the sanie, travelling only 11 hours a day? Ans. 40$ days. 12. A regiment of soldiers, consisting of 976 pen, are to be new cloaihed; each coat to contain 21 yards of cioth that is yard wide, and lined with shalloon Ž 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 deno. minator an unit (1), with as many ciphers annexed as the nun eraior has places; and it is usually expressed by setting down the numerator only, with a point before it, on the leftband Thus, yo is 4, and too is 24, and rõõo is 074, and T70700 is 00124 ; where ciphers are prefixed to make up as m.uy 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 57 f, or 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 to or . But when they are placed on the left-hand they decrease the value in a ten-fold proportion : Thus, :4 is 1o, or 4 tenths : but .04 is only toor or 4 hundredths, and .004 is only rooo, 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 ihe place of seconds, or 100ths ; the 3d is the place of thirds, or 10001hs; 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 |