EXAMPLES For Theoretical Exercise on a Slate. 1. Reduce 5 of 4 of 4 to a simple fraction. Ans. = EXPLANATIONS. In this example, you must multiply the 5, 4, and 3, the numerators, together, for a new numerator, and the 9, 8, and 4, the denominators, for a new denominator. 2. Reduce 288 60 numerator. 288 denominator. of of 15 to a simple fraction. Ans. 450. 욕 8 9 1064 360 18. 3. Reduce 4 of 5 of 7 to a simple fraction. Ans. 140 = 7 4. Reduce 4 of 1 of 1 to a simple fraction. Ans. 836 1500 RULE. Q. How do you reduce fractions of different denominators to equivalent fractions having a common denominator? A. Each numerator must be multiplied by all the denominators, except its own, for the new numerator; and all the denominators must be multiplied together for a common denominator. EXAMPLES For Theoretical Exercise on a Slate. 1. Reduce and to equivalent fractions, having a common denominator. Ans. 18, 35. EXPLANATIONS. 99 7 72 5 63 18 35 In this example, you must multiply the 9 and the 7, the denominators, together for a common denominator; and then multiply the denominator, 9, and the numerator, 2, and the 7 by the 5, for new numerators. You will readily perceive, that the value of the fraction is not altered, for each numerator and its denominator is multiplied by the same numbers, and by reducing the new fractions to their lowest terms, you would again have the given fractions. 13, 35 Ans. 2592 1980 3456 3456 3 4 5 6 2. Reduce 2, 3, and 4 of 11 to equivalent fractions, having a common denominator. Ans. 768 3. Reduce 11, 3 of 11, 7, and to equivalent fractions, having a common denominator. Ans. 8448 1296.0 7200 11520 8 6720 1152 0911 52 091152 J 4. Reduce 4,, and 10 common denominator. 400 1000 1000 1000 to equivalent fractions, having a Ans. 800 300 ADDITION OF VULGAR FRACTIONS. Q. What is Addition of Vulgar Fractions? A. Addition of Vulgar Fractions teaches to join, or add, several broken numbers, or integers, into one sum. RULE. Q. How do you add Vulgar Fractions? A. Compound fractions must first be reduced to single ones, mixed numbers to improper fractions, and fractions of different integers to those of the same. and all of them to a common denominator; then the sum of the numerators written over the common denominator, will be the surn of the fractions required. EXAMPLES For Theoretical Exercise on a Slate. 1. What is the sum of 2 and 3? Ans.31. Here, in this example, you first multiply the 2 and 8 together, making 16 for the numerator of; and then 5 and 3 together, making 15 for the numerator of 3; and then EXPLANATIONS. 2 16 numerator of 2. 15 numerator of 3. 16 15 8 add the 16 and 15, the 31 sum of the numerators. 5 for a common denomi- 40 common denominator. nator, and you then have the fraction 31. Fractions are quite dissimilar before they are reduced to a common denominator: thus, in the first fraction,, a unit is divided into 5 parts; and in the second fraction,, a unit is divided into 8 parts; and, therefore, the parts are unequal till reduced to a common denominator, and we then have 16 and 15, which make 31. That the value of the fraction is not altered by the operation is very plain, as the numerator and denominator are multiplied by the same number: hence, it is evident, that a unit in each fraction is divided into 40 parts, and, therefore, the numerators may be added, as they are parts of one common integer. 2. Add, and together. Ans. 17 3. Add 1, 4, and 1⁄2 together. Ans. 1Ų. 39 4. Add 6, 5, and 5. Add 73, and 5 7. Add 3s. and £1 together. 8. Add 1 of a week, of a day, of an hour, and 3 of a minute together. Ans. 2d. 2h. 30min. 9. Add 4 of a tun to 5 of a cut. 45sec. Ans. 9cwt. 1qr. 62lb. of an ounce. Ans. 2oz. 101pwt. 7 of a furlong. Ans. 6fur. 28po. of a yard, and a of a foot together. 10. Add of a pound troy to 11. Add 3 of a mile to 12. Add of a mile, Ans. 1540yd. 2ft. 9in. 8 SUBSTRACTION OF VULGAR FRACTIONS. Q. What is Substraction of Vulgar Fractions? A. Substraction of Vulgar Fractions teaches to take one broken number, or integer, from another. RULE. Q. How do you substract Vulgar Fractions? A. The fractions must first be prepared as in Addition; one numerator must then be substracted from the other, and the difference placed over the common denominator, will give the difference of the fraction required. EXAMPLES For Theoretical Exercise on a Slate. 1. What is the difference between 3 and 3? Ans. EXPLANATIONS. In this example, you substract 2 from 6, which leaves 4, the difference between the 6 2 two numerators. Here it 4 difference between numerators. is plain, that the difference between and is or, to 1 Ans. for the fractions have a com mon denominator; that is, a unit in each fraction is divided into eight equal parts, and, therefore, the difference of the numerators placed over the common denominator, must express the difference of the fractions. 15 Ans. 13.25. 2. From 7 take 4. Ans. 54. 3. From 14 take 13. 4. From 365 take 1 5. From 131 take 2 of 15. 6. Substract 54 from a unit. 7. From £1 take Z of a penny. 8. From 15 days take 94 days. 9. From 3 of a tun take 2 of 3 of a pound. Ans. 7cwt. 1qr. 27lb. 8oz. Ans. 364 45 10. From 5 of a pound troy take of an ounce. Ans. 9oz. 7pwt. 10 11. From 2 of a league take 7 of a mile. Ans. 1m. 2fur. 16po. 12. From 3 of a league take § of a mile. Ans. 1.7 m. 10 MULTIPLICATION OF VULGAR FRACTIONS. Q. What is Multiplication of Vulgar Fractions? A. Multiplication of Vulgar Fractions teaches to repeat a whole, or broken number, by a part or the parts of an integer. |