EXPLANATIONS. 2 24 16h. In this example, you must multiply the 2, the numerator, by 24, because twenty-four hours make a day, and also because hour is the next inferiour denomination in time. When there is a remainder of 3)48 hours or minutes, you must multiply it by 60, because sixty minutes make one hour, and sixty seconds one minute. Thus, then, it is very plain, that when you wish to continue the division, and express the fraction in the inferiour denomination, you must reduce the remainder to the next inferiour denomination by multiplying the remainder, as before directed, and divide by the denominator of the fraction. 3. What is the weight of a of a pound avoirdupois? Ans. 12oz. EXPLANATIONS. 4 3 12oz. = The value of any fraction may also be 4)16oz. tọ 12b. found by dividing the number that it takes of the next inferiour denomination to make a whole number of the denomination of the given fraction, by the denominator of the fraction, and multiply the product by the numerator of the fraction. Thus, in this example, sixteen ounces make one pound, and you must divide the 16 by 4, and then multiply the product, which is 4 also, by 3, the numerator, which gives the answer, 12oz., the same as by the other operation. If there be a remainder, proceed as with the first division, namely, divide the number that it takes of the next lower denomination to make one of the remainder. 4. What is the value of of a day? Ans. 16h, 36mın. 555 sec. 5. What is the value of Z of a hundred-weight? Ans. 3qr. 3lb. 1oz. 124dr. 6. What is the value of 2 of a pound troy? Ans. 7oz. 4prot. 7. What is the value of of a bushel? Ans. 12qt. 7 8. What is the value of 4 of a hogshead of wine? Ans. 54gal. Ans. 6fur. 26po. 11ft. 9. What is the value of 1⁄2 of a mile? 10. What is the value of § of an acre? Ans. 2r. 20po. 11. What is the value of 2 of a yard? Ans. 2qr. 22na. 12. What is the value of of an ell English? Ans. 4gr. 11na. RULE. Q. How do you reduce any given quantity or inferiour denomination to the fraction of some superiour denomination, which shall retain the same value? A. The given sum must be reduced to the lowest denomination mentioned for a numerator; then the unit must be reduced to the same denomination for a denominator, which will be the fraction required. EXAMPLES For Theoretical Exercise on a Slate. 1. Reduce 13s. 4d. to the fraction of a pound. Ans. £2. You must first reduce 13s. 4d. to pence, for a numerator, by multiplying the 13 by 12, and adding in the 4 pence, because pence is the fowest 160 S. 5) 2) 8)260-20-4-2 Ans. 3 20 integral part. 12 denomination mentioned in the numerator contains 160 similar parts, because both numerator and denominator express pence; hence, the denominator, 240, shows that a unit, or £1, is divided into 240 parts, and the numerator shows that the fraction contains 160 of those parts, which, reduced to its lowest given term, gives of a 2. Reduce 4d. 2qr. to the fraction of a shilling. Ans. §. 3. Reduce 6 hours to the fraction of a day. Ans. 1. pound. 56 4. Reduce 13cwt. 3qr. 20lb. to the fraction of a tun. Ans. 32. 5. Reduce 7oz. 4pwt. to the fraction of a pound troy. Ans.3. 6. Reduce 12qt. to the fraction of a bushel. Ans. 3. 7. Reduce 1hhd. 49gal. of wine to the fraction of a tun: Ans. . Ans. Ans. §. 8. Reduce 9gal. to the fraction of a hogshead. Ans. 4. 9. Reduce 6fur. 16po. to the fraction of a mile. 10. Reduce 2r. 20po. to the fraction of an acre. 11. Reduce 3gr. 3na. to the fraction of a yard. Ans. 15. 12. Reduce 4gr. lina. to the fraction of an ell English. Ans. z. RULE. Q. How do you reduce an improper fraction to a whole or mixed number? A. The numerator must be divided by the denominator, and the quotient will be the answer sought in a whole or mixed number. EXAMPLES For Theoretical Exercise on a Slate. 1. Reduce 22 to its equivalent whole, or mixed number, Ans. 12. EXPLANATIONS. Here, in this example, you divide 72, the numerator, by the 6, the denominator. The numerator shows how many parts the fraction contains, and the denominator shows how many of those parts it requires to make a unit. 6)72 17 2. Reduce 233 to its equivalent whole, or mixed number. Ans. 849. 3. Reduce 1 to its equivalent whole, or mixed number, Ans. 9. 17 4. Reduce 742 to its equivalent whole, or mixed number. Ans. 4417. RULE. Q. How do you reduce a mixed number to its equivalent improper fraction? A. Multiply the integer, or whole number, by the denominator of the fraction, and add the numerator to the product; then that sum must be placed above the denominator for the fraction required. EXAMPLES For Theoretical Exercise on a Slate. 1. Reduce 127 to its equivalent improper fraction. Ans. 114, 9 EXPLANATIONS. 127 9 denominator. 108 numerator added. In this example, you must multiply 12 by 9, and add the numerator,, the 7, to the product, 108; the sum, 115, is the new numerator of the fraction sought, and the denominator; thus, you will have 115 the improper fraction, equal to 127. This operation 115 new numerator. is very plain; for by multiplying the 12 by 9, the denominator, you reduce the 12 to ninths, that is, 108 ninths, and the 7 ninths, added to these, make 115 ninths, the answer. 2. Reduce 365 to its equivalent improper fraction. Ans. 293 3. Reduce 1912 to its equivalent improper fraction. Ans. 354 9 denominator. 4. Reduce 5411 to its equivalent improper fraction. Ans. $52. RULE. Q. How do you reduce a whole number to an equivalent fraction, having a given denominator? A. The whole number must be multiplied by the given denominator, and the product must then be placed over the said denominator, and it will form the fraction required. EXAMPLES For Theoretical Exercise on a Slate. 1. Reduce 6 to a fraction, whose denominator shall be 8. Ans. 48. EXPLANATIONS. Here, in this example, you must multiply the 6 by the 8, and take the product, 48, for the numerator, and the 8 for the denominator. 68 48 2. Reduce 18 to a fraction, whose denominator shall be 12. Ans. 218. 3. Reduce 29 to a fraction, whose denominator shall be 15. Ans. 4.35. 4. Reduce 9 to a fraction, whose denominator shall be 7. Ans. 3. RULE. Q. How do you reduce a compound fraction to a simple or improper fraction? A. All the numerators must be multiplied together for a new numerator, and all the denominators must be multiplied together for a new denominator, and they will form the fraction required. |