3. Boston, March 30th, 1901. John Williams bought of Edgar Peirson, 9 yards of calico @ $.12; 15 yards cambric @$.25; 16 yards sheeting @ $.183; 5 dozen towels @ $3.75. 4. April 13, 1901, New York. J. Williams & Co. sold to James Garsed, 12 yards cassimere @ $1.12; 20 yards doeskin @ $.911; 18 yards flannel @ $.62; 10 yards alpaca @ $.87. Make out and receipt the bill. 5. William Watson bought of Henry Stout, Richmond, May 1, 1901. 12 pounds Oolong tea @ $1.10; 8 pounds Young Hyson tea @ $.95; 15 pounds Rio coffee @ $.371; 20 pounds sugar @ $.124. Make out and receipt the bill. 6. Charles Foulke bought of T. P. Smith & Bro., Philadelphia, Nov. 15, 1901 8 pair calf boots, @ $5.623; 10 pair brogans, @ $1.123; 12 pair ladies' kid boots, @ $1.66;; 15 pair boys' gaiters, @ $2.25. Make out and receipt the bill. SECTION XIX. REDUCTION OF DECIMALS. CASE I. To Change a Decimal to a Common Fraction. 1. How is .2 expressed as a decimal fraction? .3? .5? .7? 2. What decimal fraction of a dollar is $.5? $.25? $.75? 3. Express.5 as a decimal fraction, and change it to halves. 4. How many halves in 50? 500? In .5? .50? .500? many 100 1000 fifths? 20 100 5. How many fourths in?? In .50? In .250? 6. In are how ? In .4? .6? .80? 7. In, how many twentieths? Tenths? Fifths? Halves? 8. Express .25 as a common fraction in its lowest terms; .375 of an acre; .625 of a ton; .0625 of a foot. 370. Principle. A decimal fraction is a decimal with the denominator expressed. Written Exercises. 371. Example 1.- Change .875 to an equivalent common fraction in its lowest terms. EXPLANATION.-Since .875 is 875 thou 7 sandths, it may be expressed in the form 8 372. Example 2.- Express 2.37-as a mixed number. 373. Rule to Change a Decimal to a Common Fraction. For the numerator, write the decimal with the decimal point omitted; and for the denominator, write 1 with as many ciphers annexed as there were places in the given decimal. the common fraction thus formed to its lowest terms. Problems. Reduce Change, or reduce, to fractions in their lowest terms 1. .4; .6; .8; .9. 3. .625; .875. |5. $.75; $.80; $.125. 2. .25; .45; .75. 4. .825; .0025. 6. $.008; $.0065. 7. Reduce.0075 and.0004 to equivalent common fractions. 8. Change .00375 to a common fraction in its lowest terms. Change to common fractions in their lowest terms To Change a Common Fraction to a Decimal. 1. In 1 dollar are how many tenths of a dollar? In $2? 1÷ 5? 2. In 1 are how many tenths? In how many? 3. How many tenths in 1 divided by 2? 4. How many tenths in 2 divided by 5, or ? 374. Analysis.—Since 1 is 10 tenths, 2 is 2 times 10 tenths, or 20 tenths; 20 tenths divided by 5 are 4 tenths. Hence, = fo, or .4. ? 5. How many hundredths in 1? In 1÷2, or 6. In how many tenths? Hundredths? Thousandths? 7. How many hundredths in ? Thousandths in g? 8. In how many hundredths? thousandths? 375. Principle. Thousandths? Ten The value of a fraction is the quotient of the numerator divided by the denominator. Written Exercises. 376. Example 1. — Change å to an equivalent decimal. SOLUTION. EXPLANATION. - is 34, or 4 of 3. = .75. 43.00 .75 Since 1 is 10 tenths, 3 is 3 times 10 tenths, or 30 tenths; of 30 tenths is 7 tenths, with 2 tenths remaining. Since 1 tenth is 10 hundredths, 2 tenths are 2 times 10 hundredths, or 20 hundredths; of 20 hundredths is 5 hundredths. The result is 7 tenths 5 hundredths, or .75, the decimal required. 377. Example 2.-Change 61 to a mixed decimal. 4)1.00 .25 Since 1 is 10 tenths, of 10 tenths is 2 tenths, etc. (Ex. 1). The result is 6 + .25, or 6.25, the mixed decimal required. 378. Rule to Change a Common Fraction to a Decimal. Annex ciphers to the numerator, and divide by the denominator; and from the right hand of the quotient point off as many places for decimals as there were decimal ciphers annexed. The quotient will be the decimal required. 21 32 3. ; ; 43. 6. 345; 695; 845.9. $65%; of $9. 40 50 10. Change,, 19 to decimals of five places each. 11. Reduce to decimals of five orders each 3, 43, 64. 61 12. 7; 8,5%. 15. 10.02; 12.043. 18. $73; $83. 13. 470; 71716. 15.0681; 20.087. 19. $.61; $.01ģ. 14. 5.2; 9.31. 17. 25.00; 50.00. 20. $1.00; $41. Review. 1. What orders of decimal units only can be added? State the principle of addition of decimals. Repeat the rule. How many decimal places in the sum of tenths and tenths? Tenths and hundredths? Tenths and thousandths? Hundredths and thousandths? 2. When only can one decimal fraction be taken from another? One decimal from another? One order of decimal units from another? State the principle of subtraction of decimals. Repeat the rule. How many decimal places in the difference between tenths and tenths? Tenths and hundredths? Hundredths and thousandths? 3. State the principle of multiplication of decimals. How many decimal places in the product of tenths by tenths? Tenths by hundredths? Hundredths by hundredths? Thousandths by hundredths? Thousandths by thousandths? In the product of any two decimals? Repeat the rule. What is to be done when the number of decimal places in the product does not equal the number in both factors? How do you multiply a decimal by 10, 100, 1000, etc.? 4. Of what two factors is the dividend the product? In decimals, the dividend contains as many decimal places as what two factors? Of what order of units is the quotient of tenths divided by tenths? Hundredths by hundredths? Hundredths by tenths? Thousandths by tenths? Of any decimal divided by another decimal? State the principle of division of decimals. Repeat the rule. What is to be done when the number of decimal places in the quotient is too small? If the dividend has not so many places as the divisor before division? If there is a remainder? How do you divide a decimal by 10, 100, etc.? 5. What is United States Money? What is the principal unit? How are dimes usually regarded? What decimal of a dollar is one cent? How many figures are needed to express cents decimally? To express mills? State the principle of notation. The general principles of all computations in United States money. Define Bill of Goods. Define debtor. Creditor. Footing of a bill. 6. In what two ways may a decimal be expressed? State the principle of changing a decimal to a common fraction. Repeat the rule. State the principle of changing a common fraction to a decimal. Repeat the rule. |