5. What fraction of a bushel is 16 qt.? What decimal of a bushel ? 6. What fraction of a pound is 15 s.? What decimal of a pound? 7. Reduce 1 ft. 6 in. to the fraction of a yard. To the decimal of a yard. 8. What fraction of 3 feet is 18 inches? 9. Reduce 30 minutes to the decimal of 2 hours. 10. What fraction of 3 bushels is 3 pecks? WRITTEN EXERCISES. 1. Reduce 10 oz. 18 pwt. 12 gr. to the fraction of a pound. ANALYSIS.-In 10 oz. 10 oz. 18 pwt. 12 gr. = 5244 gr. 18 pwt. 12 gr. there are 1 lb. = 5760 gr. 5244 gr., and in 1 lb. there are 5760 gr. 5244 $444 = 437. gr.= 5244 or 4 37 of a pound. 2. Reduce 10 oz. 18 pwt. 12 gr. to the decimal of a pound. ANALYSIS.–10 oz. 18 10 oz. 18 pwt. 12 gr. = 5244 gr. pwt. 12 gr. =437 of a 1 lb. = 5760 gr. pound. 437 of a pound 5444 = 437 = .9104 + reduced to a decimal= .9104 + of a pound. RULE. Reduce the given numbers to the lowest denomination mentioned in either. Write the number which is to become the fractional part, for the numerator of the required fraction, and the remaining number for the denominator, and change the fraction to its lowest terms, or to a decimal if necessary. 3. Reduce 16 s. 8 d. 1 far. to the fraction of a pound. To the decimal of a pound. 4. Reduce 12 cwt. 90 lb. to the decimal of a ton. 5. From a farm containing 120 A. 60 sq. rd., there were sold 40 A. 29 sq. rd. ; what fractional part of the farm was sold? 6. If £1 is worth $4.8665, what is the value of £5 9 s. 6 d.? 7. Reduce 3 pk. 7 qt. 1 pt. to the decimal of a bushel. 8. Reduce 7 oz. 5 pwt. 20 gr. to the decimal of a pound. 9. What fraction of a cord is 65 cu.ft. 144 cu.in.? 10. What decimal of a week is 1 da. 6 hr. 30 min.? PERCENTAGE. Per Cent. is an abbreviation of the Latin words per centum, meaning by the hundred, and any per cent. of a number is that many hundredths of the number. ILLUSTRATION.-In a town of 600 people, 3 per cent. can neither read nor write; this means that three in every hundred, or eighteen in all, can neither read nor write. In the above example we find three points to be considered: the base (600 people), the rate (3 per cent.), and the percentage (18 people). The Base is the number on which the percentage is computed. The Rate or Rate Per Cent. is the number in each hundred or the number of hundredths to be taken. The Percentage is the result obtained by taking as many hundredths of the base as are indicated by the rate. The sign % is generally used instead of the words per cent.; thus, 6%, 81%. As the rate per cent. is a number of hundredths, it may be expressed either decimally, or as a common fraction. Thus:1% = .01 or Too. 21% = .024 or 100 L291 33 Note.In expressing any rate per cent., when the decimal point is used, the words per cent. and the sign % are omitted; when either the sign or the words are used, the decimal point is omitted. CASE I. ORAL EXERCISES. 1. Express 5% as a common fraction in its lowest terms. ANALYSIS.—5%=160 = t. 2. Express in the same manner 10%, 20%, 25%, 40%, 50%, 60%, 75%, 80%, 121%, 161%, 33}%, 661%. 3. What is 10% of $80? ANALYSIS.—10% = 10% or 1o. 1 of $80=$8. 4. What is 20% of 60? Of 80? Of 100? Of 7? 5. What is 50% of 12 horses? Of 60 dollars ? 6. What is 33% of 18? Of 24? Of 90? 7. I bought two dozen hams, of which 25% were unfit for use; how many were good ? 8. A farmer raised 500 bushels of corn, and sold 20% of it; how many bushels did he sell? 9. A man received 124% of $800; how many dollars did he receive? 10. From a hhd. containing 63 gallons, 331% leaked out; how much remained ? 11. In a school of boys and girls containing 200 pupils, 50% are girls; how many are boys? 12. A received 20% of 100 dollars, and B 75%; how much did each get? 13. A man buys a sewing-machine and pays 10% of the price every week; in how many weeks will he have paid for it? WRITTEN EXERCISES. 1. What is 8% of 720 gallons ? ANALYSIS.—We express the rate % decimally .08 and multiply; 8%=.08, and .08 of 720 gal. = 57.60 gal. 57.6 gal. RULE. Multiply the given number, or base, by the rate expressed decimally; the product will be the percentage. What is: 2. 8% of 1220 men? I 7. 17% of $165.25? 3. 33% of $1000? 8. 36% of $2000? 4. 65% of 11692? I 9.5% of 1600 pounds? 5. 331% of 1200 sheep? 10. 112% of 540 yd. ? 6. 1% of 960? 11. 99% of 99? 12. A horse costing $150 was sold at a loss of 20% ; what was the loss ? 13. On a bill of goods amounting to $183.76, 5% was deducted for cash; how much was paid ? 14. A clerk receives a salary of $1800; he pays 16 % of this for rent, 663% for family expenses, and saves the remainder; how much does he save? 15. An agent collects $1817.12, of which he retains 21 %; how much does he hand over to his employer? 16. A man bought a house for $6500, and sold it for 6% more than he gave for it; how much did he get for the house? 17. A merchant, failing in business, paid his creditors 80 cents on the dollar; what % did he pay, and how much did the man receive to whom he owed $1854.96 ? 18. What is 5% of £18 12 s. 6 d.? CASE II. To find what per cent. one number is of another. |