now about article will a certain the exact to make -kly. Fa or 4400 price will 54. Solution of Problems.-First reread Arts. 14 and 3 Find the cost of 450 lb. of oats at 56¢ per bushel 32 lb. In the above problem the total price is wanted. As th price of one bushel is given, the total price is obtained b multiplying the number of bushels by the price of on bushel. The number of bushels in 450 lb. is found by divi ing 450 by 32, as there are 32 lb. in each bushel. In th place of dividing 450 by 32 merely indicate it; thus, 452 Then indicate that this-the number of bushels-is mu tiplied by 56. Thus: ng com oal had ely have stimate is esti close Put all of your attention on: 1. Reading and understanding the problem; 2. Putting down the numbers to indicate the necessar operations; 3. The numerical work needed-including checks; 4. Interpreting the result, which here is in dollars or cents By following these suggestions you can keep your atten tion upon one thing at a time and save work in computation: Be constantly on the lookout for an opportunity to us the opposite processes, cancellation, or any other short cu in computations. Check all final results. Before findin the exect result olwers estimate it EXERCISES 1. Explain the four processes used in so Illustrate by solving problems 3 and 4 which 2. Show the advantage of indicating the first before doing any of it. 3. What is the cost of 1,260 lb. of oats at 6 4. A dealer sells goods that are out of sea the marked price. For what will he sell an at $12? at $61? at $33? at $18? at $ Oilcloth 30 in. wide 212° 32° 5. yard. At the same rate wh cost of oilcloth 42 in. wide? 6. Five degrees on the Co mometer equal 9 degrees on t thermometer. What will be the Fahrenheit thermomete Centigrade falls 10 degrees? grees? falls 32 degrees? falls 7. What will be the change grade thermometer when th falls 36 degrees? rises 13 d 10 degrees? falls 153 degree 8. Coal which sold for $7 per ton has ad price. For what does it now sell? 9. For what fractional part of last year's p now sell which has advanced over last year 10. Coal which has advanced over last y $4 per ton. What was the price last year? price was what fractional part of this year's pr 11. If coal which sold for $5 per ton last $6 per ton this year, what part of last year's advanced? How much more will be the cos problems W. ber work bushel? belo marked 28¢ per be the vide? Le ther renheit nge in the 12 de grees? Centi nheit rises in coal for ar's for 12. A farmer owning 160 acres of land sells and the of the remainder. What part of the land has he left How many acres has he left? The acres he has left is wha fraction of the land he sold ? Often a fraction has no meaning. If such a fraction or more, the number is made one larger; if the fractio is less than the fraction is merely omitted. Thus, 37 cents become 38 cents; 293 cents become 30 cents; 48 cents become 48 cents. Similarly, 7 footballs would be footballs, 9ğ boys would be 10 boys. Give other illustration 13. Only of the business men of the United Stat are considered successful. At that rate how many are con sidered successful out of 420? out of 356 ? out of 164? 14. At the rate of 3 boxes of berries for 25 ¢, what wi be the cost of a case of 12 boxes? a case of 15 boxes? case of 32 boxes? 15. If John makes 6 safe hits in 25 times at bat, ho many safe hits will he make at the same rate in 35 times a bat? in 56 times? in 100 times? in 47 times? 16. If Henry makes 4 errors in 71 chances he has ha in the field, how many errors would he make at the sam rate in 36 chances? in 108 chances? in 15 chances? 17. How many correct plays would Henry make at th above rate in 42 chances? in 178 chances? in 28 chances 18. A certain excursion fare is $61%. What will be th cost of 12 full and 9 half-fare tickets? 19. A merchant sold a suit of clothes for $30 upon whic he made. What did the merchant pay for the suit? III DECIMAL FRACTIONS 55. Meaning of Decimals.-How many ar by each digit in 345? in 5,555 ? in 654? Hov of a digit changed by moving the digit to the ri left? About three hundred years ago mathematici write fractions in a way similar to that in which bers are written. Such fractions are called d tions, or merely decimals. A period, called point, is placed before all such fractions. The the right of the decimal point takes in unit's place, the second digit takes in unit's place, and so on. Thus in 0.76 there are which become 10%. How? Similarly, 0.045 is T or 150. How? the va the va 1 In mixed numbers the whole number is sep the fraction by the decimal point. Thus, 53.67 845.0405. 56. Reading Decimals.-Decimals are read b ing the whole number, and for the decimal point, the decimal part. Thus, 245.617 is read "tw forty-five and six hundred seventeen thousandth 57. Decimal Places. The digits and zeros in are called its decimal places. How many decima there in each number of Ex. 1. at the top of pag 1. Read the following decimals: 0.45, 0.375, 4.25, 3.0 45.67, 456.305, 30.00546, 304.40507, 4.00035, 0.00405.. 2. Write the following decimals: twenty-five and sixt nine hundredths; one hundred twenty-six and four hundr nine thousandths; ninety-seven and thirty-two tens thousandths; five and two hundred twelve millionths. 3. Write and read the following as decimals: 100, 100 405 306 100000, 100, 100000, 100. 145, 1084900, 388. 45 58. Reducing Decimals to Common Fractions.-A de imal can easily be changed to a common fraction by writi the number over 10 multiplied by itself, so as to give as ma zeros in the denominator as there are decimal places. 0.45402; 3.04 188 = 32. 304 = Thu 59. Reducing Common Fractions to Decimals.-Cor mon fractions whose denominators can be changed to 1 100, etc., are easily converted into decimals. Thus: In changing common fractions to decimals and vice ver only the form of the fraction is changed. Decimals a fractions in a different form. A little later we shall stu yet another form of fractions. EXERCISES 7 1. Change to decimals: 3, 1, 1, 18, 16, 3, 13, 1, 231, 6 291, 715. 3 2. Change to common fractions or mixed numbers: 0. 0.45, 4.56, 23.16, 17.045, 0.0065, 143.00504, 60.35, 4.4056. 3. Which is larger, or 0.3? or 0.77? or 0.9? 4. Replace the common fractions on pages 44 and 45 1 decimals and then read the problems. |