called the rate per cent, or merely the rate. The I number that is asked for is often called the per This is what has been found up to the present. We shall now find what per cent one number i other, as 54 is what per cent of 600 ? This means, what per cent of 600 is 54; or, as a what fraction of 600 equals 54? Using the idea of o or reverse operations we have: 1. What per cent of 400 equals 20? 2. What per cent of 60 equals 30? equals 15? What per cent of 56 is 7? What per cent o 3. 12? 4. 9 is what per cent of 45 ? 12 is what per cent 75 is what per cent of 300? 35 is what per 1,400 ? 5. 6. In an assignment of 20 problems John work What per cent of the whole lesson was this? 7. Henry's football team has won 5 and lost 3 What per cent of the total number played was won? is called the team's percentage. 8. Find the percentage of the football teams which won 6 games and lost 5 games; won 4 and lost 6; and lost 4; won 3 and lost 2; won 2 and lost 3. did each team mal Reds' score is what cent of Blues' SCO Blues' score is what cent of Reds' score? 11. What was lost on goods bought for $3,200 and s for $2,800? What per cent of the buying price was lo 12. Goods bought at $ 450 are sold for $ 560. How m is gained? What per cent of the buying price is this? 13. A desk marked at $6.50 is sold at a discount of $1 For what is the desk sold? The discount, $1.50, is w per cent of the marked price? 14. In a certain school there are 317 girls and 265 bo What per cent of the total enrollment is girls? is boy What does the per cent of girls plus the per cent of b equal? Why is this so? 15. A salesman received 2% commission of his to sales. One week his commission was $24.50. What his sales been that week? $24.50 is 2% of how ma dollars? 16. Mr. Robins bought an automobile for $985 and s it three years later for $500. What was the loss? The is what per cent of the buying price? 17. In a civil-service examination 35 out of 167 ap cants passed the examination. What per cent of all w tried the examination was this? 18. At the above rate how many may be expected pass out of 125 who try the examination? 70 A dairymen got 0 at of creem from 12 cel m V MEASURES 80. Abstract Numbers.-Numbers which do not to any particular kind of thing are called abstract. numbers are 5, 79, 80, 1, etc. 81. Concrete Numbers.-Numbers which refer to ticular kind of thing are called concrete. Such numbe 7 men, 3.5 yd., 5 stories, 3 baseballs, and so on. Which of the following numbers are abstract and are concrete: 3 boys? 56.2? 3.4 lb.? 7 dogs? 793 67? 29 chickens? 32 kites? 8 marbles? 82. Measures or Denominate Numbers.-Whe count we find out how many objects of a kind there a 7 apples or 3 pencils. In buying or selling we are no cerned nearly so much about how many apples or p as we are about their quality and how much there apples or of pencils. Can there be more paper in 1 pi paper than in 3 pieces of paper? Answers to all such tions of how much require measurements. The most mon measures are those of length, area, angles, vo weight, time, and value in the form of money. Mea are often called denominate numbers because they d the kind of concrete number just as the denominator common fraction denotes the kind of a fraction. Der nate numbers with two or more units, as 2 ft. 7 in., are called compound denominate numbers, or merely comp 83. Tables. The tables of measures and abbreviati will be found upon pages 225 to 228. Note the carpent and architects' abbreviations for foot and inch. Ang areas, and volumes will not be taken up before chapt VII and VIII, in which geometrical measures will be studi 84. Quantity.-Denominate numbers and measures various kinds will often be spoken of hereafter as quantiti We speak of the quantity of medicine in a bottle and of quantity of coal in a bin. EXERCISES 5 8 1. Which of the following are denominate numbers: 3 7 lb.? 5 yd.? 6 marbles? 473? $45? 67 books? § 2. Can there be more bread in 2 than in 3 loaves? m paper in 5 than in 7 sheets? more corn in 12 than in ears? more coal in 6 than in 8 loads? 85. History of Measures.-Our common system of me ures, also called the English system, had a very crude ginning. Most of the units, as is seen from their names, h to do with grains or parts of the body. Among the u are foot; hand; finger breadth; span, which is from the of the thumb to the tip of the little finger when the hand outstretched; yard, or ell, which is the old English name arm; the pace, the average length of a step; the mile, fr the Latin millia passuum, a thousand paces. In old Ro the inch meant of a foot; in France and the Scandinav countries it meant the length of the first thumb joint; the British Isles it meant the length of three barley co placed end to end. The rod was probably the length some measuring-pole. It is not known just what is origin of our unit of land measure, the acre, but it is thou to have meant the amount of land O men could plow i age may be the origin of our peck. We have no defin tory of the gallon, but the quart was likely one-qua the gallon. The pound, the unit of weight, has been of man but has always been made up from a certain nun grains of some kind, usually barley. Hundredweigh course, 100 pounds while 20 hundredweight are called How many pounds does this make a ton? A stone ing 14 pounds was used in the British Isles in we Eight of these, or 112 pounds, they called a hundred From this comes the long ton of 2,240 pounds, used mines and the custom-house. Over 4,000 years ago the people of Babylon divid circle into 360 equal parts, which we call degrees. made this division because they thought that the sur a journey around the earth every 360 days. After al years we are to-day using this convenient division of a into degrees. Month likely refers to the changing of the moon. 86. Reductions Descending.-It is often necessa change measures from one denomination to another duce 7 yd. 2 ft. 5 in. to inches. 7 3 21 2 23 ft. 7 yd. + 2 ft. = 7 x 3 ft.+ 2 ft. 12 46 23 5 281 in = 23 ft. + 5 in = 23 × 12 in + 5 in |