RATIO AND PROPORTION CHAPTER VI. Ratio, Proportion, Partitive Proportion, Partnership, INVOLUTION AND EVOLUTION Square Root, Applications of Square Root, Cube Root. MENSURATION The Circle, Areas of Circles, Areas of Triangles, Areas of Quadrilaterals, Surfaces of Prisms and Cylinders, Surfaces of Pyramids and Cones, Volumes of Prisms and Pyramids, Volumes of Cylinders and Cones, Surface of Sphere, Volume of Sphere, Circular Measure. LONGITUDE AND SOLAR TIME Standard Time, Solar Time. PAGES 310 to 328 328 to 338 339 to 358 358 to 364 Special Drills, Review of Fractions, Review of Denomi- RATIO. 391. Ratio is the relation which one number has to another of the same kind. The sign of ratio is the colon (:). The ratio of 3 to 6 is expressed 3: 6. The colon (:) is the sign used in France and Germany to indicate division as well as ratio. 310 392. The terms of the ratio are the numbers compared, the first being called the antecedent, and the second the consequent. Both terms constitute a couplet. The ratio of 3 to 6 is obtained by dividing the antecedent by the consequent; 3: 6 means, which is equal to $36.50 2. Ans. 6 pecks = Ans. 20 pecks NOTE. The antecedent and the consequent must be like numbers. 4. $19 to $95. 5. 20 mills to 1 dollar. 8. 1 gallon to 500 cubic inches. 394. Written Problems. 6. 7 tenths to 3 fifths. 7. 3 quarts to 4 gallons. 1. One line is 3 rd. 4 yd. long; the length of another is 5 rd. 1 ft. Find the ratio of the first to the second. The antecedent 3 rd. 4 yd. is to be divided by the consequent 5 yd. 1 ft. As the divisor and the dividend must be like numbers, both terms of the couplet are reduced to feet. The division is indicated by writing the antecedent above the consequent as a fraction. The concrete fraction = 3 rd. 4 yd. 611 ft. = 123 Ans. 61 ft. 831 ft. is changed to which is reduced to a simple frac tion by multiplying both terms by 2, giving 1 for the result. Make the antecedent and the consequent like numbers, and divide the former by the latter. 2. M walks in 1 hr. 47 min. as far as N walks in 2 hr. 3 min. What is the ratio of M's speed to N's? In this example is required the ratio of M's speed to N's. The antecedent is, therefore, M's speed, and the consequent is N's speed. As the distance walked is not given, x may be used to represent the number of feet or yards or miles walked by M in 107 minutes, and by N in 123 minutes. will represent the distance walked by M in х 107 3. One candle lasts 4 hr. 20 min.; another lasts 3 hr. 15 min. Find the ratio of the first to the second. 4. A pound of coffee costs 253; 1 pound of sugar costs 53. What is the ratio of price of sugar to that of coffee? 5. P earns in 199 days as much as Q in 18 days. What is the ratio of Q's daily earnings to P's? Of P's to Q's? 6. One wheel makes 600 revolutions in 84 seconds; a second makes 300 revolutions in 31 seconds. What is the ratio of the speed of the first wheel to that of the second? 7. The circumference of a circle is 12.5664 feet, and its radius is 2 feet. What is the ratio of the diameter to the circumference? 8. One train goes 40 miles in 50 minutes; another goes 24 miles in a half hour. What is the ratio of the speed of the second to that of the first? Find the number of miles each goes in an hour. 9. One window is 6 ft. 8 in. by 4 ft. 2 in.; a second is 4 ft. 8 in. by 2 ft. 1 in. What is the ratio of the area of the second to that of the first? (63 × 41) ÷ (43 × 211⁄2). 10. A mother is now 35 years old, and her son is 3 years and 6 months old. Fourteen months ago what was the ratio of the mother's age to that of her son? 11. A farm costing $4750 was sold for $5750. What is the ratio between the profit and the cost? 12. A man can do a piece of work in 42 days. What part of it can he do in a day and a half? What decimal? What per cent? 13. What is the ratio between a ton of 2000 pounds and one of 2240 pounds? 395. Oral Problems. 1. One line is a rod long; another is 5 ft. long. What is the ratio of the first to the second? 2. What is the ratio of 7 hours to one day? 3. A pound of coffee costs 30%, of sugar 64. What is the ratio of their respective prices? 4. A walks in 4 hours as far as B in 5. What is the ratio of A's speed to B's? 5. E earns in 6 days as much as D earns in 8 days. Find the ratio of E's daily earnings to D's. 6. One wheel makes 300 revolutions in 2 minutes; the second requires only 1 minutes to make the same number. Find the ratio of the number of revolutions made by the first wheel in 1 minute to the number made by the second wheel in the same time. 7. A circle whose diameter is 1 foot has a circumference of 34 feet. What is the ratio of the diameter to the circumference? 8. One train goes 40 miles an hour; a second goes 45 miles an hour. What is the ratio of the speed of the first to that of the second? = The ratio of 3 to 9 is 3, which is also the ratio of 13 to 39. This may be expressed = 18, or 3:9 13:39. Substituting a double colon (: :) for the sign of equality (=), we have the following proportion: 3:9:13:39. This is read, 3 is to 9 as 13 is to 39. In the foregoing proportion, 3 and 13 are the antecedents, and 9 and 39 are the consequents. 398. The first and the last term of a proportion constitute the extremes; the second and the third the means. In the following proportion 5:15:9:27 5 and 27 are the extremes, 15 and 9 are the means. |