15. Make a drawing of the gate to a scale 8 times as large as that of Fig. 3, p. 73. 16. Fig. 1 is a scale drawing of the side and the end views of a large book. How long is the book? How wide? How thick? 17. Make an enlarged drawing of the book to a scale 4 times as large as that of Fig. 1. 18. From your own measurements make a drawing, to any convenient scale, of a thick object, as a block, a brick, a crayonbox, showing two views as in Fig. 1. §51. Schoolhouse and Grounds. END VIEW Scale 1:16" 1. Using a foot rule, graduated to 16ths of an inch, and regarding the scale of the drawing (Fig. 2), find the width of the grounds; the length; the area in square rods. (30 sq. yd. =1 square rod.) 2. Find the length of the field; the width; the area in square rods. 3. Find the length and the width of the school yard; the area in square rods. 4. Find the length and the width of the schoolhouse; in square yards, covered by it. the area, 5. How far is the front door of the schoolhouse from the front fence? From the west front gate? From the sand pile? From the tree? 6. How far is it from the back door to the east flower bed? To the back fence? To the west fence? To the coal shed? To the northeast corner of the school yard? To the south end of the pond? To the hill? To the nearest point on the creek bank? To the foot bridge (F)? 7. How wide is the south road? The creek? The branch? 8. How many square rods in the south road in front of the grounds? In the crossing of the roads? 9. How many square rods in the meadow? In the grove? In the pasture? 10. How many square rods are covered by the creek and the branch together, within the fence lines? 11. How many rods of fence will be needed to enclose the grounds and to run along the lines indicated? $52. Ratio. RATIO AND PROPORTION Expressions like 1 to 2, 3 to 1, 12 to 13, to 3, a to x, are called ratios. 1. Other ways of writing the ratio 1 to 2 are 1:2, and Give the other ways of writing the ratios 3 to 1; 12 to 13; to; a to x. 6 10. α Read as ratios: 2:3; ; ; ; 11; %. The two numbers of a ratio are called terms of the ratio. The first term is the antecedent, and the second term is the consequent. A ratio, like a fraction, is in its simplest form when the terms are the smallest possible whole numbers. 2. Express the following ratios in their simplest forms: The value of a ratio is the quotient of the antecedent divided by the consequent. 3. Compare the values of the following pairs of ratios: When two ratios are equal they make a proportion. 1. Which pairs of ratios in problem 3 above do not make a proportion? The first, second, third, and fourth numbers of a proportion are called its first, second, third, and fourth terms. The first and fourth terms are the extremes and the second and third terms are the means of the proportion. 2. Compare the product of the means with the product of the extremes in all parts of problem 3 above that make proportions. What seems to be true of the products? In a proportion, the product of the means equals the product of the extremes. 3. Tell which of the following are proportions, by comparing the products of the means and extremes: 4. The first expression of problem 3 is read "2 to 3 as (or equals) 8 to 12;" and the ninth is read "7 to 8 equals 14 to 16." Read the expressions of problem 3. 5. Find the value of a in the proportion 4:6-8:a. SOLUTION: As the product of the means equals the product of the extremes, 4Xa =6X8, or 4a-48; a=4 of 48=12, Ans. 6. What does the letter stand for in each of these Use pencil only when needed. 1. A boat runs 30 miles in 2 hours. will it run in 6 hours at the same rate? 20 hours? = How many miles In 12 hours? In Solutions for last part (1) As 2:20 30:x, 20 or x=300. Ans. 300 mi. Or (2) As 20 is 10 twos, the boat will run 10×30, or 300 mi. in 20 hours. 2. A steamboat runs 72 knots in 3 hours. How many knots will it run in 18 hours at the same rate? In 15 hours? In 30 hours? In 161⁄2 hours? In 11⁄2 hours? 3. 3 knots equal 3.45 miles. How many miles are there in 6 knots? In 24 knots? In 72 knots? Inknot? In 33 knots? In 100 knots? In 1 knot? 4. If 10 acres of land yield 440 bushels of corn, at the same rate of yield how many acres would be needed to yield 220 bushels? 660 bushels? 1100 bushels? 4400 bushels? 5. A tree 65 feet high casts a shadow 60 feet long. How high is a tree which casts a shadow 30 feet long, at the same moment? 90 ft. long? 120 ft. long? 13 ft. long? 5 ft. long? 25 ft. long? 6. A clock ticks 7 times in 5 sec. How many times does it tick in 2 da. 6 hours? 7. If BEECH BROOK D 60 A. cost $3000, how many acres will cost $2450? 8. The line BC (Fig. 1) represents 20 rods. FE is twice as long, AF four times as long, CD and ED five times as long, and AB six times as long. Find the length of each side. ROCK RIVER WARREN BROOK SPARTA TO COLUMBUS 9. Find the value of x in the following: FIGURE 1 (1) BC: FE =AB:x (3) AF: FE =x: BC (2) BC: x =FE: CD 10. When a foot-rule is held 2 ft. (arm's length) in front of the face as shown in Figure 2, 7 in. on the ruler seems just to cover the edge of a door 7 ft. high. If the ruler is held parallel to the edge of the door, how far is the eye from the door? shadow 50 ft. long on the same day and hour? 12. The shadow cast by a 3 ft. stake is 10 ft. long. |