72 REVIEW AND SUMMARY 1. How can you tell without dividing whether or not a number is divisible by 5? 2. Which of the following numbers are divisible by 5: 63? 50? 875? 360? 417? 405? 3. What kind of a figure is a circle? What is a diameter? A radius? The length of a diameter is how many times that of the radius? 4. What is an arc?. Illustrate your answer. 5. A bicycle wheel is 26 in. in diameter; what is the length of the radius? 6. A section of the earth through the center would be approximately a circle. The diameter of the earth is about 8,000 mi.; what is the distance from the surface to the center? 7. How must fractions be expressed before they can be added or subtracted? 24. What is meant by "reducing a fraction to lower terms''? 66 "To its lowest terms'? Illustrate your answers. 25. When is a fraction said to be simplified? Reduce to lowest terms: Illustrate. PROBLEMS-REVIEW 73 1. The table shows the average cost per year of various Find the increase of cost of each item from year to year. 2. The figure shows the length and width of a curtain. Find the number of yards of cloth in 6 pairs of these curtains. What is the cost of a dozen pairs at $1.75 a pair? 3. What is the perimeter of a parallelogram whose adjacent sides are 2.6 in. and 9.7 in.? 4. How many years are there in of a year and 3 of a year? In § of a year and 9 mo.? 5. Lucy had of a dollar and spent 62 IN. of a dollar; what part of a dollar had she left? 6. Express the following numbers decimally: 3 25 65. 12 65. 40 700 10; 150: 100; 15; 10%; 12; 15; 117; 10; 108 Add and simplify the results: 100 8 in. 10.37 in. MEASUREMENT Areas of Triangles 1. Draw a parallelogram. Connect a pair of opposite corners, or vertices. This line is called a diagonal. 2. Draw rectangles and other parallelograms and their diagonals. How many diagonals can be drawn in every parallelogram? How do they compare in length? 3. Draw a parallelogram like the figure, and of the size indicated. Draw the altitude and diagonal. Cut out the triangles into which the diagonal divides the parallelogram and show that they are equal. 4 in. How is it 4. What is the area of the parallelogram? found? Each triangle is what part of the parallelogram? 5. How does the base of the triangle compare with that of the parallelogram? How do the altitudes compare? 6. The number of square units of area in a triangle equals one-half of the product of what numbers? Find the areas of the following triangles: 6 yd. 25 yd. 16.5 yd. 10 in. 6.2 in. PROBLEMS-AREAS 75 1. Find the area of a rectangle of base 4.5 in. and altitude 2. Find the area of a parallelogram of base 21.36 ft. and altitude 3.8 ft. 1 of 103.5=? 10.35 3. Find the area of a parallelogram of base 21.7 yd. and altitude 3.25 yd. 21.7 роини. 21.7 6. According to Exercise 5, how many bushels would a 5 horse-power engine grind in 10 hours? How many pounds? 7. When the gas required for the engine in grinding one hundredweight costs 1.3 cents, what will it cost for gas ton? 800 lb.? ton? ton? 1,800 lb.? enough to grind one ton?ton? ton? 1,500 lb.? 1,200 lb.? 8. If it takes 10 ft. of gas to grind 100 pounds of grain, what will it cost to grind a ton at $1.30 per 1,000 ft.? 9. A farmer can grind sufficient feed for a herd of 30 cows with a 12-foot windmill. Such a windmill and grinding equipment costs $225. If the grinding of his feed by others cost $50 per year, in how many years would the outfit pay for itself? 76 Written. MEASUREMENT OF LUMBER A square foot of lumber 1 in. or less in thickness is called a board foot. In lumber more than 1 in. thick, the number of board feet depends upon the thickness. Thus, a board 8 in. wide and 3 ft. long and in. thick contains 2 board feet, and a board 8 in. wide, 3 ft. long, and 11⁄2 in. thick contains 3 board feet. How many feet of lumber are there in : 1. 3 boards each 16 ft. long, 10 in. wide, and 1 in. thick? 2. 12 planks each 12 ft. long, 14 in. wide, and 2 in. thick? 3. 150 boards each 14 ft. long, 16 in. wide, and in. thick? 4. 25 joists each 16 ft. long, 4 in. wide, and 4 in. thick? Find the cost of the following at $22 per M (1,000): 6. The number of square units of area in a triangle equals one-half of the product of what numbers? Find the areas of the following triangles: |