29. Progress Score Try, within a limit of 15 minutes, to make a score of 100 points in this exercise, counting for each correct answer the score given in parenthesis below the letter of the problem. R. To whole or mixed numbers:1 8, 10, 12, 15, 16. (5) S. To improper fractions:1 11, 23, 51, 35, 214. (5) 1 Count 1 for each correct answer. 1. Every year, mile records are taken of the time required by men and boys in running, walking, rowing, swimming, and skating. In which kind of race do you think a mile has been covered in the least time? 2. Read the following records in order of the time taken, putting the sport first in which a mile has been covered in the least time: 3. In a boys' swimming contest, the winner swam fifty yards in 30 seconds. What part of a minute did he take? 4. In a boys' half-mile relay race (4 boys), a record of 1 minute 45 seconds has been made. Express the record in minutes. 5. Express in minutes the first record in running given on page 47; also, the record in walking. 6. What part of a foot is 6 in.? 3 in.? 9 in.? 7. Express in feet a record of 4 ft. 6 in. for a running high jump. Of 16 ft. 9 in. for a running broad jump. 31. Addition of Like Fractions I John is training for a rowing contest. Every morning he rows of a mile across a lake and then takes a course of a mile long that brings him back to his starting point. What is the distance covered in his morning row? Notice that the denominators in the two fractions and are the same. The fractions are, therefore, called like fractions. Fractions that have different denominators are called unlike fractions. 5 3 11 16, 16, 18, are like fractions.,, and are unlike fractions. To add like fractions add the numerators, place the result over the denominator, and reduce if necessary. [Without pencil.] 1. What is the sum of and? Of and ? Of and? To reach the football grounds belonging to his school, Frank must ride of a mile on a trolley car and then walk of a mile. How far must he travel? 2. 3. The sails of a boat are to be mended. One sail requires of a yard of canvas; the other sail, of a yard. How many yards are needed for the two sails? Two knapsacks are to be made. One requires 12 yards of cloth; the other, 2 yards. How many yards are required for the two? 1 yd. + 2 yd. =? The sum of the fractions equals + †, or §. § = 14. The sum of the integers equals 2 + 1, or 3. The sum of the integers and fractions equals 3 + 14, or 41. [Use pencil only when needed.] 1. Give directions for adding mixed numbers that contain like fractions. 2. What is the sum of 43 and 83? Of 65 and 84? Of 143 and 81? 3. In buying camp supplies, Henry buys 2 lb. of coffee, 4 lb. of butter, and 81⁄2 lb. of sugar. What is the weight of the supplies? 4. Going to camp, Tom had to carry one package weighing 142 pounds, and one weighing 42 pounds. How much did both weigh? 5. Fred and his brother rowed a boat down a river. The first hour they rowed 63 miles; the second hour, 53 miles; and the third hour, 5 miles. What was the distance covered? 32. Subtraction of Like Fractions I How much wider is a lake that is of a mile in width than one that is of a mile in width? To subtract like fractions, subtract the numerators, place the result over the denominator, and reduce if necessary. [Without pencil.] 1. Find the difference between and . Between 1 and 1. Between and . 4. = 6. 11-12 ? 12. 1 ? 13.244 = ? II 4. ? 7. 7-8=? 3 How much is left from a coil of wire containing 60 yards after 24 yards have been used? 60 yd. 24 yd. =? 60% 241 The difference between the fractions is, or . 361 The number of yards left in the coil of wire is 36 yards. [Use pencil only when needed.] 1. Give directions for subtracting mixed numbers that contain like fractions. 2. Subtract: 42 from 84; 51⁄2 from 9; 12 from 185. 3. In making a bow for arrows, Tom cut a piece of wood 4 inches long from a strip 40 inches long, and used the piece left for the bow. How long did he make his bow? |