357/527 264/312 492/779 418/874 854/1769 30/735 44/242 77/847 18/243 96/224 Find differences:-- 6-2/7 8-5/11 8-4/13 5-1/4 7-1/8 3-1/14 5-1/7 3-7/13 2-11/14 2-1/7 ------ ------ ------ ------- ------ Square:-- 2/3 4/5 5/7 6/9 10/11 12/13 2/7 15/16 19/20 17/18 25/30 41/53 Multiply:-- 2/11 × 33 32 × 3/14 39 × 2/13 60 × 11/28 77 × 4/11 63 × 2/27 54 × 8/45 65 × 3/13 344-16/21 432-2/7 MEASUREMENTS OF ABILITY IN APPLIED ARITHMETIC: THE SOLUTION OF PROBLEMS Stone ['08] measured achievement with the following problems, fifteen minutes being the time allowed. "Solve as many of the following problems as you have time for; work them in order as numbered: 1. If you buy 2 tablets at 7 cents each and a book for 65 cents, how much change should you receive from a two-dollar bill? 2. John sold 4 Saturday Evening Posts at 5 cents each. He kept 1/2 the money and with the other 1/2 he bought Sunday papers at 2 cents each. How many did he buy? 3. If James had 4 times as much money as George, he would have $16. How much money has George? 4. How many pencils can you buy for 50 cents at the rate of 2 for 5 cents? 5. The uniforms for a baseball nine cost $2.50 each. The shoes cost $2 a pair. What was the total cost of uniforms and shoes for the nine? 6. In the schools of a certain city there are 2200 pupils; 1/2 are in the primary grades, 1/4 in the grammar grades, 1/8 in the high school, and the rest in the night school. How many pupils are there in the night school? 7. If 3-1/2 tons of coal cost $21, what will 5-1/2 tons cost? 8. A news dealer bought some magazines for $1. He sold them for $1.20, gaining 5 cents on each magazine. How many magazines were there? 9. A girl spent 1/8 of her money for car fare, and three times as much for clothes. Half of what she had left was 80 cents. How much money did she have at first? 10. Two girls receive $2.10 for making buttonholes. One makes 42, the other 28. How shall they divide the money? 11. Mr. Brown paid one third of the cost of a building; Mr. Johnson paid 1/2 the cost. Mr. Johnson received $500 more annual rent than Mr. Brown. How much did each receive? 12. A freight train left Albany for New York at 6 o'clock. An express left on the same track at 8 o'clock. It went at the rate of 40 miles an hour. At what time of day will it overtake the freight train if the freight train stops after it has gone 56 miles?" The criteria he had in mind in selecting the problems were as follows:-- "The main purpose of the reasoning test is the determination of the ability of VI A children to reason in arithmetic. To this end, the problems, as selected and arranged, are meant to embody the following conditions:--