WRITTEN EXAMINATION ON PER CENTS 1. A bicycle was marked $48, but was sold at 16% discount. What was the net price? 2. A piano was listed at $720, but was sold at 25% discount. What was the selling price? 3. A jobber bought goods amounting to $4850. He was allowed a discount of 24%. Find the net amount of the bill. 4. A merchant bought 1680 yd. of muslin at 15¢ a yard, less 22%. How much did it cost him? 5. A merchant bought 2450 yd. of lawn for $1225, less 24%. How much did he pay per yard? 6. A grocer bought 36 doz. cans of soup listed at $3.50 a dozen. He was allowed a discount of 221%. What was the net amount of the bill? 7. One cow averages 28 lb. of milk a day, testing 3.8% of butter fat; another averages 24 lb., testing 4.2%. Butter fat being worth 36¢ a pound, which cow is the more profitable per month of 30 da., and how much more? 8. A farmer has 110 trees on an acre of woodland, of which he decides to cut 50%. If wood is worth $9.75 a cord, and he can cut 3 cords from 5 trees, how much will he receive for the wood that he cuts? 9. A dressmaker bought 37 yd. of chiffon velvet at $6.50 a yard, and received a reduction of 12% for paying cash. She sold the velvet at $6.50 a yard. How much profit did she make on the transaction? 10. A grocer bought 24 doz. pound packages of macaroni for $62.40, less 15%. He sold it for 30¢ per package. The overhead being 96¢ in all, how much did he gain? TABLES FOR REFERENCE LENGTH 12 inches (in.)=1 foot (ft.) 5 yards, or 16 feet =1 rod (rd.) SQUARE MEASURE 144 square inches (sq. in.)=1 square foot (sq. ft.) 9 square feet =1 square yard (sq. yd.) 30 square yards =1 square rod (sq. rd.) 160 square rods=1 acre (A.) 640 acres =1 square mile (sq. mi.) CUBIC MEASURE 1728 cubic inches (cu. in.)=1 cubic foot (cu. ft.) 27 cubic feet =1 cubic yard (cu. yd.) 128 cubic feet =1 cord (cd.) WEIGHT 16 ounces (oz.) =1 pound (lb.) LIQUID MEASURE 4 gills (gi.) =1 pint (pt.) For stationery and folded paper a quire is usually 24 sheets; for unfolded paper a quire is usually 25 sheets. Paper is also sold by the pound. SUGGESTIONS TO TEACHERS It frequently happens, in solving problems, that pupils are taught to calculate properly in oral work but are allowed to use long, primitive, laborious methods in written work. Economical methods should be used in both written and oral calculations. Here, as elsewhere, good judgment should control, in order that the calculations may be in reality economical. Pupils should be encouraged to use the pencil as little as possible in the solution of all problems, and the short methods given in this series of arithmetics should be used whenever possible. Closely allied to training for skill in calculation is training in estimating reasonable answers to problems, as a preliminary to their solution. This training may begin early in school life in estimating lengths, areas, capacities, and weights. Much oral and written work of this character with all kinds of problems may profitably be given until pupils have established the habit of doing mathematical work with an expectation of arriving at a reasonable result. Good textbooks give frequent suggestions and opportunities for this training. There are two kinds of exercises in arithmetic, namely, abstract and concrete. The former lead to skill in manipulation of figures, and the latter lead to interpretation and also to calculation. The concrete problem should be typical of life; its conditions should be within the comprehension of the pupils and within actual domestic, school, or business experiences. Local projects are of great value. A pupil should not be expected to solve a problem if he does not understand the social or business relations involved or the language used. It matters not how practical to the teacher a problem may appear, it is not practical to the pupil unless it is within his comprehension and comes or has come within his experience, or is within easy range of his imagination. The distinction between abstract and concrete numbers (page 22) is not observed so much as it formerly was, for all number is essentially abstract. We may specify the units (feet, yards, apples, etc.), but the number is still abstract. The custom of specifying the units in solving a problem is also tending to disappear, the pupil keeping the units in mind just as the business man does. For example, consider the following cases: If one book costs 20¢ and another book costs 30¢, both books together cost as many cents as 20+30, or 50¢. If one book costs 20¢ and another book costs 30¢, the second book costs as many cents more than the first as 30 20, or 10¢. If 1 orange costs 5¢, 4 oranges will cost as many cents as 4 × 5, or 20¢. If 1 orange costs 5¢, one can buy as many oranges for 20¢ as 205, or 4 oranges. If 4 oranges cost 20¢, each orange costs as many cents as 20 ÷ 4, or 5¢. In the study of problems pupils should be led to consider (1) what is given, (2) what is required, and (3) what arithmetic processes are necessary for solving them. Much trouble arises because pupils are not able to discriminate between (1) and (2). In dealing with a problem there are three methods of procedure: (1) let the pupil tell what is to be done, without performing the operations, or let him indicate the solution, or diagram the work; (2) let him give an approximate answer; (3) let the pupil do all the work but in the most economical way. In order to give more practice in reasoning than is possible under the last method, (1) and (2) should be employed more frequently than is usually the case. The habit of checking work as it progresses should be fixed in the early grades. This checking consists of repeating one process before the next process is begun. The repetition should be made after each part of the problem has been solved rather than after the entire problem has been solved. This is the business custom. |