Multiplying by 121, 25, 50 Preparatory Exercises 1. What is (a) 1⁄2 of 100? (b) of 100? of 100 ? 2. What part of 100 is (a) 50? 3. a. 50 100 =? (b) 25? (c) 121? = 5. Multiply. First cancel 24 and the denominator of each fraction. 100 = C. 50 = ? 1. At 3 pairs for $1, what will be the cost of 24 pairs of stockings? 2. Find the area of a piece of ground 25 feet wide, 124 feet long. 3. At 48 bushels per acre, how many bushels of corn will 12 acres yield? 4. How many miles will a train go in 18 hours at the rate of 25 miles per hour? 5. At 25 cents per hour, how much will a man earn in 6 days of 8 hours each? Written Exercises 1. Find the area of a rectangle 264 yards long, when its width is (a) 12 yards. (b) 25 yards. (e) 50 yards. SUGGESTION. Write the examples as shown below. Mentally affix two ciphers to the multiplicand. Divide the new multiplicand (a) by 8, (b) by 4, and (c) by 2, respectively. Test the results by rejecting two ciphers and multiplying by 8, by 4, and by 2, respectively. 2. Multiply by 25: a. 136. b. 256. c. 332. d. 464. 3. Multiply by 12: a. 136. b. 256. c. 336. d. 464. 4. Multiply by 50 a. 136. b. 256. c. 336. d. 474. Written Problems 1. At $3 per dozen pairs, what will be the cost of 42 pairs of socks? 2. Find the area of a building lot 25 feet by 138 feet. 3. At 46 bushels per acre, how many bushels of corn would 112 acres yield? 4. How many miles could a steamer go in a week at the rate of 25 miles per hour? 5. At 25 cents per hour, how much could a man earn in a year of 309 working days if he worked 8 hours per day? 6. At 12 cents per pound, find the value of 8 chickens. averaging 7 pounds each. Dividing by 50, 25, 121 Preparatory Exercises 1. What part of 100 is (a) 50? (b) 25? (c) 121? 1. How long will it require a man to travel 675 miles at the rate of (a) 25 miles per hour? (b) 12 miles? (c) 50 miles? Divide the dividend and the divisor by 100. This makes the former 63 in each case, and the latter, }, and 1, respectively. Divide the new dividend by the new divisor; that is, multiply the former by the latter inverted; 4, 8, 2, respectively. 1. A row of houses extends 800 feet along a street. How many houses are there when each is (a) 20 feet wide? (b) 25 feet wide? 2. When the average yield per acre is 25 bushels, how many acres will yield 925 bushels? 3. A drover paid $1125 for 25 cows; what was the average price? 4. A rectangular field contains 2225 square rods. Its width is 25 rods. What is its length? Written Exercises 1. How many acres will yield 2450 bushels of grain when the yield per acre is (a) 12 bushels? (b) 25 bu.? (c) 50 bu.? ANALYSIS (a) 2450 ÷ 121 = 241 ÷ 1 = 241 × 8=196 (A.). Ans. 241 ÷ 1 = 241 × 4 = 98 (A.). Ans. 241 + 1 = 24 × 2 = 49 (A.). Ans. 2. Divide by 121: a. 2700. b. 3850. c. 4300. d. 5550. e. 6200. 3. Divide by 25: a. 2900. b. 3650. c. 4400. d. 5350. e. 6400. 4. Divide by 50: a. 2700. b. 3950. c. 4700. d. 5750. e. 6900. Written Problems 1. At 25 passengers to a boat, how many lifeboats would carry 675 passengers? 2. How many acres would be required to produce 2125 bushels of wheat at the rate of 25 bushels to the acre? 3. At 50 pounds to the bushel, what is the weight of 47 bushels of apples? Sight Problems 1. If a cow gives 750 pounds of milk during June, what is the average per day? 2. If of the milk is butter fat, how many pounds of butter fat are contained in 750 pounds of milk? 3. At $1.50 per week for feed and labor, what is the cost of keeping a cow for 52 weeks? Inexact Division Preparatory Exercises 1. If 51 marbles are divided among 6 boys, how many marbles will each receive? 2. What is the average price of a pig when 6 pigs cost $51? 3. How many hens can be properly accommodated in a pen containing 51 square feet, if each hen requires 6 square feet? 4. How many trips must a lifeboat make to bring ashore 51 passengers if 6 can be taken on each trip? Although each of the foregoing questions involves the division of 51 by 6, each answer differs from the others. To the first, the answer should indicate that there are 3 marbles left after the division is made; the answer to the second is $81; to the third, the answer is 8 hens, no reference being necessary to the three extra square feet; to the fourth, the answer is 9 trips. Written Problems 1. At $6 each, how many pigs can be bought for $500? 2. If each pupil requires 18 square feet of floor space, how many pupils can be properly accommodated in a classroom 25 feet long and 24 feet wide? 3. When a lifeboat can carry 24 persons, how many boats are required to carry 500 persons? 4. A farmer raised 500 bushels of wheat on a field of 40 acres. What was the average yield per acre? 5. How many men must be hired to do a piece of work in 16 days if 1 man would require 500 days to do it? 6. What is the average number of pupils to a class when 16 classes contain 500 pupils? NOTE. In giving averages, express fractions of pupils, etc. |