REVIEW. 1. All integral numbers are either prime or composite. 17 is 31 is 95 is 242 is 370 is 2. Reduce each of the following improper fractions to a whole number or to a mixed number: 17, 35, 37, 18, 25. (a) 324. (b) 185. (c) 256. (d) 891. 3. Reduce each of the following to its lowest terms: 5. If of a bushel of potatoes costs 204, 24 bushels will cost (1) If of a ton of straw costs $2.25, how much will 3.2 tons cost? 6. Change the following to tons: 4200 lb. (m) 5750 lb. (n) 7320 lb. (0) 3150 lb. 7. Find the area and the perimeter of each of the following rectangular surfaces: 7 feet by 5 feet. (p) 27 feet by 12 feet. (q) 15 inches by 15 inches. 8. If 2 gallons of molasses are worth 604, 3 gallons are worth cents. (r) If 2 loads of brick are worth $12.60, how much are 3 loads worth? MISCELLANEOUS PROBLEMS. 1. In a school there are 35 pupils; of the pupils are of the pupils are girls; there are boys; and girls. boys (a) In a school there are 392 pupils; of the pupils are boys. How many girls are in the school? cost 2. If 3 melons cost 364, at the same rate 5 melons will cents. (b) If 3 acres of land cost $525, how much will 5 acres cost at the same rate? 3. Harry exchanged 5 lb. of butter at 20¢ a pound for coffee at 25¢ a pound; he should receive pounds of coffee. (c) Harry's father exchanged 6 cords of wood at $5.20 a cord for cedar posts at 204 each. How many posts should he receive? 4. 3+2+6+4+5+8+1+7+9+4+7+3+2 (d) 275 +361 +554+732 +598 +236 +347 +256 = 5. If Mark saves $4 a month, in 1 year he will save dollars. (e) If Mark's father saves $21.50 a month, how much will he save in 1 year? 6. A common brick is 8 inches long, 4 in. wide, and 2 in. thick; it has two faces each of which is 4 in. by 8 in., two faces each of which is in., and two faces each of which is in. by (f) Find the sum of the areas of all the faces of a common brick. (g) Change 674 inches to feet and inches. SIMPLE NUMBERS. 1. Any exact integral divisor of a number (except the number itself and 1) is called a factor of the number. The factors of 6 are The factors of 10 are and and 2. A factor that is itself a prime number is called a prime factor. A factor that is itself a composite number is called a composite factor. 2 and 3 are 4 and 6 are factors of 24. factors of 24. 3. Every composite number may be resolved into prime factors. The prime factors of 12 are 2, 2, and 3. The prime factors of 18 are 2, 3, and 3. 4. From the above it will be seen that a number is equal to the product of its prime factors. 3 and 7 are the prime factors of; 2, 2, and 7, of (j) Find the sum of 863, 953, and 87. 5. From subtract 1. (Change to) (k) Find the difference of 873 and 2493. 6. Divide by. This means, find how many times is contained in 3. I can change fourths and thirds to -ths. 3 twelfths twelfths are contained in times. Story-James can husk a row of corn in of an hour; in 3 of an hour he can husk and rows. (1) ÷ ÷ 1. (m) 2 ÷ 1. (n) ÷ 1. (0) 5 acres)288 acres. This means, find how many times 5 acres are contained in 288 acres. (p) 5)625 acres. This means, find 1 fifth of 625 acres. Story. (a) Multiply $374 by .03. This means, find 3 hundredths (f) At $875 an acre, how much will .04 of an acre of *The pupil should understand that he multiplies $3.74 (not $374) by 3, and should be taught to write the decimal point in the product immediately after writing the tenths' figure of the product. This means, find how many times 4 hundredths are contained in 576 hundredths. |