16. If he paid $18.75 apiece for cotton planters and sold them at $25 each, what was his gain on 36? 17. In one month he made $180 by buying disc culti vators at $22.50 and selling at $30. How many did he sell? 18. At $1.28 each, how much will 24 umbrellas cost? 19. What is the cost of 15 tons of coal at $6.75 a ton, and 6 cords of wood at $7.50 a cord? (1) Total cash sales in each department for the week. (2) Total charge sales in each department for the week. (3) Total cash sales on each day of the week. (4) Total charge sales on each day of the week. (5) Total sales in each department for the week. (6) Total sales in all departments for the week. (7) Total sales in all departments for each day. (8) Total daily sales in all departments for the week. 21. A telephone rental is $3.50 a month. What is the yearly rental? 22. A business man pays yearly $36 for his office telephone, and $27 for his house telephone. How much does he pay every month? 23. Boxwood 2-foot rules are bought at 8 cents and sold for 10 cents. How many must be sold to gain one dollar? 24. At $1.62 a yard, a piece of silk cost $84.24. How many yards in the piece? 1. Name five numbers between 10 and 100 and tell their factors. 2. What are the factors of a number? A number that can be separated into factors is a com. posite number. 3. Name the composite numbers below 26; between 26 and 47; 47 and 73; 73 and 100. A number that cannot be separated into factors is a prime number. 4. Name the prime numbers below 25; between 25 and 50; between 50 and 75; between 75 and 100. A prime number used as a factor is a prime factor. 5. Name the prime factors of 60. We may think of 60 as 6 x 10. The prime factors of 6 are 2 and 3; the prime factors of 10 are 2 and 5; therefore, the prime factors of 60 are 2, 2, 3, and 5. 6. Name the prime factors of: 28 36 40 48 54 56 72 80 81 144 NOTE. Going rapidly around the class, let the pupils recite as fol. lows: 1 is a prime number; 2 is a prime number; 3 is a prime number; is a composite number, its prime factors are 2 and 2; 5 is a prime number; 6 is a composite number, its prime factors are 2 and 3; and so on to 100. When several equal factors occur in the answer, a smal} figure, called an exponent, is written at the right and a little above the factor to show how many times the factor is used. Thus, 23 means that 2 is used as a factor three times. 2 x 2 x 2 = 8. The factors of 72-2, 2, 2, 3, 3-are written 28 x 32. 7. What number does 52 represent? 25? 8. 2 x 52 are the prime factors of what number? 9. Of what number are 22 x 32 the prime factors? 10. The prime factors of a number are 22 × 3 × 5o. What is the number? 11. What are the prime factors of 168? Written To find the prime factors of a number not readily factored by inspection, we divide the number by one of its prime factors; then divide the resulting quotient by one of its prime factors, and continue the division until the resulting quo tient is prime. The several divisors and the last quotient are the prime factors. 1. What is the greatest number that will exactly divide 12 and 18? The greatest number that will exactly divide two or nore numbers is their greatest common divisor (g. c. d.). 22. What is the greatest common divisor of 48, 84, and 90? 248 84 90 2x3=6, the g, c. d. When the g. c. d. is not readily found by inspection, use this method. Arrange the numbers in a row and successively divide them by any number that will exactly divide all of them. Repeat the process with the resulting quotients. Continue the division until there is no number that will exactly divide all of the quotients. The product of the several divisors is the greatest common divisor. 2 and 3 are common divisors of all the numbers. Their product, 6, is the greatest common divisor of the numbers. Find the greatest common divisor of: A multiple of a number is a number obtained by using that number as a factor. Thus, 2, 4, 6, 8, 10, etc., are multiples of 2. 1. Name some multiples of 3. 2. Name some multiples of both 2 and 3. Since 6, 12, 18 are multiples of both 2 and 3, they are common multiples of 2 and 3. A number that is a multiple of two or more numbers is a common multiple of the numbers. The least multiple common to two or more numbers is their least common multiple (1. c. m.). Name the least common multiple of: 11. Find the least common multiple of 8, 10, and 12. 28 10 12 2 5 3 2 × 2 × 2 × 5 × 3 = 120 When the least common multiple is not readily seen, use this method. Divide the numbers by any factor common to two or more of them. Continue the division of the resulting quotients until no two of them have a common factor. The divisors and the remaining quotients are the factors of the least common multiple. Find, in the easiest way possible, the least common multiple of: 14. 16, 20 15. 20, 35 12. 12, 28 13. 18, 24 16, 24, 30 †20. 9, 12, 15†21. 12, 15, 18×22. 16, 20, 24×23. 15, 18, 24 USE OF SIGNS Operations in arithmetic are indicated by signs. The signs most commonly used are +, −, ×, ÷. When several operations are indicated in the same expression, operations indicated by x and are performed |