1. Name the terms used in division. 2. What is division? 3. Make an example in division, the quotient of which must be an abstract number. A concrete number. 4. The dividend is 27 and the divisor 9. Express this example in three ways. 5. What is the sign of division? 6. The divisor is 3 and the dividend is 15 ft. Express this example using the sign. Read the example as you have written it. 15. How do you divide a number by 10? By 100? By 1000? By 2000? By 500? 16. Divide the following by 100: a. 675; b. 106; c. 281. a. 2461; b. 1074; 17. Divide the following by 1000: a. 2461; c. 8635; d. 3807. 18. Divide the following by 2000: a. 8400; b. 6200; c. 8000; d. 12,600. 19. Divide the following by 50: a. 200; b. 450; c. 500. 20. State the quickest way of finding how many articles can be bought for a given amount at 25 each. At 50g each. At 20. At 331. 21. At 20 each, how many articles can be bought for $10? For $15? $4? $21? $100? 22. At 50 each, how many articles can be bought for $3? $2.50? $6? $4.50? $75? $250? 23. At 331 each, how many articles can be bought for $1? $7? $20? $60? $110? $320? 24. At 25 each, how many articles can be bought for $4? $1.50? $2.25? $8? $10? $40? 1. A grocer paid $1,148.40 for flour at $4.35 a barrel. If he sold it at $5.15 a barrel, how much did he gain? 2. The area of Porto Rico is 3606 sq. mi. and the population is 953,243. Find to the nearest unit the population of each square mile. 3. Porto Rico exports annually $14,867,000 worth of goods. Find to the nearest dollar the amount of exports for each person. 4. The area of France is 207,054 sq. mi. and the value of her exports is $1,119,400,000. Find to the nearest dollar the value of the exports for each square mile. A realty company issues the following statements: 5. Find the value of the assets. Find the value of the liabilities. 6. Subtract the liabilities from the assets to find the profits. 7. Two automobiles start from two towns 105 miles apart and travel toward each other. They meet in 3 hours. If the first traveled 15 miles an hour, how many miles did the second travel an hour? 8. A dealer sold 96 yd. of carpeting at $1.871⁄2 a yard. If he gained $38.40, how much did it cost him a yard? 9. How many farms containing 90 acres each can be formed in a town that is in the form of a rectangle 6 miles long and 4 miles wide? There are 640 acres in a square mile. 10. If 63 is added to a certain number, it will contain forty-two 246 times. What is the number? 1. Name two numbers that multiplied together give 15 as their product. 2. Name then the two factors of 15. 3. What is a factor? 4. What are the factors of 35? 21? 12? 42? 5. Of the following numbers name those that can be exactly divided by other numbers: 7; 14; 11; 20; 19; 27. 6. What are composite numbers? Prime numbers? 7. Which of these numbers are divisible by 2? By 3? By 5? By 9? 8. Name the prime numbers between 1 and 50. 9. Name the composite numbers between 1 and 50. 10. Name all the numbers that can be exactly divided by 2 between 0 and 20. an 11. A number that can be exactly divided by 2 is called number. 12. Name all the odd numbers between 1 and 25. 13. Name two numbers that are both odd and prime. 14. Name 5 numbers that are both odd and composite. 15. Name 5 numbers that are both even and composite. 16. Name the factors of 15. Name the factors of 25. What factor is common to both, that is, is found in both numbers? 17. Name a common factor or divisor of 12 and 20. 18. What is the greatest common divisor of 12 and 20? 19. Name some numbers that are divisible by 3. By 5. 20. Name a number that is divisible by both 3 and 5, that is, name a common multiple of 3 and 5. 21. Name a common multiple of 4 and 10. 22. Name a common multiple of 2, 3, and 5. The greatest common divisor or measure of two or more numbers is the greatest number that exactly divides each of the numbers. What is the greatest common divisor of 18, 30, and 48? 2)18-30-48 3)9-15-24 3-5-8 2 x 3 = 6 Arrange the numbers as indicated. Divide by 2, the smallest common prime factor. The quotients are 9, 15, and 24. Divide these by 3, the smallest common prime factor. The quotients are 3, 5, and 8, which have no common factor. The greatest common divisor is the product of the prime factors, 2 and 3. Find the greatest common measure of 1001 and 1144. 1001)1144(1 The greatest common divisor of numbers not easily factored will seldom be required. If necessary this method may be used: Divide the larger number by the smaller. Divide the divisor by the remainder, and continue till there is no remainder. The last divisor will be the greatest common divisor. In the following examples find the greatest common divisor of the numerator and denominator and divide each term by it to reduce the fraction to its lowest terms : 10. 212 11. 435 12. 155 13. 164 14. 672 15. 275 371 522 279 205 784 625 Find the least common multiple of 12, 20, and 30. 2)12-20-30 2)6-10-15 A common multiple of two or more numbers contains all 3)3- 5-15 the factors of each of the numbers. Arrange the numbers as indicated. Divide by any prime number that will divide one or more. When a number is not divisible write it in the line below without change. Continue to divide till the quotients are unity. The product of all the divisors will be the least common multiple. 5)1-5-5 1-1-1 2×2×3× 5 = 60 In the following change to common denominators by finding the least common multiple of the denominators : 16. What is the smallest quantity of apples that can be exactly measured by the 2 quart, 4 quart, and 8 quart measure? 17. Find the least number of marbles that can be equally divided among 6, 9, or 12 boys. 18. What is the smallest distance that can be exactly measured by a 2 foot, 3 foot, and 8 foot measure? 19. What is the smallest number of yards of cloth that can be exactly cut into 7 yd. lengths, 5 yd. lengths, or 3 yd. lengths. 20. Two forces are pulling a weight upward. If one force lifts 163 lb. and the other force 1215 lb., what is the weight of the object? |