THE MEANING OF DIVISION PROBLEMS 11. a) What number times 100 will be 287? Answer using the division To see the answer, pass your mouse over the colored area. 287 ÷ 100 = 2.87 11. b) Read your answer to part a). 287 divided by 100 equals (or is) 2.87. 11. c) What is 287 called? The dividend. 11. d) What is 100 called? The divisor. 11. e) What is 2.87 called? The quotient. 11. f) Prove your answer to part a). 2.87 × 100 = 287 12. Practice the following.
13. a) Let this straight line represent 24, and illustrate 24 ÷ 4.
13. b) Prove 24 ÷ 4 = 6. 6 × 4 = 24 13. c) Illustrate 24 ÷ 6.
13. d) Prove 24 ÷ 6 = 4. 4 × 6 = 24 14. a) How many times could you subtract 8 from 40? 5 13. b) Write that problem using the division sign ÷ . 40 ÷ 8 = 5 14. c) Write that problem using the division bar.
14 d) In that form, what is 40 called? The dividend. 14. e) What is 8 called? The divisor. 14. f) What is 5 called? The quotient. 15. a) From a bottle that contains 48 oz, how many times could you fill 15. b) From a bottle that contains 2 quarts, how many times could you 8 times. 64 oz ÷ 8 oz = 8 To divide, the units must be of the same kind. 16. A farmer has a field that is 100 yards long, and he wants to put a
How many times is 4 feet contained in 100 yards? To answer, we have to change yards to feet because, again, the units must be the same. Since 1 yard = 3 feet, then 100 yards = 300 feet. How many 4's are there in 300? Now, 100 is made up of twenty-five 4's: 100 = 25 × 4. Therefore, 300 = (3 × 25) × 4 = 75 × 4. The farmer must put 75 fence posts. (Alternatively, to divide a number by 4 is equivalent to taking its fourth part. And to take the fourth part, we can take half of half. Lesson 15, Question 8. Half of 300 is 150. Half of 150 is 75.) But what about the fence post at the beginning of the field -- at the "zero" point? In reality, then, he would put 76 fence posts! 17. If you divide a number by 8, what are the possible remainders? 1, 2, 3, 4, 5, 6, 7. 18. Divide each number by 8 mentally. Write the whole number 17 18 2 R 2. 29 3 R 5. 39 4 R 7. 54 6 R 6. 76 9 R 4. 19. Divide each number by 7 mentally. Write the whole number 19. 17 2 R 3. 25 3 R 4. 31 4 R 3. 41 5 R 6. 61 8 R 5. 10. Divide each number by 9 mentally. Write the whole number 19. 17 1 R 8. 25 2 R 7. 31 3 R 4. 41 4 R 5. 62 6 R 8. 11. Prove: 157 ÷ 14 = 11 R 3 11 × 14 = 140 + 14 = 154, plus 3 is 157. 12. How will 436 change if you multiply it by 10 and then divide by 10? It will not change! 13. Divide.
15. The divisor composed of factors.
16. Say that the quotient of two numbers is 10, and 50 16. b) you multiply the divisor by 5. What will be the new quotient? 2 16. c) you multiply the dividend and the divisor by 5. What will be the 10 17. What property of division allows us to write the following:
If we multiply the dividend and divisor by the same number 18. To divide, the divisor must be a whole number.
19. The order of multiplying and dividing does not matter.
20. Show three ways of doing this problem:
21. Find a multiple of the divisor in the dividend.
22. A stack of CD's is 8 inches high. Each CD is .25 inches thick. How
23. Write the first five multiples of 23. a) 12. 12, 24, 36, 48, 60. 23. b) 18. 18, 36, 54, 72, 90. 23. c) 75. 75, 150, 225, 300, 375. 23. d) If you divide $6,000 equally among 12 people, how much will 23. e) How many 18's are there in 540? 30 23. f) How many times could you subtract 75 from 3,000? 40 24. Inexact division. Write each quotient as a mixed number.
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