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Understanding Whole Numbers

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  1. Understanding Whole Numbers COURSE 1 LESSON 1-1 (For help, go to Skills Handbook p.654.) Write the value of the digit 2 in each number. 1. 28 2. 8,672 3. 612,980 4. 7,249,800,401 1-1

  2. Understanding Whole Numbers COURSE 1 LESSON 1-1 Solutions 1. 2 tens 2. 2 ones 3. 2 thousand 4. 2 hundred million 1-1

  3. Understanding Whole Numbers COURSE 1 LESSON 1-1 1 2 A pizza has 8 equal slices. You put only mushrooms on of them, and only sausage on of them. How many slices are left without a topping? 3 8 1 slice 1-1

  4. Standard form: 42,046,708,002 Use commas to separate the periods. Understanding Whole Numbers COURSE 1 LESSON 1-1 Write $42,046,708,002 in standard form and in words. Words: First write the number in expanded form. 42,000,000,000 + 46,000,000 + 708,000 + 2 42 billions 46 millions 708 thousands two forty-two billion, forty-six million, seven hundred eight thousand, two 1-1

  5. Understanding Whole Numbers COURSE 1 LESSON 1-1 a. Use < or > to complete: 60,201 ? 60,102. 60,201 is to the right of 60,102. So 60,201 > 60,102 1-1

  6. 3 is greater than 2, so 13,341 is the greatest number. The first digits are the same. 12,374 13,341 Compare the hundreds digit in the remaining numbers. 4 is greater than 3, so 12,472 is 12,472 the next greatest number. Understanding Whole Numbers COURSE 1 LESSON 1-1 (continued) b. Write in order from least to greatest: 12,374; 13,341; 12,472. The order from least to greatest is: 12,374; 12,472; 13,341. 1-1

  7. Understanding Whole Numbers COURSE 1 LESSON 1-1 Pages 6–7 Exercises 1. 25; twenty-five 2. 3,200; three thousand, two hundred 3. 508,310; five hundred eight thousand, three hundred ten 4. 890; eight hundred ninety 5. 7,000,002,031,000; seven trillion, two million, and thirty-one thousand 6. > 7. < 8. > 9. > 10. < 11. > 12. 20,304; 20,403; 23,040; 23,404 13. 51,472; 51,572; 54,172; 57,142 14. 7,890; 7,901; 7,910 15. 17,414; 17,444; 17,671; 18,242 16. 4 hundreds or 400 17. 4 ten thousands or 40,000 18. 4 ten millions or 40,000,000 1-1

  8. Understanding Whole Numbers COURSE 1 LESSON 1-1 32. Answers may vary. Sample: First method: compare the digits starting with the highest place values. Second method: attempt to subtract one from the other. 33. fifteen, eighteen 34. D 35. G 36. C 37. 390 19. 4 thousands or 4,000 20. 4 tens or 40 21. 4 ones or 4 22. 4 hundred thousands or 400,000 23. 4 hundreds 24. 687 25. 26. Answers may vary. Sample: 12,463; 27. Braeburn, Empire, Idared, York, McIntosh 28. <, < 29. >, > 30. >, > 31. <, < 1-1

  9. Understanding Whole Numbers COURSE 1 LESSON 1-1 38. 126 39. 2,129 40. 4,521 1-1

  10. Understanding Whole Numbers COURSE 1 LESSON 1-1 1. Write three hundred four thousand in standard form. 2. Write 20,259 in words. 3. Write in order from least to greatest: 6,947; 6,794; 9,644. 304,000 twenty thousand, two hundred fifty-nine 6,794, 6,947, 9,644 1-1

  11. Reading and Writing Decimals COURSE 1 LESSON 1-2 (For help, go to Lesson 1-1.) Write each whole number in words. 1. 28 2. 8,672 3. 612,980 4. 58,026,113 1-2

  12. Reading and Writing Decimals COURSE 1 LESSON 1-2 Solutions 1. 20 + 8 twenty-eight 2. 8,000 + 600 + 70 + 2 8 thousands 6 hundreds 70 2 eight thousand, six hundred seventy-two 3. 612,000 + 900 + 80 612 thousands 9 hundreds 80 six hundred twelve thousand, nine hundred eighty 4. 58,000,000 + 26,000 + 100 + 13 58 millions 26 thousands 1 hundred 13 fifty-eight million, twenty-six thousand, one hundred thirteen 1-2

  13. Reading and Writing Decimals COURSE 1 LESSON 1-2 If 300 cheeseburgers are ordered for lunch on a field trip and one out of every five must have mustard on it, how many will have mustard on them? 60 1-2

  14. Reading and Writing Decimals COURSE 1 LESSON 1-2 Write 608.0459 in expanded form. six eight four five nine ten- hundred hundredths thousandths thousandths 608.0459 = 600 + 8 + 0.04 + 0.005 + 0.0009 1-2

  15. One and nine hundred thirty-six ten-thousandths Reading and Writing Decimals COURSE 1 LESSON 1-2 Write 1.0936 in words. 1.0936 Four decimal places indicate ten-thousandths. 1-2

  16. 0 Write the whole number part. 0. Place the decimal point. 0.? ? ? ? Ten-thousandths is 4 places to the right of the decimal point. 0.4536 Place 4536. Reading and Writing Decimals COURSE 1 LESSON 1-2 There are four thousand five hundred thirty-six ten-thousandths kilograms in one pound. Write this number in standard form. 1-2

  17. Reading and Writing Decimals COURSE 1 LESSON 1-2 Pages 10–12 Exercises 1. 500 + 30 + 0.3 + 0.04 2. 3 + 0.004 3. 0.2 + 0.03 4. 7 + 0.5 5. 400 + 30 + 3 + 0.0005 6. 1 + 0.2 + 0.08 7. 90 + 3 + 0.6 + 0.08 8. 100 + 30 + 0.6 9. two and three tenths 10. six and two hundredths 11. nine and five tenths 12. six thousandths 13. two and sixty-one thousandths 14. three and eight ten- thousandths 15. forty hundredths 16. fifty and six thousand three ten-thousandths 17. 40.009 18. 600.000004 19. 0.0012 20. 26.2 21. 8 + 0.2; eight and two tenths 1-2

  18. Reading and Writing Decimals COURSE 1 LESSON 1-2 31. 4 tenths, or 0.4 32. 4 tens, or 40 33. 4 ten-thousandths, or 0.0004 34. 4 thousands, or 4,000 35. $.006 36. $.207 37. $.053 38. $.328 22. 90 + 1 + 0.9 + 0.01; ninety-one and ninety-one hundredths 23. 90 + 1 + 0.09 + 0.001; ninety-one and ninety-one thousandths 24. 1,000,000 + 600 + 50 + 0.02; one million, six hundred fifty and two hundredths 25. 0.20 26. 0.05 27. 0.25 28. 0.35 29. The value of each 2 is 10 times greater than the value of the 2 to its right. 30. a. $0.9 million b. $900,000 c. $1.6 million d. $1,600,000 1-2

  19. Reading and Writing Decimals COURSE 1 LESSON 1-2 39. 0.618 40. a. one millionth b. one ten-millionth c. Ten-millionths; this amount is one tenth of one millionth. 41. 216 42. C 43. I 44. C 45. I 46. > 47. < 48. > 1-2

  20. Reading and Writing Decimals COURSE 1 LESSON 1-2 1. Write 99.124 in expanded form. 2. Write fifty-five and thirty-four thousandths in standard form. 3. Write 500.04 in words. 4. Write 3,800.205 in words. 90 + 9 + 0.1 + 0.02 + 0.004 55.034 five hundred and four hundredths three thousand eight hundred and two hundred five thousandths 1-2

  21. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 (For help, go to Lesson 1-1.) Use < or > to compare values. 1. 430 340 2. 2,005 205 3. 80,020 8,020 4. 473 347 5. Two whole numbers have the same number of digits. To compare them, do you begin with the digits on the left or on the right? 1-3

  22. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Solutions 1. 430 > 340 2. 2,000 > 200. So 2,005 > 205. 3. 80 > 8. So 80,020 > 8,020. 4. 4 > 3. So 473 > 347. 5. digits on the left 1-3

  23. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Write the decimal for two hundred six hundred-thousandths. 0.00206 1-3

  24. Use a tenths grid for 0.5. Use a hundredths grid for 0.54. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Draw models for 0.5 and 0.54. Which number is larger? A greater area is shaded for 0.54 than for 0.5, so 0.54 is greater than 0.5. 1-3

  25. Make a number line showing tenths. Then mark the hundredths. Graph the points. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Order the decimals 0.34, 0.04, 0.08, and 0.4 on a number line. All the numbers are between 0 and 0.4. 1-3

  26. Write a zero at the end of 0.1 0.10 so each number has the same 0.10 number of decimal places. The ones digits are the same. The tenths and hundredths digits are the same. Compare digits starting with 0.10 the highest place values. 0.10 Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Use <, =, or > to complete each statement. a. 0.1 ? 0.10 Since all the digits are the same, 0.1 = 0.10. 1-3

  27. Compare digits starting with 0.28 the highest place values. 0.82 The ones digits are the same. The tenths digits are different. 2 is less than 8. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 (continued) b. 0.28 ? 0.82 Since the 2 tenths in 0.28 < the 8 tenths in 0.82, 0.28 < 0.82. 1-3

  28. Write a zero at the end of 0.6 0.60 so each number has the same 0.16 number of decimal places. Compare digits starting with 0.60 the highest place values. 0.06 The ones digits are the same. The tenths digits are different. 6 is greater than 0. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 (continued) c. 0.6 ? 0.06 Since the 6 tenths in 0.60 > the 0 tenths in 0.06, 0.6 > 0.06. 1-3

  29. 0 is the least tenths digit, so 0.084 is the least decimal. 0.800 0.800 0.084 0.084 0.480 0.480 4 is the next least tenths digit, so 0.480 is the next least decimal. 0.840 0.840 8 is the greatest tenths digit. 0 hundredths is less than 4 hundredths, so 0.800 is the third least decimal and 0.840 is the greatest. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Order 0.8, 0.084, 0.48, and 0.84 from least to greatest. Write zeros at the end of 0.8, 0.48, and 0.84. Then compare the digits starting with the highest place values. The decimals from least to greatest are 0.084, 0.48, 0.8, and 0.84. 1-3

  30. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Pages 16–17 Exercises 1. 0.5 is greater. 2. 0.53 is greater. 3. 0.2 is greater. 1-3

  31. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 17. 9.02, 9.024, 9.2, 9.209 18. 1.79, 1.979, 1.991, 2.185, 2.19 19. 5.5506, 5.561, 5.5660, 5.58, 5.665 20. Jakarta, Delhi, Karachi 21. Answers may vary. Sample: 2.21, 2.211, 2.212, 2.213, 2.214, 2.215 22. 4.198, 4.2025 4. 5. 6. 7. 8. < 9. > 10. = 11. > 12. = 13. < 14. 0.5, 0.65, 0.7 15. 13.7, 17.1, 17.7 16. 0.503, 0.529, 0.53 1-3

  32. 23. 0.6595, 0.6095, 0.62 24. 10.54, 10.75, 10.82, 10.94, 10.97 25. Alia; 11.88 < 11.9 26. 11,114; 11,116; XMCXIV < XMCXVI 27.A: 0.25; B: 0.77; C: 1.05 28. 031.02, 370.973, 398.2, 398.9, 709.52, 944, 952 29. 24 items Comparing and Ordering Decimals COURSE 1 LESSON 1-3 30. C 31. I 32. B 33. 125 34. 34,079 35. 10,136 36. 29 37. 377 38. 1,881 1-3

  33. Comparing and Ordering Decimals COURSE 1 LESSON 1-3 Order from least to greatest. 1. 0.54, 0.511, 0.5, 0.55 2. 2.79, 2.7, 2.708, 2.77 0.5, 0.511, 0.54, 0.55 2.7, 2.708, 2.77, 2.79 1-3

  34. Estimating With Decimals COURSE 1 LESSON 1-4 (For help, go to Skills Handbook p.655.) Round each number to the nearest ten. 1. 45 2. 65,328 3. 132,798 Round each number to the nearest thousand. 4. 30,910,067 5. 5,555 6. 15,345,357 1-4

  35. Estimating With Decimals COURSE 1 LESSON 1-4 Solutions 1.2. 45 rounds to 50. 65,328 rounds to 65,330. 3.4. 132,798 rounds to 132,800. 30,910,067 rounds to 30,910,000. 5. 5,555 rounds up to 6,000. 6. 15,345,357 rounds down to 15,345,000. 1-4

  36. Estimating With Decimals COURSE 1 LESSON 1-4 A 12-in. submarine sandwich is divided into 6 slices, and a second 12-in. sandwich is divided into 8 slices. Which sandwich has the larger slices? the sandwich with 6 slices 1-4

  37. 15.66 16 + 4.1 + 4 20 8.43 8 + 6.73 + 7 56 So, 8.43  6.73 56. So, 15.66 + 4.1 20. Estimating With Decimals COURSE 1 LESSON 1-4 Estimate by first rounding to the nearest whole number. a. 15.66 + 4.1 b. 8.43  6.73 1-4

  38. 28.75 ÷ 9.2 30 ÷ 10 = 3 Use compatible numbers such as 30 and 10. 28.75 ÷ 9.2 3 2.9796.5 3100 = 300 Use compatible numbers such as 3 and 100. 2.97  96.5 300 147.3 – 96.99 150 – 100 = 50 Use compatible numbers such as 150 and 100. 147.3 – 96.99 50 Estimating With Decimals COURSE 1 LESSON 1-4 Use compatible numbers to estimate. a. 28.75 ÷ 9.2 b. 2.97  96.5 c. 147.3 – 96.99 1-4

  39. Step 1 Add the front-end digits, the dollars. $ 1.79 1.29 + 1.49 $ 3 Step 2 Look at the cents and adjust the estimate. $ 1.79 1.29 + 1.49 about $.50 $ 3 about $1.50 about $1 Estimating With Decimals COURSE 1 LESSON 1-4 A lemonade costs $1.79, sodas cost $1.29, and water costs $1.49. Use front-end estimation to estimate the total cost of one of each drink. The total cost is about $3 + $1.50, or $4.50. 1-4

  40. Estimating With Decimals COURSE 1 LESSON 1-4 Pages 21–23 Exercises 1. about 37 2. about 10 3. about 34 4. about 45 5. about 54 6. about 3 7. about 23 8–15. Answers may vary. Samples are given. 8. about 9 9. about 600 10. about 350 11. about 270 12. about 6 13. about 8 14. about 100 15. about 6 16. about $9 17. about $15 18. about $106 19. about $48 20. about 3,300 grams 21. about 9 22. about 1.2 oz 1-4

  41. Estimating With Decimals COURSE 1 LESSON 1-4 39. about 58 40. Answers may vary. Sample: about $13; higher, because the total was rounded up to $39 41.a. about $9 b. Compatible numbers make the division easy to compute mentally. 42. about 6 times 43. about 24 23. about 3.1 oz 24. about 0.6 oz 25. about 1.9 oz 26. 1.4 27. 70 28. 5.13 29. 2.320 30. 310 31. 11 32. 0.35 33. 10 34–39. Answers may vary. Samples are given. 34. about 13 35. about 4 36. about 7 37. about 83 38. about 80 1-4

  42. Estimating With Decimals COURSE 1 LESSON 1-4 54. < 55. > 56. 7.8 57. 0.23 58. 208.1 59. 0.0038 44. about $24 45. about 15 46. about $120 47. Answers may vary. Sample: 10.646 48. Answers may vary. Sample: First, I would determine the number of cups in a gallon: 1  4  4 = 16 cups; 48. (continued) then I would estimate 268 ÷ 16 using the compatible numbers 300 and 15. So, our class should buy 300 ÷ 15, or 20 gallons. 49. B 50. G 51. B 52. F 53. < 1-4

  43. Estimating With Decimals COURSE 1 LESSON 1-4 Estimate by first rounding to the nearest whole number. 1. 24.35 – 6.8 2. 14.9  6.355 Use compatible numbers to estimate. 3. 38.56 ÷ 9.73 4. 4.71  19.71 about 17 about 90 about 100 about 4 1-4

  44. Adding and Subtracting Decimals COURSE 1 LESSON 1-5 (For help, go to Lesson 1-4.) Round each decimal to the nearest whole number. 1. 8.7 2. 9.5 3. 4.94 4. 0.92 5. 2.982 6. 3.090 1-5

  45. < – Solutions 1. 7 5, so 8.7 9 2. 5 5, so 9.5 10 3. 9 5, so 4.94 5 4. 9 5, so 0.92 1 5. 9 5, so 2.982 3 6. 0 5, so 3.090 3 > > > > > – – – – – Adding and Subtracting Decimals COURSE 1 LESSON 1-5 1-5

  46. 1 16 1 32 1 64 1 128 , , Adding and Subtracting Decimals COURSE 1 LESSON 1-5 Find the pattern and write the next three numbers in the sequence. , , , 1 2 1 4 1 8 1-5

  47. Estimate 6.8 + 4.65 + 2.125 7 + 5 + 2, or 14 Add. 6.800Line up the decimal points. 4.650Write zeros so that all decimals have + 2.125 the same number of digits to the right 13.575 of the decimal point. Adding and Subtracting Decimals COURSE 1 LESSON 1-5 First estimate and then find the sum 6.8 + 4.65 + 2.125. Check for Reasonableness The sum 13.575 is reasonable since it is close to 14. 1-5

  48. What you think 18 and 7 are easy to add. Adding 18 and 7 gives you 25. Adding 25 and 25 gives you 50. So, 25 + 18 + 7 = 50. Why it works 25 + 18 + 7 = 25 + (18 + 7) Associative Property of Addition = 25 + 25 Add inside the parentheses. = 50 Simplify. Adding and Subtracting Decimals COURSE 1 LESSON 1-5 Use mental math to find each sum. a. 25 + 18 + 7 1-5

  49. What you think 8.5 and 1.5 are easy to add. Adding 8.5 and 1.5 gives you 10. Adding 10 and 0.65 gives you 10.65. So, 8.5 + 0.65 + 1.5 = 10.65. Why it works 8.5 + 0.65 + 1.5 = 8.5 + (1.5 + 0.65) Commutative Property of Addition = (8.5 + 1.5) + 0.65 Associative Property of Addition = 10 + 0.65 Add inside the parentheses. = 10.65 Simplify. Adding and Subtracting Decimals COURSE 1 LESSON 1-5 Use mental math to find each sum. (continued) b. 8.5 + 0.65 + 1.5 1-5

  50. What you think 2.34 and 5.66 are easy to add. Adding 2.34 and 5.66 gives you 8. Adding 8 and 6.42 gives you 14.42. So, 2.34 + 6.42 + 5.66 = 14.42. Why it works 2.34 + 6.42 + 5.66 = 2.34 + (5.66 + 6.42) Commutative Property of Addition = (2.34 + 5.66) + 6.42 Associative Property of Addition = 8 + 6.42 Add inside the parentheses. = 14.42 Simplify. Adding and Subtracting Decimals COURSE 1 LESSON 1-5 Use mental math to find each sum. (continued) c. 2.34 + 6.42 + 5.66 1-5