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1 Add & Subtract Fractions 1. Copyright 2013 Edmentum - All rights reserved. A. B. C. D. Add & Subtract Decimals = Using the addition equation above, solve the subtraction equation below =??? A B C D Powers of Ten 3. Calculate the following = A B C. 3.5 D Model Division of Whole Numbers = 560 Using the multiplication equation above, solve the division equation below =? A. 28 B. 20 C. 560 D /42

2 Multiply Whole Numbers Add & Subtract Decimals = Using the subtraction equation above, solve the addition equation below =??? A B C D Add & Subtract Decimals A. 1.8 B. 2.2 C. 2.8 D. 2.6 Multiply & Divide Decimals = 11.7 Using the division equation above, solve the multiplication equation below =? A B C D Model Division of Whole Numbers 9. Complete the division problem and choose the answer with the correct equation. 2/42

3 A. 462 = B. 462 = C. 462 = D. 462 = Model Division of Whole Numbers 10. Complete the division problem and choose the answer with the correct equation A. 2,652 = B. 2,652 = C. 2,652 = D. 2,652 = Add & Subtract Decimals =? A B C D Representations of Decimals 12. How is the following decimal number read? A. four hundred forty-nine and eleven hundredths B. two hundred fourteen and sixty-two hundredths C. two hundred twenty-four and thirty-six hundredths D. four hundred ninety-four and eleven hundredths Comparing Decimals 13. Select the correct symbol. 7.46? A. < B. = 3/42

4 C. > Add & Subtract Decimals = A B C D Rounding Decimals 15. Round to the nearest whole number A. 646 B. 60 C. 65 D. 64 Representations of Decimals 16. Write the following in expanded form A. B. C. D. Multiply & Divide Decimals A B C. 3,560.7 D Real World Problems 18. At the grocery store, Vanessa bought 1.64 pounds of ground beef, 2.8 pounds of tomatoes, and 2.82 pounds of chicken. How much did these three items weigh altogether? A pounds B pounds C pounds D pounds 4/42

5 D pounds Powers of Ten 19. What happens to the decimal point in a number when the number is divided by 1,000? A. The decimal moves four places to the left. B. The decimal moves four places to the right. C. The decimal moves three places to the left. D. The decimal moves three places to the right. Representations of Decimals 20. Write the following in standard form. A B C D Comparing Decimals 21. Select the correct symbol. 0.91? A. > B. = C. < Representations of Decimals 22. Which of the following is equal to sixty-seven and forty-seven hundredths? A B C D Multiply & Divide Decimals A. 0.5 B. 11 C. 5 D. 1.1 Multiply & Divide Decimals 24. Which of the following is equal to ? 5/42

6 24. Which of the following is equal to ? A. (18 2) + (0.8 2) B. (18 2) - (0.8 2) C. (18 2) - (8 2) D. (18 2) + (2 0.8) Comparing Decimals 25. Select the correct symbol. 9.04? A. = B. < C. > Model Division of Whole Numbers 26. Complete the division problem and choose the answer with the correct equation A. 270 = B. 270 = C. 270 = D. 270 = Comparing Decimals 27. Select the correct symbol ? A. = B. > C. < Representations of Decimals 28. Write the following in standard form. A B C D Multiply Whole Numbers 29. 5, /42

7 17 Add & Subtract Decimals = A B C D Add & Subtract Decimals = A B C D Multiply Whole Numbers , Real World Problems 33. A law firm ordered a set of file cabinets to be delivered. The set of file cabinets weighs a total of 957 pounds. If there are 29 file cabinets, how much does each file cabinet weigh? A. 30 pounds B. 26 pounds C. 37 pounds D. 33 pounds Add & Subtract Fractions 34. A. B. C. 7/42

8 C. D. Multiply & Divide Decimals A B. 5.7 C D. 5.6 Representations of Decimals 36. How is the following decimal number read? 93.5 A. ninety-three and five tenths B. ninety-three five C. ninety-three and five hundredths D. ninety and thirty-five tenths Representations of Decimals 37. Which of the following is equal to forty-five and fifteen thousandths? A B C D Multiply Whole Numbers Rounding Decimals 39. Round to the nearest tenth A. 9.8 B C /42

9 C. 10 D. 9.9 Real World Problems 40. Brandon is competing in a long jump competition. He jumped 20 feet on his first jump. In his next two jumps, he jumped feet and feet. What is the total distance for all three jumps? A feet B feet C feet D feet Add & Subtract Fractions 41. A. B. C. D. Model Division of Whole Numbers = 893 Using the multiplication equation above, solve the division equation below =? A. 846 B. 47 C. 893 D. 19 Add & Subtract Fractions 43. Simplify the following expression. A. B. C. 9/42

10 D. Real World Problems 44. Luke has 29 lots for sale. Each lot is 0.33 acres. How much land does Luke have for sale? A acres B acres C. 9.9 acres D acres Powers of Ten 45. Calculate the following = A. 6.4 B. 640 C. 64 D. 6,400 Multiply & Divide Decimals A B C D Multiply Whole Numbers Real World Problems 48. Each class at an art design school costs $336. To finish school, students must take 33 classes. How much will it cost a student to complete art design school? A. $11,078 B. $11,058 C. $11,188 D. $11,088 Multiply & Divide Decimals 10/42

11 Multiply & Divide Decimals 49. The model represents the quotient of two decimals. Which expression does this model represent? A B C D Real World Problems 50. Tamara travels by plane to visit her sister in California once a month. If Tamara travels a total distance of 2,859 miles each time she visits her sister, how many miles does she travel to visit her sister each year? Note: There are 12 months in a year. A. 34,208 B. 34,328 C. 34,278 D. 34,308 Powers of Ten 51. When a natural number is multiplied by 100, the product is. A. that number with two zeros added to the end B. that number with three zeros added to the end C. that number with three zeros subtracted from the end D. that number with two zeros subtracted from the end Add & Subtract Fractions 52. A. B. C. D. Model Division of Whole Numbers 53. Use the following model to divide 143 by /42

12 A. 11 B. 13 C. 14 D. 12 Comparing Decimals 54. Select the correct symbol. 0.68? A. < B. = C. > Multiply Whole Numbers , Model Division of Whole Numbers 56. Which of the following is equal to 68 2? A. (60 2) + (8 2) B. (60 2) - (8 2) C. (60 8) + (60 2) D. (60 + 2) (8 + 2) Powers of Ten 57. In the number 9, , what is the difference between the 9 in the tenths place and the 9 in the place to its right? A. The 9 in the tenths place represents 10 times what the 9 to its right represents. B. The 9 in the tenths place represents 100 times what the 9 to its right represents. C. The 9 in the tenths place represents of what the 9 to its right represents. D. The 9 in the tenths place represents of what the 9 to its right represents. 12/42

13 Rounding Decimals 58. Round to the nearest whole number A. 10 B. 13 C. 12 D Model Division of Whole Numbers = 1,200 Using the multiplication equation above, solve the division equation below. 1, =? A. 1,152 B. 48 C. 1,200 D. 25 Comparing Decimals 60. Select the correct symbol ? 0.57 A. = B. < C. > Comparing Decimals 61. Select the correct symbol. 0.07? 0.05 A. = B. > C. < Comparing Decimals 62. Select the correct symbol ? A. > B. = C. < 13/42

14 Model Division of Whole Numbers 63. Complete the division problem and choose the answer with the correct equation A. 66 = 11 7 B. 66 = 11 6 C. 66 = D. 66 = 11 5 Rounding Decimals 64. Round to the nearest whole number A. 70 B. 77 C. 768 D. 76 Representations of Decimals 65. Write the following in expanded form A. B. C. D. Add & Subtract Fractions 66. Simplify the following expression. A. B. C. D. Rounding Decimals 14/42

15 6/14/13 Rounding Decimals Printable Worksheet 67. Round to the nearest tenth: A. 0.7 B. 0 C D. 0.6 Rounding Decimals 68. Round to the nearest whole number: A B. 91 C. 72 D. 90 Real World Problems 69. Marla ran 4.7 miles a day for 20 days straight. How many miles did Marla run altogether during the 20 day stretch? A B. 74 C. 94 D. 114 Powers of Ten 70. In the number 7, , what is the difference between the 7 in the tens place and the 7 in the column to its left? A. The 7 in the tens place represents of what the 7 to its left represents. B. The 7 in the tens place represents 100 times what the 7 to its left represents. C. The 7 in the tens place represents of what the 7 to its left represents. D. The 7 in the tens place represents 10 times what the 7 to its left represents. Add & Subtract Fractions 71. A. B. C. D. 15/42

16 Multiply & Divide Decimals 72. The product of 0.5 and 0.3 is shown on the grid below. Based on the grid, what is the product of 0.5 and 0.3? A B. 1.5 C D. 0.8 Add & Subtract Fractions 73. A. B. C. D. Representations of Decimals 74. Write the following in expanded form A. B. 16/42

17 C. D. Add & Subtract Decimals A B C D Real World Problems 76. Annabel sent 90 text messages to her brother during the last 18 days. How many text messages did she send her brother each day if she sent him the same number of text messages each day? A. 4 text messages each day B. 7 text messages each day C. 5 text messages each day D. 6 text messages each day Add & Subtract Decimals 77. Which of the following is equivalent to the addition problem below? A. ( ) + (9 + 4) + ( ) + ( ) B. ( ) + (9 + 6) + ( ) + ( ) C. ( ) + (9 + 4) + ( ) + ( ) D. ( ) + (9 + 7) + ( ) + ( ) Multiply Whole Numbers 78. 1,351 4 Rounding Decimals 79. Round to the nearest hundredth A /42

18 A B C. 3.8 D. 3 Add & Subtract Fractions 80. A. B. C. D. Rounding Decimals 81. Round to the nearest whole number: A. 73 B C. 74 D Representations of Decimals 82. How do you read the following decimal number? A. three and one thousandths B. three and ten hundredths C. three and one tenths D. three and one hundredths Rounding Decimals 83. Round to the nearest tenth A. 4.3 B C. 4.1 D. 4.2 Multiply Whole Numbers /42

19 Real World Problems 85. Sadie needs 4.4 yards to make one costume for each choir member in the play. How much fabric will she need if she has to make 7 costumes? A yards B yards C yards D yards Powers of Ten 86. Evaluate the following A. 100 B. 20 C. 10 D. 1,000 Comparing Decimals 87. Select the correct symbol ? 0.91 A. = B. < C. > Add & Subtract Fractions 88. Simplify the following expression. A. B. C. D. 19/42

20 Multiply & Divide Decimals 89. Which of the following is equal to 6.3 3? A. (6 3) - (3 3) B. (6 3) + (3 0.3) C. (6 3) - (0.3 3) D. (6 3) + (0.3 3) Rounding Decimals 90. Round to the nearest tenth: A B C D Multiply Whole Numbers , Comparing Decimals 92. Select the correct symbol. 0.3? 0.2 A. > B. < C. = Powers of Ten 93. Calculate the following = A B. 9.4 C. 940 D. 9,400 Multiply & Divide Decimals 94. Which of the following is equal to 8.9 5? A. (8 5) (0.9 5) 20/42

21 B. (8 + 5) ( ) C. (8 5) + (0.9 5) D. (8 5) + (0.9 8) Powers of Ten 95. Calculate the following ,000 = A B C D Powers of Ten 96. In the number 4, , what is the difference between the 4 in the hundredths place and the 4 in the place to its left? A. The 4 in the hundredths place represents of what the 4 to its left represents. B. The 4 in the hundredths place represents 10 times what the 4 to its left represents. C. The 4 in the hundredths place represents 100 times what the 4 to its left represents. D. The 4 in the hundredths place represents of what the 4 to its left represents. Real World Problems 97. A law firm ordered a set of file cabinets to be delivered. The set of file cabinets weighs a total of 864 pounds. If there are 27 file cabinets, how much does each file cabinet weigh? A. 25 pounds B. 32 pounds C. 36 pounds D. 29 pounds Model Division of Whole Numbers = 903 Using the multiplication equation above, solve the division equation below =? A. 21 B. 882 C. 903 D. 43 Multiply Whole Numbers /42

22 99. 7, Add & Subtract Decimals A B C D Answers 1. A 2. C 3. A 4. A , A 7. A 8. C 9. C 10. C 11. A 12. D 13. B 14. C 15. C 16. B 17. A 18. A 19. C 20. C 21. A 22. C 23. B 24. A 25. A 26. B 27. C 28. B , C 31. A 32. 5,121, D 34. C 35. B 36. A 37. A D 40. C 41. B 22/42

23 41. B 42. D 43. A 44. A 45. B 46. C , D 49. A 50. D 51. A 52. D 53. B 54. C ,951, A 57. A 58. B 59. D 60. B 61. B 62. C 63. B 64. B 65. B 66. C 67. D 68. D 69. C 70. C 71. A 72. A 73. B 74. A 75. B 76. C 77. A 78. 5, A 80. A 81. A 82. A 83. D , C 86. A 87. B 88. A 89. D 90. C 91. 2,510, A 93. C 94. C 95. A 96. A 97. B 98. D 99. 4,037, A Explanations 1. Rewrite the problem using a common denominator of 4 and then write them as improper fractions. 23/42

24 Remember that when subtracting fractions with like denominators, the denominators stay the same and subtract the numerators. 2. Addition and subtraction are opposite operations. Use the addition equation, = to solve the subtraction equation, = The number 100 has 2 zeros in it. To divide a decimal by 100, just move the decimal point 2 places to the left. 3.5 becomes = Multiplication and division are opposite operations. The multiplication equation, = 560, can be used to solve the division equation, = multiply 474 0: 0 multiply : 14,220 multiply : 284,400 add the results together: 298, Addition and subtraction are opposite operations. Use the subtraction equation, = to solve the addition equation, = Make sure to line up the decimal points when subtracting decimals. 24/42

25 7. Make sure to line up the decimal points when subtracting decimals Multiplication and division are opposite operations. The division equation, can be used to solve the multiplication equation, = 11.7, = Divide 46 by 22 to get 2 plus a remainder. Place 44 below Subtract 44 from 46 to get 2. Bring the 2 down from Divide 22 by 22 to get 1. Place 22 below Subtract 22 from 22 to get The correct equation is 462 = Divide 265 by 51 to get 5 plus a remainder. Place 255 below Subtract 255 from 265 to get 10. Bring the 2 down from Divide 102 by 51 to get 2. Place 102 below Subtract 102 from 102 to get 0. 0 The correct equation is 2,652 = The model on the left equals 91 hundredths or 0.91, because 91 out of 100 parts are shaded. The model on the right equals 38 hundredths or 0.38, because 38 out of 100 parts are shaded. Since both models show the same-sized parts, simply subtract the numbers. 91 hundredths - 38 hundredths = 53 hundredths The number 53 hundredths is also written as In this number, 4 is in the hundreds place, 9 is in the tens place and 4 is in the ones place. So, four hundred ninety-four is before the decimal place. 25/42

26 The decimal place is read, "and." To the right of the decimal place, 1 is in the tenths place and 1 is in the hundredths place. So, there are eleven hundredths to the right of the decimal. So the number is read, "four hundred ninety-four and eleven hundredths." 13. The number 7.46 is equal to Any final zeros to the right of a decimal point have no value. The symbol for "equal" is =. Thus, 7.46 = First, line up the decimal points of the two numbers. Subtract the digits in the hundredths column. Since 5 is less than 7, use regrouping to take one tenth from the tenths column, and add that tenth (10 hundredths) to the 5 hundredths (10+5=15), then subtract = Subtract the digits in the tenths column. Since 4 is less than 5, use regrouping to take one one from the ones column, and add that one (10 tenths) to the 4 tenths (10+4=14), then subtract = Subtract the digits in the ones column. 8-3 = Subtract the digits in the tens column. Since 4 is less than 9, use regrouping to take one hundred from the hundreds column, and add that hundred (10 tens) to the 4 tens (10+4=14), then subtract = Subtract the digits in the hundreds column. 0-0 = Therefore, = In this problem, 4 is in the ones place. Look at the number in the tenths place to determine whether or not to round up. In this problem, 6 is in the tenths place. Remember, if the number in the tenths place is less than five, do not round up. If the number in the tenths place is greater than or equal to five, round up. Therefore, 64.6 rounded to the nearest whole number is /42

27 Therefore, 64.6 rounded to the nearest whole number is A number written in expanded notation is broken down by place value. There is a 3 in the tens place. There is a 9 in the ones place. There is a 4 in the tenths place. There is a 4 in the hundredths place. There is a 7 in the thousandths place. Thus, is the following in expanded notation. 17. To multiply decimals, first rewrite the problem ignoring the decimal points Now, solve multiply 913 9: 8,217 multiply : 27,390 add the results together: 35,607 Finally, move the decimal point of the solution to the left to equal the total number of decimal places in the original factors. In this case, 91.3 has 1 decimal place, and 3.9 has 1 decimal place, for a total of 2 decimal places. Move the decimal point of the solution 2 places to the left. This gives as the final solution. 18. To find the total weight of the items, add their weights together pounds pounds pounds = 7.26 pounds 19. When a number is divided by a multiple of 10, the decimal point moves one place to the left for every zero. Since there is 3 zeros in 1,000, the decimal moves three places to the left. 27/42

28 Since there is 3 zeros in 1,000, the decimal moves three places to the left. 20. To transform a number written in expanded notation to standard notation just add the numbers together. Make sure to keep the place values. First, look at 6 10, which gives 6 for the tens place. Then, look at 5 1, which gives 5 for the ones place. Next, look at 8, which gives 8 for the tenths place. Then, look at 2, which gives 2 for the hundredths place. Finally, look at 5, which gives 5 for the thousandths place. Add the numbers together. So, the number in standard form is Compare the place values of both numbers, starting with the tenths place. The number 0.91 has a tenths place value of 9. The number has a tenths place value of 4. Since 9 is greater than 4, 0.91 is greater than The symbol for "greater than" is >. Thus, 0.91 > In this number, sixty-seven will be before the decimal place. So, 6 will be in the tens place and 7 will be in the ones place. "Forty-seven hundredths" means 4 will be in the tenths place and 7 will be in the hundredths place. Therefore, the number sixty-seven and forty-seven hundredths equals For the divisor 0.05, move the decimal 2 places to the right to get rid of the decimal point. Do the same for the dividend becomes becomes 55 Now do the division as you normally would /42

29 05 1. Divide 5 by 5 to get 1. Place 5 below Subtract 5 from 5 to get 0. Bring the 5 down from Divide 5 by 5 to get 1. Place 5 below Subtract 5 from 5 to get Divide using the distributive property. First, break up the 18.8 into " " Then, distribute the 2 by dividing both 18 and 0.8 by = ( ) 2 = (18 2) + (0.8 2) = = The number 9.04 is equal to Any final zeros to the right of a decimal point have no value. The symbol for "equal" is =. Thus, 9.04 = Divide 27 by 15 to get 1 plus a remainder. Place 15 below Subtract 15 from 27 to get 12. Bring the 0 down from Divide 120 by 15 to get 8. Place 120 below Subtract 120 from 120 to get 0. 0 The correct equation is 270 = The number is 3 thousandths less than The symbol for "less than" is <. Thus, < To transform a number written in expanded notation to standard notation just add the numbers together. Make sure to keep the place values. Start with 5 100, which gives 5 for the hundreds place. Then, look at 1 10, which gives 1 for the tens place. Then, look at 5 1, which gives 5 for the ones place. Next, look at 2, which gives 2 for the tenths place. Then, look at 9, which gives 9 for the hundredths place. 29/42

30 Finally, look at 6, which gives 6 for the thousandths place. Add the numbers together. So, the number in standard form is multiply : 38,304 multiply : 54,720 add the results together: 93, First, line up the decimal points of the two numbers. Subtract the digits in the hundredths column. 6-1 = Subtract the digits in the tenths column. 2-0 = Subtract the digits in the ones column. 5-0 = Subtract the digits in the tens column. 7-2 = Therefore, = Add the digits in the right column = 14. Place the 1 above the next column, and place the 4 below: Now, add the next column to the left = 8. Place the 8 below: /42

31 Now, add the next column to the left = 4. Place the 4 below: Therefore, = multiply : 667,980 multiply : 4,453,200 add the results together: 5,121, Divide the total weight of the set of file cabinets, 957, by the number of file cabinets in the set, 29. Each file cabinet weighs 33 pounds. 957 pounds 29 file cabinets = 33 pounds per file cabinet 34. First, find a common denominator. Since there are denominators of 7 and 14, let 14 be the common denominator and rewrite the problem using the common denominator. Now that the denominators are the same, subtract the numerators and simplify, if possible. 35. For the divisor 6.2, move the decimal 1 place to the right to get rid of the decimal point. Do the same for the dividend. 6.2 becomes becomes Now do the division as you normally would The decimal point in your answer will line up with the decimal point of the dividend. Fill in zeros as needed. 2. Divide 353 by 62 to get 5 plus a remainder. Place 310 below Subtract 310 from 353 to get 43. Bring the 4 down from Divide 434 by 62 to get 7. Place 434 below Subtract 434 from 434 to get In this number, 9 is in the tens place and 3 is in the ones place. So, ninety-three is before the decimal place. The decimal place is read, "and." To the right of the decimal place, 5 is in the tenths place. 31/42

32 To the right of the decimal place, 5 is in the tenths place. So the number is read, "ninety-three and five tenths." 37. In this number, forty-five will be before the decimal place. So, 4 will be in the tens place and 5 will be in the ones place. "Fifteen thousandths" means 0 will be in the tenths place, 1 will be in the hundredths place, and 5 will be in the thousandths place. Therefore, the number forty-five and fifteen thousandths equals First, multiply 4 by 0 from = 0. Place 0 below: Next, multiply 4 by 1 from = 4. Place 4 below: Next, multiply 4 by 1 from = 4. Place 4 below: Therefore, = In this problem, 8 is in the tenths place. Look at the number in the hundredths place to determine whether to round up or not. In this problem, 5 is in the hundredths place. Remember, if the number in the hundredths place is less than five, do not round up. If the number in the hundredths place is greater than or equal to five, round up. Therefore, the answer to this question is To figure out the total distance of the three jumps, add the distances of his 3 individual jumps together. 20 feet feet feet = feet 41. First, find a common denominator. Since there are denominators of 2 and 4, let 4 be the common denominator and rewrite the problem using the common denominator. Now that the denominators are the same, subtract the numerators and simplify, if possible. 42. Multiplication and division are opposite operations. The multiplication equation, can be used to solve the division equation, = 893, 32/42

33 = First, find a common denominator. Since there are denominators of 4 and 8, let 8 be the common denominator and rewrite the problem using the common denominator. Now that the denominators are the same, just add the numerators and simplify, if possible. 44. To find out how much land Luke has for sale, multiply the 29 lots by 0.33 acres. 29 lots 0.33 acres = 9.57 acres So, Luke has 9.57 acres for sale. 45. The number 100 has 2 zeros in it. To multiply a decimal by 100, just move the decimal 2 places to the right. 6.4 becomes = To multiply decimals, first rewrite the problem ignoring the decimal points Now, solve multiply 755 2: 1,510 multiply : 45,300 add the results together: 46,810 Finally, move the decimal point of the solution to the left to equal the total number of decimal places in the original factors. In this case, 75.5 has 1 decimal place, and 0.62 has 2 decimal places, for a total of 3 decimal places. Move the decimal point of the solution 3 places to the left. This gives as the final solution multiply 528 7: 3,696 multiply : 5,280 multiply : 52,800 add the results together: 61, Multiply the number of classes required to complete school by the cost of each class. $336 per class 33 classes = $11,088 An art design school student pays $11,088 for 33 classes. 49. The shaded portion of the model is equal to 3.2. The shaded portion is then broken into sections that are equal to /42

34 equal to 0.4. So, the correct expression that this model represents is Multiply the number of miles she travels in a month by the number of months in a year. 2,859 miles per month 12 months = 34,308 miles Tamara travels 34,308 miles each year to visit her sister. 51. When a natural number is multiplied by a power of 10, a zero is added to the end of the number for every zero in the power of 10. Since there are 2 zeros in 100, the product is that number with two zeros added to the end. 52. Rewrite the problem using a common denominator of 6 and then write them as improper fractions. Remember that when subtracting fractions with like denominators, the denominators stay the same and subtract the numerators. 53. Manipulate the blocks until they are in columns of 11. Notice there are 13 columns of 11 blocks. Therefore, = Compare the place values of both numbers, starting with the tenths place. The number 0.68 has a tenths place value of 6. The number has a tenths place value of 1. Since 6 is greater than 1, 0.68 is greater than The symbol for "greater than" is >. Thus, 0.68 > multiply : 0 multiply : 1,177,440 multiply : 11,774, /42

35 multiply : 11,774,400 add the results together: 12,951, Divide using the distributive property. First, split 68 into " " Then, distribute the 2 by dividing both 60 and 8 by The 9 in the tenths place represents "0.9". The 9 in the place to its right represents "0.09" = (60 + 8) 2 = (60 2) + (8 2) = = 34 Since 0.09 times 10 is 0.9, the 9 in the tenths place represents 10 times what the 9 to its right represents. 58. In this problem, 2 is in the ones place. Look at the number in the tenths place to determine whether or not to round up. In this problem, 6 is in the tenths place. Remember, if the number in the tenths place is less than five, do not round up. If the number in the tenths place is greater than or equal to five, round up. Therefore, rounded to the nearest whole number is Multiplication and division are opposite operations. The multiplication equation, can be used to solve the division equation, = 1,200, 1, = Compare the place values of both numbers, starting with the tenths place. The number has a tenths place value of 2. The number 0.57 has a tenths place value of 5. Since 2 is less than 5, is less than The symbol for "less than" is <. Thus, < The number 0.07 is 2 hundredths greater than The symbol for "greater than" is >. Thus, 0.07 > The number is 2 thousandths less than The symbol for "less than" is <. Thus, < Below is a fact family that should be memorized: = = x 6 = 66 6 x 11 = 66 The correct equation is 66 = In this problem, 6 is in the ones place. Look at the number in the tenths place to determine whether or not to round up. In this problem, 8 is in the tenths place. 35/42

36 to round up. In this problem, 8 is in the tenths place. Remember, if the number in the tenths place is less than five, do not round up. If the number in the tenths place is greater than or equal to five, round up. Therefore, 76.8 rounded to the nearest whole number is A number written in expanded notation is broken down by place value. There is a 1 in the hundreds place. There is a 6 in the tens place. There is an 8 in the ones place. There is a 6 in the tenths place. There is a 2 in the hundredths place. There is a 3 in the thousandths place. Thus, is the following in expanded notation. 66. First, find a common denominator. Since there are denominators of 3 and 6, let 6 be the common denominator and rewrite the problem using the common denominator. Now that the denominators are the same, just add the numerators and simplify, if possible. 67. In this problem, 6 is in the tenths place. Look at the number in the hundredths place to determine whether to round up or not. In this problem, 1 is in the hundredths place. Remember, if the number in the hundredths place is less than 5, do not round up. If the number in the hundredths place is 5 or greater, round up. Therefore, the answer to this question is When rounding to the nearest whole number, look at the number in the tenths place to determine whether to round up or not. In this problem, 1 is in the tenths place. Remember, if the number in the tenths place is less than 5, do not round up. If the number in the tenths place is greater than or equal to 5, round up. Therefore, rounded to the nearest whole number is To find out how many miles Marla ran in 20 days, multiply the miles per day, 4.7 miles, by the number of 36/42

37 69. To find out how many miles Marla ran in 20 days, multiply the miles per day, 4.7 miles, by the number of days, 20 days. 4.7 miles per day 20 days = 94 miles. 70. The 7 in the tens place represents "70". The 7 in the place to its left represents "700". Since 700 times is 70, the 7 in the tens place represents of what the 7 to its left represents. 71. Rewrite the problem using a common denominator of 8. Break the problem up into an addition of whole numbers and an addition of fractions. 72. Start by examining the model. There are 10 columns and 5 are shaded. This represents 0.5. There are 10 rows and 3 of them have a pattern. This represents 0.3. Now, look at the space shaded by both 0.5 and 0.3. This area represents the product of 0.5 and 0.3. So, the product of 0.5 and 0.3 is First, find a common denominator. Since there are denominators of 2 and 14, let 14 be the common denominator and rewrite the problem using the common denominator. Now that the denominators are the same, subtract the numerators and simplify, if possible. 37/42

38 74. A number written in expanded notation is broken down by place value. There is a 3 in the tens place. There is a 6 in the ones place. There is a 4 in the tenths place. There is a 3 in the hundredths place. There is a 6 in the thousandths place. Thus, is the following in expanded notation. 75. Make sure to line up the decimal points when adding decimals Divide the number of text messages Annabel sent her brother, 90, by the number of days, text messages 18 days = 5 text messages each day Annabel sent her brother 5 text messages each day. 77. To find which expression is equivalent, find the answer choice that matches the numbers in each place value. Break each number into tens, ones, tenths, and hundredths. Then, combine the like place values from each number. ( ) + (9 + 4) + ( ) + ( ) 78. First, multiply 4 by 1 from = 4. Place 4 below: Next, multiply 4 by 5 from = 20. Place 2 above the next digit in 1351, and place 0 below: /42

39 04 Next, multiply 4 by 3 from = 12. Then add the 2 above to get 14. Place 1 above the next digit in 1351, and place 4 below: Next, multiply 4 by 1 from = 4. Then add the 1 above to get 5. Place 5 below: Therefore, = 5, In this problem, 8 is in the hundredths place. The number in the thousandths place determines whether to round up or not. In this problem, 6 is in the thousandths place. Remember, if the number in the thousandths place is less than five, do not round up. If the number in the thousandths place is greater than or equal to five, round up. Therefore, the answer is Rewrite the problem using a common denominator of 12. Break the problem up into an addition of whole numbers and an addition of fractions. 81. When rounding to the nearest whole number, look at the number in the tenths place to determine whether to round up or not. In this problem, 4 is in the tenths place. Remember, if the number in the tenths place is less than 5, do not round up. If the number in the tenths place is greater than or equal to 5, round up. Therefore, rounded to the nearest whole number is In this number, 3 is in the ones place. So three is before the decimal place. The decimal place is read, "and." To the right of the decimal place, 1 is in the thousandths place. So the number is read, "three and one thousandths." 83. In this problem, 2 is in the tenths place. Look at the number in the hundredths place to determine whether to round up or not. In this problem, 2 is in the hundredths place. Remember, if the number in the hundredths place is less than five, do not round up. If the number in the hundredths place is greater than or equal to five, round up. Therefore, the answer to this question is /42

40 multiply 203 1: 203 multiply : 16,240 add the results together: 16, To find out how much fabric Sadie will need, multiply the 4.4 yards of fabric needed to make one costume by 7 costumes. So, Sadie needs 30.8 yards of fabric is read "Ten raised to the second power." 4.4 yards 7 costumes = 30.8 yards Ten raised to the second power means two tens are being multiplied together, as shown below = = 100 When ten is raised to a power, the number of zeros on the resulting value is equal to the power. For example, in this case, ten is raised to the second power, so the resulting value will have two zeros. The number 100 has two zeros. 87. Compare the place values of both numbers, starting with the tenths place. The number has a tenths place value of 1. The number 0.91 has a tenths place value of 9. Since 1 is less than 9, is less than The symbol for "less than" is <. Thus, < First, find a common denominator. Since there are denominators of 3 and 15, let 15 be the common denominator and rewrite the problem using the common denominator. Now that the denominators are the same, just add the numerators and simplify, if possible. 89. Divide using the distributive property. First, break up the 6.3 into " " Then, distribute the 3 by dividing both 6 and 0.3 by = ( ) 3 = (6 3) + (0.3 3) = = In this problem, 5 is in the tenths place. The number in the hundredths place determines whether to round up or not. In this problem, 6 is in the hundredths place. Remember, if the number in the hundredths place is less than 5, do not round up. If the number in the hundredths place is 5 or greater, round up. 40/42

41 Therefore, the answer is multiply : 579,450 multiply : 1,931,500 add the results together: 2,510, The number 0.3 is 1 tenth greater than 0.2. The symbol for "greater than" is >. Thus, 0.3 > The number 10 has 1 zero in it. To multiply a number by 10, just put 1 zero on the end of the number. So, 94 becomes = Multiply using the distributive property. First, break up the 8.9 into " " Then, distribute the 5 by multiplying both 8 and 0.9 by = ( ) 5 = (8 5) + (0.9 5) = = The number 1,000 has 3 zeros in it. To divide a decimal by 1,000, just move the decimal 3 places to the left becomes ,000 = The 4 in the hundredths place represents "0.04". The 4 in the place to its left represents "0.4". Since 0.4 times is 0.04, the 4 in the hundredths place represents of what the 4 to its left represents. 97. Divide the total weight of the set of file cabinets, 864, by the number of file cabinets in the set, pounds 27 file cabinets = 32 pounds per file cabinet Each file cabinet weighs 32 pounds. 98. Multiplication and division are opposite operations. The multiplication equation, = 903, can be used to solve the division equation, = multiply : 21, /42

42 multiply : 430,260 multiply : 3,585,500 add the results together: 4,037, Make sure to line up the decimal points when adding decimals /42