Name: Number: Number and Operations in Base Ten Key

Name: Number: Number and Operations in Base Ten Key

1.1 Multiplying and Dividing by Powers of Ten 8 x (6 + 3) = 72 12 (13-7) = 2 9 x (5 3) 2 = 9 3 x (2 + 4) (9-3) = 12 Write the numbers in the table: 24,438. Thousands Ones Hundreds Tens Ones Hundreds Tens Ones 2 4 4 3 8 Complete each sentence. In the number 24,438, the number 4 in the thousands place is 10 times as much as the 4 in the hundreds place. In the number 24,438, the number 4 in the hundreds place is 1/10 the value of the 4 in the thousands place. Andrea wrote the number 897,747. How does the value of the 7 in the thousands place compare to the value of 7 in the hundreds place? The 7 in the thousands place is 1/10 the value of the 7 in the hundreds place. Lauren wrote the number 922,221. How does the value of the 2 in the tens place compare to the value of 2 in the hundreds place? The 2 in the tens place is 10 times as much as the 2 in the hundreds place.

1.2 Multiplying and Dividing by Powers of Ten (12 x 4) 2 + 7 = 31 [10 + (11-5)] x 2 = 32 63 (9-2) = 9 10 x (2 + 7) = 90 Multiply or divide. 93 x 10 3 10 3 = 10 x 10 x 10 = 1000 93 x 1000 = 93,000 9 10 3 10 3 = 10 x 10 x 10 = 1000 9 1000 = 0.009 3.5 10 2 10 2 = 10 x 10 = 100 3.5 100 = 0.035 74 x 10 2 10 2 = 10 x 10 = 100 74 x 100 = 7,400 13 x 10 2 = 1300 34 10 3 = 0.034 5.21 x 10 4 = 52,100 5.8 10 2 = 0.058 Breanna multiplied 94 by a power of ten. She got 94,000. By what power of ten did Breanna multiply 94? 10 3 David multiplied 73 by a power of ten. He got 7,300. By what power of ten did David multiply 73? 10 2

2.1 Using Place Value to Read and Write Decimals (15-7) x 2-9 = 7 [13 - (9 + 1)] x 6 = 18 72 (12-4) = 9 5 x (15-4) = 55 Write the number name and the expanded form for each decimal. 28.345 Number name: twenty-eight and three hundred forty-five thousandths. Expanded form: (2 x 10) + (8 x 1) + (3 x ) + (4 x ) + (5 x ). 42.91 Number name: forty-two and ninety-one hundredths. Expanded form: (4 x 10) + (2 x 1) + (9 x ) + (1 x ). 0.528 Number name: five hundred twenty-eight thousandths. Expanded form: (5 x ) + (2 x ) + (8 x ). 7.2 Number name: seven and two tenths. Expanded form: (7 x 1) + (2 x ). Elena s grandma s house is 2,321.879 miles away. What is this decimal in expanded form? (2 x 1000) + (3 x 100) + (2 x 10) + (1 x 1) + (8 x ) + (7 x ) + (9 x ).

2.2 Using Place Value to Read and Write Decimals (4 x 3) + (6 x 6) = 48 (8-2) x 5 = 30 8 x (96 12) = 64 56 (4 x 2) = 7 Write each decimal. Twelve hundredths 0.12 One and ninety-three thousandths 1.093 Eighty-seven and three tenths 87.3 Three hundred and sixty-four hundredths 300.64 (5 x 10) + (3 x 1) + (9 x ) + (2 x ) + (5 x ) 53.925 (3 x 1) + (1 x ) + (8 x ) + (4 x ) 3.184 (9 x 100) (4 x 10) + (5 x 1) + (3 x ) + (2 x ) 945.32 (7 x 10) + (6 x 1) + (1 x ) 76.1 Joe s odometer reads 9,468.91 miles on his car. What is this decimal in expanded form? (9 x 1000) + (4 x 100) + (6 x 10) + (8 x 1) + (9 x ) + (1 x ).

Number and Operations in Base Ten 3.1 Comparing Decimals 11 x (4 + 5) = 99 (14 2) x 5 = 35 (6 x 6) 3 + 15 = 27 [8 + (13-5)] 4 = 4 Compare. Write >, <, or =. > 15.993 15.874 0.067 0.137 29.34 29.57 19.459 19.459 < 123.873 123.873 6643.0 6643.0 = 9.3 9.1 8.777 8. > 84.572 84.571 15.993 15.874 > < = = > > Belle and David both opened savings accounts at the same time. So far, Belle has saved $200.25 and David has saved $200.15. What has saved the greater amount so far? Belle has saved the greater amount so far.

3.2 Comparing Decimals 9 x (2-1) = 9 (24 8) x 9 = 27 (6 x 2) 1 + 7 = 19 [5 + (2 x 4)] - 3 = 10 Put the decimals in order from least to greatest. 0.47, 0.5, 0.53,.489, 0.57 0.47,.489, 0.5, 0.53, 0.57 0.36, 0.495, 0.36, 0.947,.24.24, 0.36, 0.36, 0.495, 0.947 0.548, 0.89,.539, 0.26, 0.397 0.26, 0.397,.539, 0.548, 0.89.93, 0.502, 0.028, 0.32, 0.834 0.028, 0.32, 0.502, 0.834,.93 0.368, 0.018, 0.193,.072, 1.075 0.018,.072, 0.193, 0.368, 1.075 1.45, 1.5, 1.08, 1.384, 2 1.08, 1.384, 1.45, 1.5, 2 What happens to the value of a number if it is moved one place value to the right? The value decreases. Ava measured the growth of her plants in her science experiment. Her first plant was 4.629 cm tall. Her second plant was 4.891 cm tall. Which of one of her plants grew the tallest? Ava s second plant is the tallest.

4.1 Rounding Decimals Using Place Value (9-6) x 4-2 = 10 [15 - (8 + 2)] x 9 = 45 108 (15-3) = 9 4 x (8-2) = 24 Round to the nearest hundredth: 6.934 6.39 6.521 6.52 9.825 9.83 1.098 1.10 Round to the nearest tenth: 6.55 6.6 2.14 2.1 7.884 7.9 3.56 3.6 Round to the nearest whole number: 5.687 6 4.1 4 2.394 2 0.643 1 Jessica has $924.84 saved. What is $924.84 rounded to the nearest tens place? $920.00 Adam runs at the average speed of 180.937 miles per hour. What is his average speed to the nearest hundredth place? 180.94

4.2 Rounding Decimals Using Place Value (2 x 5) x 9-2 = 88 [45 - (4 x 6)] + 7 = 28 132 (12-1) = 12 7 x (3-3) = 0 Round to the nearest hundredth: 8.335 6.34 5.302 5.30 6.258 9.26 1.742 1.74 Round to the nearest tenth: 4.13 4.1 5.283 5.3 9.323 9.3 9.82 9.8 Round to the nearest whole number: 9.89 10 4.7 5 4.25 4 3.21 3 Nancy gave $450.32 to her mom to put in her bank account. What is $450.32 rounded to the nearest hundreds place? $500.00 Bob goes hiking once a month. This month, Bob hiked 27.395 miles. What is 27.395 rounded to the nearest hundredths place? 27.40

5.1 Multiplying Whole Numbers 4 x (8 + 1) = 36 36 (12-6) = 6 8 x (8 2) 2 = 24 3 x (4 + 5) (3-1) = 25 Multiply. 59,008 X 6 354,048 3,521 X 4 14,084 833 X 24 19,992 5,397 X 32 172,704 Complete the sentence. The product of 327 and 49 is 16,023. Each car at the car dealership costs $22,598. If the dealership sells 8 cars, how much money would the dealership make? $180,784

5.2 Multiplying Whole Numbers (9 x 2) + (5 x 3) = 33 (8-4) x 7 = 28 2 x (63 9) = 14 42 (3 x 2) = 7 Multiply. 67,349 X 3 202,047 8,389 X 37 310,393 251 X 54 13,554 4,746 X 8 37,968 Complete the sentence. The product of 13,845 and 9 is 124,605. A box of chocolate has 14 pieces inside. If there are 3,485 boxes of chocolate, how many pieces of chocolate are there? 48,790

6.1 Dividing Whole Numbers (6 x 8) + (2 x 4) = 56 (7-3) x 7 = 28 6 x (64 8) = 48 35 (5 x 1) = 7 Divide. 26 4 104 24 55 1,320 75 62 4,650 48 92 4,416 Complete the sentence. 574 X 31 = 17,794 is the opposite of 17,794 574 = 31. Michael has 5,022 stickers in his collection. He put 27 stickers on each page of his sticker album. How many pages did he use? 5,022

6.2 Dividing Whole Numbers (8 x 3) 4 = 6 (25 5) + (55 5) = 16 13 + (9-3) = 19 (4 x 6) x (9 x 3) = 648 Divide. 89 17 1,513 36 9 324 19 82 1,558 29 48 1,392 Complete the sentence. 99 X 54 = 5,346 is the opposite of 5,346 99 = 54. Aiden has 1,978 dinosaurs. He groups them in groups of 86. How many groups will he have? 1,978

7.1 Adding and Subtracting Decimals (66 11) - 4 = 2 (10 2) x (5 x 1) = 25 8 x (24 2) = 96 7 + (5 x 10) = 57 Add or subtract. 25.89 + 12.74 38.63 89.26 + 10.98 100.24 74.12 + 26.8_ 100.92 64.87-5.43 59.44 98.31-71.34 27.31 42.17-16.53 25.64 Lily drove 24.61 miles to get to work and 14.93 miles to get to the store after work. How many miles did Lily drive total? 24.61 + 14.93 =39.54

7.2 Adding and Subtracting Decimals (9 7) + (3 1) = 4 (29 x 0) + 5 = 5 6 x (9 3) = 36 5 x (30 10) = 15 Add or subtract. 75.68 + 9.71 85.39 98.47 + 63.74 162.21 83.61 + 52.87_ 136.48 63.50-42.19 21.31 31.90-4.36 27.54 86.41-83.17 3.24 Ethan has $46.92. He bought a toy for $19.38. How much money does he have left after he bought his toy? $46.92 - $19.38 = $27.54

8.1 Multiplying Decimals (15 x 2) 10 = 3 (12 2) x (4 x 6) = 144 [2 + (5 3)] x 4 = 16 19 + (1 x 10) = 29 Multiply. 2.34 X 6 14.04 11.92 X 34 405.28 9.13 X 50 456.50 2.6 X 0.25 0.65 92.5 X 0.6 55.5 64.17 X 1.6 102.672 Alivia bought 6.3 pounds of apples for $0.60 each pound. How much money did Alivia spend on apples? 6.3 x 0.60 = 3.78. Alivia spent $3.78 on apples.

8.2 Multiplying Decimals (8 x 3) 6 = 4 (36 9) x (3 x 2) = 24 [7 + (2 x 2)] x 4 = 44 39 + (6 x 12) = 111 Multiply. 5.76 X 8 46.08 19.57 X 28 547.96 8.19 X 68 556.92 5.4 X 0.3 1.62 89.2 X 0.15 13.38 74.39 X 1.3 96.707 Kayla weighs 93.4 pounds. Her mom weighs 1.3 times as much as Kayla weighs. How many pounds does Kayla s mom weigh? 93.4 x 1.3 = 121.42. Kayla s mom weighs 121.42 pounds.

9.1 Dividing Decimals (9 x 3) + 54 = 81 (10 + 2) x (3 x 4) = 144 6 x (36 2) = 108 3 + (8 x 3) = 27 Divide. 3.85 5 19.25 9.4 8.3 78.02 0.25 899 224.75 1.8 24.1 43.38 Over a 3 day period, Jessica s plant grew 2.34 centimeters. What was the average height Jessica s plant grew each day? 2.34 3 = 0.78.

9.2 Dividing Decimals (54-19) + 96 = 131 (9 x 9) + (8 x 7) = 137 8 x (24 12) = 16 16 + (6 x 7) = 58 Divide. 2.16 8 17.28 9.6 7.2 69.12 750 0.25 187.50 1.5 23.55 23.55 Trevor drove 629 miles in 8.5 hours. How many miles per hour did he drive? 629 8.5 = 74.