Book 2 Place Value and Decimal Fractions
Module 1 Book 2 Place Value and Decimal Fractions
Name _________________________ Class Code __________ 1
Numbers in Words 1 – one 2 – two 3 – three 4 – four 5 – five 6 – six 7 – seven 8 – eight 9 – nine 10 – ten 11 – eleven 12 – twelve 13 – thirteen 14 – fourteen
15 – fifteen 16 – sixteen 17 – seventeen 18 – eighteen 19 – nineteen 20 – twenty 30 – thirty 40 – forty 50 – fifty 60 – sixty 70 – seventy 80 – eighty 90 – ninety
100 – hundred 1,000 – thousand 1,000,000 – million .1 – tenth .01 – hundredth .001 – thousandth .0001 – ten thousandth $ - Dollars ¢ - Cents
2
Vocabulary Sum – The answer to an addition problem. Difference – The answer to a subtraction problem. Factors – The numbers you multiply together in a multiplication sentence. 5 x 6 = 30 Factor Factor Product – The answer to a multiplication problem. 5 x 6 = 30 Product Divisor – The amount that another amount is divided by. 30 ÷ 5 = 6 Divisor Dividend – The amount being split up in a division problem. 30 ÷ 5 = 6 Dividend Quotient – The answer to a division problem 30 ÷ 5 = 6 Quotient Remainder – The amount left over in whole number division
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4
NOTES
If you line up the decimal points it helps you to line up the place values. Remember to put a zero in the empty spaces to help you add and subtract.
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Adding Decimals Lesson 9 Application Problem 6,455 + 7,822 = 7,000 – 4,322 = Ten baseballs weigh 1,417.4 grams. About how much does 1 baseball weigh? Round your answer to the nearest tenth of a gram. Round your answer to the nearest gram.
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Write the numbers in standard form 2 tenths + 6 tenths Now add vertically lining the numbers up by their place value. Write the numbers in standard form 2 ones 3 thousandths + 6 ones 1 thousandth Now add vertically lining the numbers up by their place value. Add using the same procedure 2 tenths 5 thousandths + 6 hundredths Write the answer in standard form 1.8 + 13 tenths 8
Write in standard form and then add. Make sure you line up your decimals in order to line up your place values a) 1 hundred 8 hundredths + 2 ones 4 hundredths b) 148 thousandths + 7 ones 13 thousandths
c) 0.74 + 0.59 d) 7.048 + 5.196 e) 7.44 + 0.774
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Lesson 9 Problem Set 1. Solve by writing the numbers in standard form first and then write your sum in standard form.
a. 1 tenth + 2 tenths = ___________
b. 14 tenths + 9 tenths = ___________
c. 1 hundredth + 2 hundredths = ___________
d. 27 hundredths + 5 hundredths = ___________
e. 1 thousandth + 2 thousandths = ___________
f. 35 thousandths + 8 thousandths = __________
g. 6 tenths + 3 thousandths = _________
h. 7 ones 2 tenths + 4 tenths = _________
i. 2 thousandths + 9 ones 5 thousandths = __________ 10
2. Solve using the standard algorithm. a. 0.3+ 0.82 = ____________
b. 1.03 + 0.08 = ___________
c. 7.3 + 2.8 = ____________
d. 57.03 + 2.08 = __________
e. 62.573 + 4.328 =
f. 85.703 + 12.197 =
____________
____________
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3. Van Cortlandt Park’s walking trail is 1.02 km longer than Marine Park. Central Park’s walking trail is 0.242 km longer than Van Cortlandt’s. a. Fill in the missing information in the chart below. New York City Walking Trails Central Park
________ km
Marine Park
1.28 km
Van Cortlandt Park
________ km
b. If a tourist walked all 3 trails in a day, how many km would they have walked? 4. Meyer has 0.64 GB of space remaining on his iPod. He wants to download a pedometer app (0.24 GB) a photo app (0.403 GB) and a math app (0.3 GB). Which combinations of apps can he download? Explain your thinking. 12
Lesson 9 Homework 1. Solve by writing the numbers in standard form first and then write your sum in standard form. a. 3 tenths + 4 tenths = ____________
b. 12 tenths + 9 tenths = ____________
c. 3 hundredths + 4 hundredths = ____________
d. 27 hundredths + 7 hundredths = ____________
e. 4 thousandth + 3 thousandths = ____________
f. 39 thousandths + 5 thousandths = _____________
g. 5 tenths + 7 thousandths = ____________
h. 4 ones 4 tenths + 4 tenths = ____________
i. 8 thousandths + 6 ones 8 thousandths = ____________ 13
2. Solve using the standard algorithm. a. 0.4 + 0.7 = ____________
b. 2.04 + 0.07 = ____________
c. 6.4 + 3.7 = ____________
d. 56.04 + 3.07 = ____________
e. 72.564 + 5.137 = __________
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f. 75.604 + 22.296 = _________
3. The walkway over the Hudson, a bridge that crosses the Hudson River in Poughkeepsie, is 2.063 kilometers. Anping Bridge, which was built in China 850 years ago, is 2.07 kilometers long. a. Which bridge is longer? How much longer? Show your thinking. b. Leah likes to walk her dog on the walkway over the Hudson. If she walks across and back, how far do she and her dog walk?
4. For his parents’ anniversary, Danny spends $5.87 on a photo. He also buys 3 balloons for $2.49 each and a box of strawberries for $4.50. How much money does he spend all together?
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Lesson 10 – Subtracting Decimals Round 357.89 to the nearest whole number
Round 367.894 to the nearest tenth
Write 5,256.32 in word form
Application Problem Lesson 10 At the 2012 London Olympics, Michael Phelps won the gold medal in the men’s 100 meter butterfly. He swam the first 50 meters in 26.96 seconds. The second 50 meters took him 25.39 seconds. What was his total time? 16
1. Subtract the following using the same method you used to add decimals. Write your final answer in standard form a) 5 tenths – 3 tenths b) 7 ones 5 thousandths – 2 ones 3 thousandths c) 9 hundreds 5 hundredths – 3 hundredths When you subtract decimals what must you make sure you do?
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2) Write the numbers in standard form and then subtract a) 83 tenths – 6.4 b) 9.2 – 6 ones 4 tenths c) 0.831 – 0.292 d) 4.003 – 1.29 e) 6 – 4.08
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Lesson 10 Problem Set 1. Subtract, writing the difference in standard form. a. 5 tenths – 2 tenths = _______
b. 5 ones 9 thousandths – 2 ones = _________
c. 7 hundreds 8 hundredths – 4 hundredths = _________
d. 37 thousandths – 16 thousandths = _________ 19
2. Solve using the standard algorithm. a. 1.4 – 0.7 = ______
b. 91.49 – 0.7 = ___
c. 191.49 – 10.72 = _
d. 7.148 – 0.07 = ___
e. 60.91 – 2.856 = _
f. 361.31 – 2.841 = _
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3. Mrs. Fan wrote 5 tenths minus 3 hundredths on the board. Michael said the answer is 2 tenths because 5 minus 3 is 2. Is he correct? Explain.
4. A pen costs $2.09. It costs $0.45 less than a marker. Ken paid for one pen and one marker with a five dollar bill. Use a tape diagram with calculations to determine his change.
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Lesson 10 Homework
1.
Subtract, writing the difference in standard form. a. 9 tenths – 3 tenths = ___________ b. 9 ones 2 thousandths – 3 ones = ___________ c. 4 hundreds 6 hundredths – 3 hundredths = ________ d. 56 thousandths – 23 thousandths = ________
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2.
Solve using the standard algorithm. a. 1.8 – 0.9 = _____
b. 41.84 – 0.9 = ___
c. 341.84 – 21.92 = _
d. 5.182 – 0.09 = __
e. 50.416 – 4.25 = _
f. 741. – 3.91 = ____
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3. Mr. House wrote 8 tenths minus 5 hundredths on the board. Maggie said the answer is 3 hundredths because 8 minus 5 is 3. Is she correct? Explain.
4. A clipboard costs $2.23. It costs $0.58 more than a notebook. Lisa buys two clipboards and one notebook, and paid with a ten dollar bill. Use a tape diagram with calculations to show her change
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Adding and Subtracting Decimals Practice – Topic D Review 1) 87 – 17.28
2) 32.58 + 5.635
38.215 3) 17. 3 – 5.09
4) 88.0 + 35.60
123.6 5) 65.04 - 50.414
6) 32. + 1.1
7) 47. - 1. 3
8) 80 + 29.6
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109.6 9) 66. - 38.3
10) 78.9 - 55.779
11) 73 + 48.7
12) 41.3 - 20.65
13) 46 + 39.5
14) 72 - 67.01
15) 65 + 56.8
16) 58 - 45.183
17) 79.3 + 10.21
18) 17 - 1.2
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19) 92 + 8.83
20) 67.15 - 24.302
21) 96 + 37.367
22) Jerry bought 6.95 lbs of cherry and lime jelly beans for his birthday party. If 1.75 lbs were cherry flavor, how many pounds were lime flavor
23) Paige was measuring how much taller she got over two years. In the first year she grew 4.62 cm. In the second year she grew 7.7 cm. How much taller did she get altogether?
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1) Vanessa downloaded two apps which were 17.73 kb total. If one app was 8.63 kb, how big was the other app?
2) Nancy was buying food for her birthday party. She bought a 52.93 oz bag of barbeque chips and a 79.6 oz bag of regular chips. How many ounces did she buy all together?
3) Tom was weighing the amount of candy he received for Halloween. If he received 8.30 kg and his brother received 1.8 kg, how much candy did they get all together?
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27) John ate a snack with 80.79 total calories. If the chips he ate were 43.39 calories, how many calories were in the rest of his snack?
28) A computer programmer had two files with a total size of 93 gigabytes. If one of the files was 50.30 gigabytes, how big is the second file?
29) A weatherman was measuring the amount of rain two cities received over a week. City A received 3.74 inches while City B received 9.8 inches. How much rain did they get total?
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30) During a science experiment, Mary found the mass of two rocks to be 41.4 grams and 74.3 grams. What is the total mass of these two rocks?
31) Ned and Sarah were running a relay race. The race was 22.01 kilometers total. If Ned ran 9.41 kilometers how far did Sarah run?
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Addition and Subtraction of Decimals Rewrite each problem and then add or subtract. a. 0.45 + 0.34 =
b. 1.06 + 2.32 =
c. 7.8 + 0.46 =
d. 2.54 + 10.8 =
e. 1.76 + 6.3 =
f. 2.865 + 93.71 =
g. 0.65 – 0.24 =
h. 1.24 – 0.17 =
i. 3.08 – 2.6 =
j. 3.62 – 1.9 =
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k. 2 + 3.9 =
l. 9 – 4.8
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Adding and Subtracting Decimals When adding and subtracting decimals, make sure that you always line the number up using the decimal so that the same place values are being added together. Rewrite the problem vertically and then solve. a)
0.25 + 0.4 =
b)
0.8 + 0.6 =
c)
0.6 + 0.26 =
d)
0.45 + 0.47 =
e)
0.67 + 1.09 =
f)
0.3 + 0.87 =
g)
1.47 + 0.03 =
h)
0.85 – 0.2 =
i)
1.3 – 0.95 =
j)
0.6 – 0.08 =
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Adding and Subtracting Decimals a)
0.124 + 2.33 =
b)
1.14 – 1.08 =
c)
3.1 + 0.13 =
d)
3.706 – 1.59 =
e) There are 15.1 servings in a box of popular cereal. How many servings are there in two boxes? Show your work.
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f) Andrew wants to buy a $5.00 binder for his notes. He has saved $3.60 so far. How much more money does Andrew need to save?
g) Emily and Amanda pooled their money to buy some snacks. They had $9.57 altogether. If Amanda gave $4.65, how much money did Emily give?
h)
42.34 + 87.9 =
i)
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1.79 - .99 =
Application Problem – After school, Marcus ran 3.2km and Cindy ran 1.95km. Who ran farther? How much farther? 36
Multiply Whole Numbers using the algorithm 1 Example 4 2 X 8 3 3 6 First Multiply the ones place (2 x 8) You get 16 so place the 6 in the ones place and carry the 1 on top of the 4 Then multiply the 8 times the 4 in the tens place You get 32 and then add the 1 that you carried from the 16 so you get 33 Solve using the algorithm A) 20 × 9
B) 58 x 3
C) 71 x 6
D) 61 x 7
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E) 76 x 5
F) 91 x 5
G) 78 x 8
H) 76 x 2
I) 75 x 2
J) 83 x 3
K) 18 x 5
L) 40 x 4
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M) 84 x 5
N) 13 x 2
O) 46 x 3
P) 20 x 3
Q) 81 × 4
R) 37 x 9
S) 52 x 9
T) 84 x 4
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A) 763 × 3
B) 440 x 3
C) 222 x 9
D) 721 x 2
E) 839 x 2
F) 234 x 8
G) 899 x 7
H) 637 x 6
I) 936 x 5
J) 442 x 7
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K) 135 x 8
L) 406 x 2
M) 830 x 3
N) 840 x 5
O) 405 x 2
P) 702 x 6
Q) 294 x 9
R) 302 x 2
S) 583 x 3
T) 400 x 7
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A) 57 x 7.1
B) 3.3 x 5.8
C) .97 x 45
D) 3.7 x .42
E) 7.7 x .56
F) 4.7 x 67
G) 74 x 9.9
H) .26 x 1.7
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Lesson 11 pt2 Multiplying Whole Numbers using the algorithm A) 27 x 39
B) 74 x 92
C) 13 x 52
D) 63 x 86
E) 64 x 90
F) 92 x 20
G) 73 x 60
H) 34 x 48
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I) 74 x 94
J) 78 x 10
K) 51 x 11
L) 97 x 60
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Lesson 11 pt 3 A) 164 x 39
B) 459 x 15
C) 224 x 92
D) 862 x 79
E) 261 x 76
F) 667 x 89
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G) 360 x 11
H) 631 x 43
I) 155 x 51
J) 165 x 73
K) 630 x 35
L) 927 x 86
M) 519 x 30
N) 527 x 33
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O) 808 x 54
P) 625 x 93
Q) 230 x 82
R) 630 x 38
S) 670 x 44
T) 401 x 44
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Lesson 11 Pt 4 Notes Multiplying with decimals
When multiplying decimals you multiply the numbers without the decimals. Then you count the number of digits in each of the factors. The product should have the same number of total digits in the decimal place as the factors.
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Multiplying Decimals A) 63.9 × 7
B) 44.8 × .84
C) 88 x 5.1
D) 7.9 x 4
E) 14.3 x .49
F) 80.1 x 2.8
49
G) 5.9 x 3.9
H) 5.6 x .62
Lesson 11 Pt 4 H.W. I) 63.1 x .42
J) 7.5 x 8
K) 325 x .78
L) 39.6 x 8
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Lesson 11 pt 5 56.7 + 25 =
36 - 27.4 =
Application Problem Louis buys 4 chocolates. Each chocolate costs $2.35. Louis multiplies 4 x 235 and gets 940. Place the decimal to show the cost of the chocolates.
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Divide Whole Numbers by 1 digit Divisors with or without Remainders D - Divide M – Multiply S - Subtract B – Bring Down C – Circle
44 ÷ 2 = 22
86 ÷ 2 = 43
27 ÷ 2 = 13
47 ÷ 5 = 9 r2
32 ÷ 3 =
61 ÷ 9 = 6
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31 ÷ 3 =
96 ÷ 2 =
20 ÷ 8 = 2
40 ÷ 6 =
98 ÷ 2 =
72 ÷ 2 =
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804 ÷ 7 =
695 ÷ 7 =
458 ÷ 7 =
393 ÷ 9 =
509 ÷ 6 =
622 ÷ 8 =
496 ÷ 9 =
680 ÷ 3 =
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869 ÷ 8 =
162 ÷ 8 =
438 ÷ 8 =
991 ÷ 2 =
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Lessons 14 and 15 – Division of Decimals Write 75.34 in word form and expanded form
68 x 32 =
Application Problem Lesson 14 A bag of potato chips contains 0.96 grams of sodium. If the bag is split into 8 equal servings, how many grams of sodium will each serving contain? 56
NOTES Dividing with
decimals
Dividing with decimals (rounding the answer).
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There can be no remainders when you divide decimals 6.72 ÷ 3 = ___ 5.16 ÷ 4 = ____________ 6.72 ÷ 4 = ________ 20.08 ÷ 8 = _________ 6.372 ÷ 6 = _________ 4.236 ÷ 3 = ______
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What is different with the following two division problems? 1.7 ÷ 2 2.6 ÷ 4 Solve the division problems 17 ÷ 4 22 ÷ 8 7.7 ÷ 4 0.84 ÷ 4 59
1.324 ÷ 2 = ______ 7.28 ÷ 4 = ______
0.78 ÷ 3 =
17.45 ÷ 5 = _____
5.7 ÷ 4 = _______
0.5 ÷ 2 = _______ 60
0.9 ÷ 2 =
9.1 ÷ 5=
0.98 ÷ 4 =
91 ÷ 4 =
9 ÷ 6 = 9.3 ÷ 6 =
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Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals. How much netting did she use per goal?
Esperanza usually buys avocados for $0.94 apiece. During a sale, she gets 5 avocados for $4.10. How much money did she save per avocado? Use a tape diagram and show your calculations. Six bakers shared 7.5 kg of flour equally. How much flour did they each receive?
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Mrs. Henderson makes punch by mixing 10.9 liters of apple juice, 600 milliliters of orange juice, and 8 liters of ginger ale. She pours the mixture equally into 6 large punch bowls. How much punch is in each bowl? Express your answer in liters.
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Homework Lessons 14 and 15 Solve 5.241 ÷ 3 = _______ 0.64 ÷ 4 =
3.445 ÷ 5 = _______
6.45 ÷ 5 = _____
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16.404 ÷ 6 =
0.7 ÷ 4 = _______
8.1 ÷ 5 = _______
0.7 ÷ 2 =
9 ÷ 4 =
3.9 ÷ 6 =
65
0.92 ÷ 2 =
9.4 ÷ 4 =
91 ÷ 8 = Mrs. Mayuko paid $40.68 for 3 kg of shrimp. What’s the cost of 1 kg of shrimp?
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Lesson 14 & 15 Pt 2 The total weight of 6 pieces of butter and a bag of sugar is 3.8 lb. If the weight of the bag of sugar is 1.4 lb., what’s the weight of each piece of butter? A rope 8.7 m long is cut into 5 equal pieces. How long is each piece? Yasmine bought 6 gallons of apple juice. After filling up 4 bottles of the same size with apple juice, she had 0.3 gallon of apple juice left. What’s the amount of apple juice in each bottle?
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Word Problems 1) Mr. Frye distributed $126 equally among his 4 children for their weekly allowance. How much money did each child receive? 2) Brandon mixed 6.83 lbs. of cashews with 3.57 lbs. of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.35 lbs. of nuts left. What was the weight of each bag? 3) Ava is 23 cm taller than Olivia, and Olivia is half the height of Lucas. If Lucas is 1.78 m tall, how tall are Ava and Olivia? Express their heights in centimeters. 68
4) Mr. Hower can buy a computer with a down payment of $510 and 8 monthly payments of $35.75. If he pays cash for the computer, the cost is $699.99. How much money will he save if he pays cash for the computer instead of paying for it in monthly payments? 5) The bakery bought 4 bags of flour containing 3.5 kg each. 475 g of flour are needed to make a batch of muffins and 0.65 kg is needed to make a loaf of bread. a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms. b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.
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Decimal Division
392.58 ÷ 9 =
1404 ÷ 6 =
31.77 ÷ 5 =
347.9 ÷ 7 =
1404.9 ÷ 3 =
217.04 ÷ 4 =
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Lesson 14 & 15 pt 2 H.W.
122.76 ÷ 2 =
392.44 ÷ 4 =
195.2 ÷ 8 =
748.2 ÷ 6 =
You and three of your friends spend Saturday morning running the bake school at the school basketball tournament. After the bake sale there were 94 cupcakes that just didn’t sell so you and your friends decide to split them evenly. How many cupcakes will you each get?
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Module 1 – Topics E and F Review Find the product 1. 5 x .7 =
2.
2 × 8.52 =
Find the quotient 3.
2.4 ÷ 8 =
4.
0.36 ÷ 9 =
5.
0.028 ÷ 4 =
6.
3.5 ÷ 7 =
72
7.
8.16 ÷ 8 =
Solve using long division 8. 6.484 ÷ 2 = _______ 9. 0.132 ÷ 5 = _______
10.
0.7 ÷ 4 = _______
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At the end of Module 1 you should be able to do the following:
Add decimals using place value strategies and relate those strategies to a written method. Subtract decimals using place value strategies and relate those strategies to a written method. Multiply a decimal fraction by a single digit whole number, relate to a written method through application of the area model and place value understanding and explain the reasoning used. Multiply a decimal fraction by single‐digit whole numbers, including using estimation to confirm the placement of the decimal point. Divide decimals by single‐digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. Divide decimals with a remainder. Solve word problems using decimal operations. 74
End of Module Review 1)
7.782 x 10 =
2)
465.84 ÷ 1000 =
3)
Write a multiplication sentence that is equivalent to 10000 using 10’s.
4)
What is the standard form of 7.65 x 103
5)
Convert 7 meters to centimeters
6)
Convert 500 milliliters to liters
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7)
What is four thousandths as a decimal?
8)
What is 89.65 in words?
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9)
What is the expanded form of 89.65 using decimals?
10)
What is the expanded form of 89.65 using fractions?
11)
Compare 854.65 to 854.56
12)
Which lists (there may be more than one) is in ascending order (Least to Greatest)? a) 75.3, 75.2, 78.1 b) 78.1, 79.5, 76.3 c) 950.2, 950.02, 950.002 d) 9.3, 9.02, 9.32
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13)
Round 8.43 to the nearest tenth.
14)
Round 78.383 to the nearest hundredth.
15)
Solve. 8.76 + 5.7
16)
Solve. 5.4 – 0.6
78
17)
Write a word problem for the problem 9.18 ÷ 3?
18)
Write the number sentence using unit form: 4.05 ÷ 5 =
19)
Solve. 8.32 ÷ 4
79
Name _________________________ Class Code __________ 1
Numbers in Words 1 – one 2 – two 3 – three 4 – four 5 – five 6 – six 7 – seven 8 – eight 9 – nine 10 – ten 11 – eleven 12 – twelve 13 – thirteen 14 – fourteen
15 – fifteen 16 – sixteen 17 – seventeen 18 – eighteen 19 – nineteen 20 – twenty 30 – thirty 40 – forty 50 – fifty 60 – sixty 70 – seventy 80 – eighty 90 – ninety
100 – hundred 1,000 – thousand 1,000,000 – million .1 – tenth .01 – hundredth .001 – thousandth .0001 – ten thousandth $ - Dollars ¢ - Cents
2
Vocabulary Sum – The answer to an addition problem. Difference – The answer to a subtraction problem. Factors – The numbers you multiply together in a multiplication sentence. 5 x 6 = 30 Factor Factor Product – The answer to a multiplication problem. 5 x 6 = 30 Product Divisor – The amount that another amount is divided by. 30 ÷ 5 = 6 Divisor Dividend – The amount being split up in a division problem. 30 ÷ 5 = 6 Dividend Quotient – The answer to a division problem 30 ÷ 5 = 6 Quotient Remainder – The amount left over in whole number division
3
4
NOTES
If you line up the decimal points it helps you to line up the place values. Remember to put a zero in the empty spaces to help you add and subtract.
5
Adding Decimals Lesson 9 Application Problem 6,455 + 7,822 = 7,000 – 4,322 = Ten baseballs weigh 1,417.4 grams. About how much does 1 baseball weigh? Round your answer to the nearest tenth of a gram. Round your answer to the nearest gram.
6
7
Write the numbers in standard form 2 tenths + 6 tenths Now add vertically lining the numbers up by their place value. Write the numbers in standard form 2 ones 3 thousandths + 6 ones 1 thousandth Now add vertically lining the numbers up by their place value. Add using the same procedure 2 tenths 5 thousandths + 6 hundredths Write the answer in standard form 1.8 + 13 tenths 8
Write in standard form and then add. Make sure you line up your decimals in order to line up your place values a) 1 hundred 8 hundredths + 2 ones 4 hundredths b) 148 thousandths + 7 ones 13 thousandths
c) 0.74 + 0.59 d) 7.048 + 5.196 e) 7.44 + 0.774
9
Lesson 9 Problem Set 1. Solve by writing the numbers in standard form first and then write your sum in standard form.
a. 1 tenth + 2 tenths = ___________
b. 14 tenths + 9 tenths = ___________
c. 1 hundredth + 2 hundredths = ___________
d. 27 hundredths + 5 hundredths = ___________
e. 1 thousandth + 2 thousandths = ___________
f. 35 thousandths + 8 thousandths = __________
g. 6 tenths + 3 thousandths = _________
h. 7 ones 2 tenths + 4 tenths = _________
i. 2 thousandths + 9 ones 5 thousandths = __________ 10
2. Solve using the standard algorithm. a. 0.3+ 0.82 = ____________
b. 1.03 + 0.08 = ___________
c. 7.3 + 2.8 = ____________
d. 57.03 + 2.08 = __________
e. 62.573 + 4.328 =
f. 85.703 + 12.197 =
____________
____________
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3. Van Cortlandt Park’s walking trail is 1.02 km longer than Marine Park. Central Park’s walking trail is 0.242 km longer than Van Cortlandt’s. a. Fill in the missing information in the chart below. New York City Walking Trails Central Park
________ km
Marine Park
1.28 km
Van Cortlandt Park
________ km
b. If a tourist walked all 3 trails in a day, how many km would they have walked? 4. Meyer has 0.64 GB of space remaining on his iPod. He wants to download a pedometer app (0.24 GB) a photo app (0.403 GB) and a math app (0.3 GB). Which combinations of apps can he download? Explain your thinking. 12
Lesson 9 Homework 1. Solve by writing the numbers in standard form first and then write your sum in standard form. a. 3 tenths + 4 tenths = ____________
b. 12 tenths + 9 tenths = ____________
c. 3 hundredths + 4 hundredths = ____________
d. 27 hundredths + 7 hundredths = ____________
e. 4 thousandth + 3 thousandths = ____________
f. 39 thousandths + 5 thousandths = _____________
g. 5 tenths + 7 thousandths = ____________
h. 4 ones 4 tenths + 4 tenths = ____________
i. 8 thousandths + 6 ones 8 thousandths = ____________ 13
2. Solve using the standard algorithm. a. 0.4 + 0.7 = ____________
b. 2.04 + 0.07 = ____________
c. 6.4 + 3.7 = ____________
d. 56.04 + 3.07 = ____________
e. 72.564 + 5.137 = __________
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f. 75.604 + 22.296 = _________
3. The walkway over the Hudson, a bridge that crosses the Hudson River in Poughkeepsie, is 2.063 kilometers. Anping Bridge, which was built in China 850 years ago, is 2.07 kilometers long. a. Which bridge is longer? How much longer? Show your thinking. b. Leah likes to walk her dog on the walkway over the Hudson. If she walks across and back, how far do she and her dog walk?
4. For his parents’ anniversary, Danny spends $5.87 on a photo. He also buys 3 balloons for $2.49 each and a box of strawberries for $4.50. How much money does he spend all together?
15
Lesson 10 – Subtracting Decimals Round 357.89 to the nearest whole number
Round 367.894 to the nearest tenth
Write 5,256.32 in word form
Application Problem Lesson 10 At the 2012 London Olympics, Michael Phelps won the gold medal in the men’s 100 meter butterfly. He swam the first 50 meters in 26.96 seconds. The second 50 meters took him 25.39 seconds. What was his total time? 16
1. Subtract the following using the same method you used to add decimals. Write your final answer in standard form a) 5 tenths – 3 tenths b) 7 ones 5 thousandths – 2 ones 3 thousandths c) 9 hundreds 5 hundredths – 3 hundredths When you subtract decimals what must you make sure you do?
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2) Write the numbers in standard form and then subtract a) 83 tenths – 6.4 b) 9.2 – 6 ones 4 tenths c) 0.831 – 0.292 d) 4.003 – 1.29 e) 6 – 4.08
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Lesson 10 Problem Set 1. Subtract, writing the difference in standard form. a. 5 tenths – 2 tenths = _______
b. 5 ones 9 thousandths – 2 ones = _________
c. 7 hundreds 8 hundredths – 4 hundredths = _________
d. 37 thousandths – 16 thousandths = _________ 19
2. Solve using the standard algorithm. a. 1.4 – 0.7 = ______
b. 91.49 – 0.7 = ___
c. 191.49 – 10.72 = _
d. 7.148 – 0.07 = ___
e. 60.91 – 2.856 = _
f. 361.31 – 2.841 = _
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3. Mrs. Fan wrote 5 tenths minus 3 hundredths on the board. Michael said the answer is 2 tenths because 5 minus 3 is 2. Is he correct? Explain.
4. A pen costs $2.09. It costs $0.45 less than a marker. Ken paid for one pen and one marker with a five dollar bill. Use a tape diagram with calculations to determine his change.
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Lesson 10 Homework
1.
Subtract, writing the difference in standard form. a. 9 tenths – 3 tenths = ___________ b. 9 ones 2 thousandths – 3 ones = ___________ c. 4 hundreds 6 hundredths – 3 hundredths = ________ d. 56 thousandths – 23 thousandths = ________
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2.
Solve using the standard algorithm. a. 1.8 – 0.9 = _____
b. 41.84 – 0.9 = ___
c. 341.84 – 21.92 = _
d. 5.182 – 0.09 = __
e. 50.416 – 4.25 = _
f. 741. – 3.91 = ____
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3. Mr. House wrote 8 tenths minus 5 hundredths on the board. Maggie said the answer is 3 hundredths because 8 minus 5 is 3. Is she correct? Explain.
4. A clipboard costs $2.23. It costs $0.58 more than a notebook. Lisa buys two clipboards and one notebook, and paid with a ten dollar bill. Use a tape diagram with calculations to show her change
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Adding and Subtracting Decimals Practice – Topic D Review 1) 87 – 17.28
2) 32.58 + 5.635
38.215 3) 17. 3 – 5.09
4) 88.0 + 35.60
123.6 5) 65.04 - 50.414
6) 32. + 1.1
7) 47. - 1. 3
8) 80 + 29.6
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109.6 9) 66. - 38.3
10) 78.9 - 55.779
11) 73 + 48.7
12) 41.3 - 20.65
13) 46 + 39.5
14) 72 - 67.01
15) 65 + 56.8
16) 58 - 45.183
17) 79.3 + 10.21
18) 17 - 1.2
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19) 92 + 8.83
20) 67.15 - 24.302
21) 96 + 37.367
22) Jerry bought 6.95 lbs of cherry and lime jelly beans for his birthday party. If 1.75 lbs were cherry flavor, how many pounds were lime flavor
23) Paige was measuring how much taller she got over two years. In the first year she grew 4.62 cm. In the second year she grew 7.7 cm. How much taller did she get altogether?
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1) Vanessa downloaded two apps which were 17.73 kb total. If one app was 8.63 kb, how big was the other app?
2) Nancy was buying food for her birthday party. She bought a 52.93 oz bag of barbeque chips and a 79.6 oz bag of regular chips. How many ounces did she buy all together?
3) Tom was weighing the amount of candy he received for Halloween. If he received 8.30 kg and his brother received 1.8 kg, how much candy did they get all together?
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27) John ate a snack with 80.79 total calories. If the chips he ate were 43.39 calories, how many calories were in the rest of his snack?
28) A computer programmer had two files with a total size of 93 gigabytes. If one of the files was 50.30 gigabytes, how big is the second file?
29) A weatherman was measuring the amount of rain two cities received over a week. City A received 3.74 inches while City B received 9.8 inches. How much rain did they get total?
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30) During a science experiment, Mary found the mass of two rocks to be 41.4 grams and 74.3 grams. What is the total mass of these two rocks?
31) Ned and Sarah were running a relay race. The race was 22.01 kilometers total. If Ned ran 9.41 kilometers how far did Sarah run?
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Addition and Subtraction of Decimals Rewrite each problem and then add or subtract. a. 0.45 + 0.34 =
b. 1.06 + 2.32 =
c. 7.8 + 0.46 =
d. 2.54 + 10.8 =
e. 1.76 + 6.3 =
f. 2.865 + 93.71 =
g. 0.65 – 0.24 =
h. 1.24 – 0.17 =
i. 3.08 – 2.6 =
j. 3.62 – 1.9 =
31
k. 2 + 3.9 =
l. 9 – 4.8
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Adding and Subtracting Decimals When adding and subtracting decimals, make sure that you always line the number up using the decimal so that the same place values are being added together. Rewrite the problem vertically and then solve. a)
0.25 + 0.4 =
b)
0.8 + 0.6 =
c)
0.6 + 0.26 =
d)
0.45 + 0.47 =
e)
0.67 + 1.09 =
f)
0.3 + 0.87 =
g)
1.47 + 0.03 =
h)
0.85 – 0.2 =
i)
1.3 – 0.95 =
j)
0.6 – 0.08 =
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Adding and Subtracting Decimals a)
0.124 + 2.33 =
b)
1.14 – 1.08 =
c)
3.1 + 0.13 =
d)
3.706 – 1.59 =
e) There are 15.1 servings in a box of popular cereal. How many servings are there in two boxes? Show your work.
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f) Andrew wants to buy a $5.00 binder for his notes. He has saved $3.60 so far. How much more money does Andrew need to save?
g) Emily and Amanda pooled their money to buy some snacks. They had $9.57 altogether. If Amanda gave $4.65, how much money did Emily give?
h)
42.34 + 87.9 =
i)
35
1.79 - .99 =
Application Problem – After school, Marcus ran 3.2km and Cindy ran 1.95km. Who ran farther? How much farther? 36
Multiply Whole Numbers using the algorithm 1 Example 4 2 X 8 3 3 6 First Multiply the ones place (2 x 8) You get 16 so place the 6 in the ones place and carry the 1 on top of the 4 Then multiply the 8 times the 4 in the tens place You get 32 and then add the 1 that you carried from the 16 so you get 33 Solve using the algorithm A) 20 × 9
B) 58 x 3
C) 71 x 6
D) 61 x 7
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E) 76 x 5
F) 91 x 5
G) 78 x 8
H) 76 x 2
I) 75 x 2
J) 83 x 3
K) 18 x 5
L) 40 x 4
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M) 84 x 5
N) 13 x 2
O) 46 x 3
P) 20 x 3
Q) 81 × 4
R) 37 x 9
S) 52 x 9
T) 84 x 4
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A) 763 × 3
B) 440 x 3
C) 222 x 9
D) 721 x 2
E) 839 x 2
F) 234 x 8
G) 899 x 7
H) 637 x 6
I) 936 x 5
J) 442 x 7
40
K) 135 x 8
L) 406 x 2
M) 830 x 3
N) 840 x 5
O) 405 x 2
P) 702 x 6
Q) 294 x 9
R) 302 x 2
S) 583 x 3
T) 400 x 7
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A) 57 x 7.1
B) 3.3 x 5.8
C) .97 x 45
D) 3.7 x .42
E) 7.7 x .56
F) 4.7 x 67
G) 74 x 9.9
H) .26 x 1.7
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Lesson 11 pt2 Multiplying Whole Numbers using the algorithm A) 27 x 39
B) 74 x 92
C) 13 x 52
D) 63 x 86
E) 64 x 90
F) 92 x 20
G) 73 x 60
H) 34 x 48
43
I) 74 x 94
J) 78 x 10
K) 51 x 11
L) 97 x 60
44
Lesson 11 pt 3 A) 164 x 39
B) 459 x 15
C) 224 x 92
D) 862 x 79
E) 261 x 76
F) 667 x 89
45
G) 360 x 11
H) 631 x 43
I) 155 x 51
J) 165 x 73
K) 630 x 35
L) 927 x 86
M) 519 x 30
N) 527 x 33
46
O) 808 x 54
P) 625 x 93
Q) 230 x 82
R) 630 x 38
S) 670 x 44
T) 401 x 44
47
Lesson 11 Pt 4 Notes Multiplying with decimals
When multiplying decimals you multiply the numbers without the decimals. Then you count the number of digits in each of the factors. The product should have the same number of total digits in the decimal place as the factors.
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Multiplying Decimals A) 63.9 × 7
B) 44.8 × .84
C) 88 x 5.1
D) 7.9 x 4
E) 14.3 x .49
F) 80.1 x 2.8
49
G) 5.9 x 3.9
H) 5.6 x .62
Lesson 11 Pt 4 H.W. I) 63.1 x .42
J) 7.5 x 8
K) 325 x .78
L) 39.6 x 8
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Lesson 11 pt 5 56.7 + 25 =
36 - 27.4 =
Application Problem Louis buys 4 chocolates. Each chocolate costs $2.35. Louis multiplies 4 x 235 and gets 940. Place the decimal to show the cost of the chocolates.
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Divide Whole Numbers by 1 digit Divisors with or without Remainders D - Divide M – Multiply S - Subtract B – Bring Down C – Circle
44 ÷ 2 = 22
86 ÷ 2 = 43
27 ÷ 2 = 13
47 ÷ 5 = 9 r2
32 ÷ 3 =
61 ÷ 9 = 6
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31 ÷ 3 =
96 ÷ 2 =
20 ÷ 8 = 2
40 ÷ 6 =
98 ÷ 2 =
72 ÷ 2 =
53
804 ÷ 7 =
695 ÷ 7 =
458 ÷ 7 =
393 ÷ 9 =
509 ÷ 6 =
622 ÷ 8 =
496 ÷ 9 =
680 ÷ 3 =
54
869 ÷ 8 =
162 ÷ 8 =
438 ÷ 8 =
991 ÷ 2 =
55
Lessons 14 and 15 – Division of Decimals Write 75.34 in word form and expanded form
68 x 32 =
Application Problem Lesson 14 A bag of potato chips contains 0.96 grams of sodium. If the bag is split into 8 equal servings, how many grams of sodium will each serving contain? 56
NOTES Dividing with
decimals
Dividing with decimals (rounding the answer).
57
There can be no remainders when you divide decimals 6.72 ÷ 3 = ___ 5.16 ÷ 4 = ____________ 6.72 ÷ 4 = ________ 20.08 ÷ 8 = _________ 6.372 ÷ 6 = _________ 4.236 ÷ 3 = ______
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What is different with the following two division problems? 1.7 ÷ 2 2.6 ÷ 4 Solve the division problems 17 ÷ 4 22 ÷ 8 7.7 ÷ 4 0.84 ÷ 4 59
1.324 ÷ 2 = ______ 7.28 ÷ 4 = ______
0.78 ÷ 3 =
17.45 ÷ 5 = _____
5.7 ÷ 4 = _______
0.5 ÷ 2 = _______ 60
0.9 ÷ 2 =
9.1 ÷ 5=
0.98 ÷ 4 =
91 ÷ 4 =
9 ÷ 6 = 9.3 ÷ 6 =
61
Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals. How much netting did she use per goal?
Esperanza usually buys avocados for $0.94 apiece. During a sale, she gets 5 avocados for $4.10. How much money did she save per avocado? Use a tape diagram and show your calculations. Six bakers shared 7.5 kg of flour equally. How much flour did they each receive?
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Mrs. Henderson makes punch by mixing 10.9 liters of apple juice, 600 milliliters of orange juice, and 8 liters of ginger ale. She pours the mixture equally into 6 large punch bowls. How much punch is in each bowl? Express your answer in liters.
63
Homework Lessons 14 and 15 Solve 5.241 ÷ 3 = _______ 0.64 ÷ 4 =
3.445 ÷ 5 = _______
6.45 ÷ 5 = _____
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16.404 ÷ 6 =
0.7 ÷ 4 = _______
8.1 ÷ 5 = _______
0.7 ÷ 2 =
9 ÷ 4 =
3.9 ÷ 6 =
65
0.92 ÷ 2 =
9.4 ÷ 4 =
91 ÷ 8 = Mrs. Mayuko paid $40.68 for 3 kg of shrimp. What’s the cost of 1 kg of shrimp?
66
Lesson 14 & 15 Pt 2 The total weight of 6 pieces of butter and a bag of sugar is 3.8 lb. If the weight of the bag of sugar is 1.4 lb., what’s the weight of each piece of butter? A rope 8.7 m long is cut into 5 equal pieces. How long is each piece? Yasmine bought 6 gallons of apple juice. After filling up 4 bottles of the same size with apple juice, she had 0.3 gallon of apple juice left. What’s the amount of apple juice in each bottle?
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Word Problems 1) Mr. Frye distributed $126 equally among his 4 children for their weekly allowance. How much money did each child receive? 2) Brandon mixed 6.83 lbs. of cashews with 3.57 lbs. of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.35 lbs. of nuts left. What was the weight of each bag? 3) Ava is 23 cm taller than Olivia, and Olivia is half the height of Lucas. If Lucas is 1.78 m tall, how tall are Ava and Olivia? Express their heights in centimeters. 68
4) Mr. Hower can buy a computer with a down payment of $510 and 8 monthly payments of $35.75. If he pays cash for the computer, the cost is $699.99. How much money will he save if he pays cash for the computer instead of paying for it in monthly payments? 5) The bakery bought 4 bags of flour containing 3.5 kg each. 475 g of flour are needed to make a batch of muffins and 0.65 kg is needed to make a loaf of bread. a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms. b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.
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Decimal Division
392.58 ÷ 9 =
1404 ÷ 6 =
31.77 ÷ 5 =
347.9 ÷ 7 =
1404.9 ÷ 3 =
217.04 ÷ 4 =
70
Lesson 14 & 15 pt 2 H.W.
122.76 ÷ 2 =
392.44 ÷ 4 =
195.2 ÷ 8 =
748.2 ÷ 6 =
You and three of your friends spend Saturday morning running the bake school at the school basketball tournament. After the bake sale there were 94 cupcakes that just didn’t sell so you and your friends decide to split them evenly. How many cupcakes will you each get?
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Module 1 – Topics E and F Review Find the product 1. 5 x .7 =
2.
2 × 8.52 =
Find the quotient 3.
2.4 ÷ 8 =
4.
0.36 ÷ 9 =
5.
0.028 ÷ 4 =
6.
3.5 ÷ 7 =
72
7.
8.16 ÷ 8 =
Solve using long division 8. 6.484 ÷ 2 = _______ 9. 0.132 ÷ 5 = _______
10.
0.7 ÷ 4 = _______
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At the end of Module 1 you should be able to do the following:
Add decimals using place value strategies and relate those strategies to a written method. Subtract decimals using place value strategies and relate those strategies to a written method. Multiply a decimal fraction by a single digit whole number, relate to a written method through application of the area model and place value understanding and explain the reasoning used. Multiply a decimal fraction by single‐digit whole numbers, including using estimation to confirm the placement of the decimal point. Divide decimals by single‐digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. Divide decimals with a remainder. Solve word problems using decimal operations. 74
End of Module Review 1)
7.782 x 10 =
2)
465.84 ÷ 1000 =
3)
Write a multiplication sentence that is equivalent to 10000 using 10’s.
4)
What is the standard form of 7.65 x 103
5)
Convert 7 meters to centimeters
6)
Convert 500 milliliters to liters
75
7)
What is four thousandths as a decimal?
8)
What is 89.65 in words?
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9)
What is the expanded form of 89.65 using decimals?
10)
What is the expanded form of 89.65 using fractions?
11)
Compare 854.65 to 854.56
12)
Which lists (there may be more than one) is in ascending order (Least to Greatest)? a) 75.3, 75.2, 78.1 b) 78.1, 79.5, 76.3 c) 950.2, 950.02, 950.002 d) 9.3, 9.02, 9.32
77
13)
Round 8.43 to the nearest tenth.
14)
Round 78.383 to the nearest hundredth.
15)
Solve. 8.76 + 5.7
16)
Solve. 5.4 – 0.6
78
17)
Write a word problem for the problem 9.18 ÷ 3?
18)
Write the number sentence using unit form: 4.05 ÷ 5 =
19)
Solve. 8.32 ÷ 4
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