Extra Practiceblm 1.1

Name: ______Date: ______

Extra PracticeBLM 1.1

1.1 Understand Exponents

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1.Identify the base and the exponent of each power.

a)54______

b)93______

c)75______

2.Write the number each diagram represents as a power and in words.

a)b)

______

3.Write in exponential form, then evaluate.

a)6  6  6  6

______

b)3  3  3  3  3

______

c)7  7  7  7  7  7  7

______

4.Write each number in expanded form using exponents.

a)16 936.03

______

b)258.009

______

c)1 251 010

______

5.Write each power in exponential form using the indicated base.

a)256 as a power of 4______

b)243 as a power of 3______

c)169 as a power of 13______

6.Does 45 equal 4  5? Explain.

______

7.Express each number as a power of 3, as a power of 9, and as a power of 27. Show your work.

a)729 = ______

b)531 441 = ______

8.For each sequence of numbers:

i) 4, 16, 64, 256, … ii) 1, 4, 9, 16, …

a)Describe the pattern.

______

b)Write the next five numbers or terms.

______

c)Rewrite each term in the sequence using powers.

______

9.A backyard is square with a side length of 6m. A roll of sod is 35 cm wide and 4m long.

a)What is the area of the yard?

______

b)How many rolls of sod are needed to cover the yard?

______

10.Use patterning to find the last digit in 915.

______

Extra PracticeBLM 1.2

1.2 Scientific Notation

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1.Write each number in scientific notation.

a)479 000______

b)377 000 000______

c)723  102______

d)67.3  105______

2.Write each number in standard form.

a)3.09  103______

b)4.67  105______

c)1.999  106______

d)7.042  104______

3.Express each value in scientific notation.

a)Mount Everest is approximately 8848 m above sea level.

______

b)The diameter of an atom is about
0.000 000 01 cm.

______

c)The population of China in 2005 was about 1 313 973 713.

______

d)In 2004, there were about 14 984 000 cell phones in Canada.

______

4.Write each number in standard form.

a)In 2005, the total Canadian public debt was approximately $775 billion.

______

b)More than 400 thousand deaths in the U.S. each year are from smoking-related illnesses.

______

c)In 2005, there were 20.9 million Internet users in Canada.

______

5.Mr. Steiner’s herd of 413 sheep consumes 79 kg of grass per day. How much grass is needed to feed the herd for one year? Express your answer in scientific notation.

______

6.Write a number that is ten times larger than each number.

a)2.9  107

______

b)1.199  103

______

c)7.6  1011

______

d)6.7  1021

______

7.Explain why 32.1  106 and 3.21  107 represent the same number. Which form scientific notation? How can you tell?

______

8.Assume that one drop of water has a volume of 1 mL. How many drops of water could fill a bathtub measuring 250cm long, 110 cm wide, and 60 cm high? Express your answer in scientific notation.
(Hint: 1 mL = 1 cm3)

______

Extra Practice BLM 1.3

1.3 Divisibility Rules

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1.Are these numbers divisible by:

• 3? • 4? • 6? • 9?

Explain how you know.

a)2589

______

b)614 892

______

c)12 195

______

2.Fill in the missing digit to make each number divisible by 6. Is there more than one correct answer?

a)12___6b)777___12

c)8___70d)151 43___

e)16___2 232f)1 253 24___

______

3.Fill in the missing digit to make each number divisible by 9.

a)2___22b)1___72

c)78 9___4d)56___1

e)981___0 121f)1 3___4999

4.Determine if the following statements are true or false. Explain your reasoning.

a)All even numbers are divisible by 4.

______

b)All numbers divisible by 9 are also divisible by 3.

______

c)All numbers divisible by 16 are also divisible by 2 and 4.

______

d)All numbers divisible by 3 are also divisible by 9.

______

5.112 students are divided into groups of six for a floor hockey tournament. How does the coach know there will be extra students?

______

6.Find two numbers in the thousands that are divisible by 2, 3, 4, 6, and 9.

______

7.Four friends won 2780 jellybeans. Can each person get an equal share? How many jellybeans will each person get?

______

8.Trevor is building a 3 m by 8 m stone walkway. Each stone is 50 cm by 70 cm. Can he build it without any waste?

______

9.Use the divisibility rules to determine if the following numbers are prime.

a)7 259 254 187______

Extra Practice BLM 1.4

1.4 Factors and Multiples

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1.Find the LCM by using prime factorization.

a)16, 28______

b)45, 75______

c)26, 39______

d)8, 50______

2.List the first four common factors of each set of numbers.

a)4, 9, 12______

b)2, 5, 10______

c)2, 3, 12______

d)5, 6, 12______

3.Find the GCF by listing the factors.

a)16, 36______

b)75, 175______

c)13, 24, 68______

d)12, 36, 48______

4.Three numbers have a GCF of 7. One of the numbers is 49. What could the other two numbers be?

______

5.Aleem started his factor tree for 72 with 3 and 24. Karen started her factor tree for 72 with 9 and 8. Karen says that the prime factors will be different because they started with different numbers. Aleem disagrees. Who is correct? Why?

______

6.Three numbers have a LCM of 36. One of the numbers is 12. What could the other two numbers be? Is there more than one solution?

______

7.Gary visits his maternal grandparents in Halifax every four months. He visits his paternal grandparents in Charlottetown every three months. In how many months of the year does he visit both sets of grandparents?

______

8.Jennifer and Todd are part-time tutors at their local high school. Todd works every third day. Jennifer works every fifth day. The tutorial centre is open seven days a week. When will they work together?

______

9. At the opening of a new restaurant, every 8th customer will get a free drink, every 12th customer will get a free Extra Practice BLM 1.5

1.5 Order of Operations

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name ______Date ______

1.Evaluate each expression.

a)7  2 + 3  9 = ______

b)5 – 9  3 + 9 = ______

c)2 + (9 + 3)  3 = ______

d)(3.4 + 3.8)  (4.5 – 2.1) = ______

2.Answer this challenge question.

4 + 8  (9 – 1) – 24  12 = ?

Show all your steps.

______

3.Identify which operation must be done first. Then evaluate each expression.

a)(2 + 5) – 4  2  4______

b)2 + 5 – 4  2  4______

c)2 + 5(4  2  4)______

d)2 + 5(4  2)  4______

4.Add brackets to make each equation true.

a)3  8 + 4  2 – 12 = 6

b)3  72 + 2 – 100 = 49

c)4  2 + 32 – 19 = 16

d)22  6 + 1 + 22 + 5 = 7

5.Fill in an operation (+, –, , or ) to make each statement true.

a)32 ___ 9 + 7 = 25

b)(6 ___ 2)11 – 3 ___ 2 = 32

c)4 + [(6 ___ 2) ___ 2] ___ 9 = 0

d)9 ___ (12 – 1) ___ 5 = 15

6.Find an expression that shows the total cost of seven items at $12 and two items at $9. What is the total cost?

______

7.One week, Sue worked three 5 h shifts and two 7 h shifts. She earns $9.15/h.

a)Write an expression for her earnings for the week. How much money did she earn in total?

______

b)The next week, she worked two 4.5 h shifts and one 8 h shift. How much did she earn the second week?

______

c)How much more did Sue earn the first week than the second?

______

8.Brad drove for 5 h at 80 km/h and 6 h at 100 km/h. Write an expression to represent his total distance travelled. Calculate this distance.

______

9.Mike calculated the following expression.

3 + (5 + 3  42 – 40) + 1

= 3 + (5 + 122 – 40) + 1

= 3 + (5 + 144 – 40) + 1

= 3 + 5 + 104 + 1

= 3 + 109 + 1

= 112 + 1

= 113

His answer of 113 is incorrect. What did Mike do wrong? Correct Mike’s mistakes.

______

desert, and every 20th customer will get a free meal. Which customer will be the first to get all three prizes?

______

10.What pair of numbers are we?

• Our GCF is 8.

• Our LCM is 224.

• We are both even numbers.

• We are both two-digit numbers.

______

Chapter 1 Extra Practice Answer Key

Get Ready

1. 16 cm2

2. 125 m3

3. a) 1 flat, 4 rods, 2 unit cubes b) 1 thousand cube, 9 rods, 9 unit cubes

4. a) six hundred seventy-one b) 63 020 c) two thousand, eight hundred ninety-one d) 396

5. a) 1, 2, 3, 4, 6, 8, 12, 24 b) 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

6. a) The units digit is not even. b) The units digit is not 0 or 5. c) The units digit is not 0.

7. Answers may vary. With subtraction and division, you are taking things away so the order of the numbers is important. 9 –5 = 4 but 5 – 9 = –4. With addition and multiplication, you are grouping things together, so it doesn't matter which number you start with. 5 + 4 = 4 + 5

8. a) 37 + (28 + 22); 87 b) (73 + 27) + 9; 109

9. Answers may vary. a) 3  20 + 3  4; 72 b) 7  10 + 7  4; 98

10. a) 13 and 26 b) 35 and 37 c) 13 and 12

1.1 Understand Exponents

1. a) base: 5, exponent: 4 b) base: 9, exponent: 3 c) base: 7, exponent: 5

2. a) 62;thirty-six b) 53; one hundred twenty-five

3. a) 64; 1296 b) 35; 243 c) 77; 823 543

4. a) 1  104 + 6  103 + 9  102 + 3  101 + 6  100 + 3 

b) 2  102 + 5  101 + 8  100 + 9 c) 1  106 + 2  105 + 5  104 + 1  103 + 1  101

5. a) 44b) 35c)132

6. No; 45= 4  4  4  4  4 = 1024, but 4  5 = 20.

7. a) 36, 93, 272b) 312, 96, 274

8. a) i) Each term is 4 times the previous term. ii) The base increases by 1 and the exponent is 2.b) i) 1024, 4096, 16 384, 65 536, 262144 ii) 25, 36, 49, 64, 81

c) i) 45, 46, 47, 48, 49ii) 52, 62, 72, 82, 92

9. a) 36 m2, b) 26

10. 9

1.2 Scientific Notation

1.a) 4.79  105b) 3.77  108c) 7.23  104d) 6.73  106

2. a) 3090 b) 467 000 c) 1 999 000 d) 70 420

3. a) 8.848  103 m b) 1.0  10–8 cm c) 1.314  109d) 1.4984  107

4. a) $775 000 000 000 b) 400 000 c) 20 900 000

5. 2.8835  104g

6. a) 2.9  108b) 1.199  104c) 7.6  1012d) 6.7  1022

7. In standard form, both numbers equal 32 100 000; 3.21  107is in scientific notation since the first factor is at least 1 and less than 10 and the second factor is written in a power of 10.

8. 1.65  106 drops

1.3 Divisibility Rules

1. a) By 3 only. Sum of digits is divisible by 3 but not 9. Not divisible by 2, so not divisible by 4 or 6. b) By 3, 4, and 6. Sum of digits is divisible by 3 but not 9. Last 2 digits are divisible by 4. Divisible by 2 and 3, so is divisible by 6. c) By 3 and 9.Sum of digits is divisible by 3 and 9. Not divisible by 2, so not divisible by 4 or 6.

2.a) 0, 3, 6, 9 b) 0, 3, 6, 9 c) 0, 3, 6, 9 d) 4 e) 2, 5, 8 f) 4

3. a) 3 b) 8 c) 8 d) 6 e) 5 f) 1

4. Explanations may vary. a) False. 10, 14 are even numbers that are not divisible by 4.

b) True. 3 is a factor of 9. c) True. 2 and 4 are factors of 16.

d) False. 6, 12, 15 are divisible by 3 but not by 9.

5. 6 does not divide into 112 evenly because 112 is not divisible by 3.

6. Answers may vary. 2016, 2124.

7. Yes. 695 jelly beans each.

8. No.

9. a), c) Yes. b), d) No. Divisible by 3.

1.4 Factors and Multiples

1. a) 112 b) 225 c) 78 d) 200

2. a) 36, 72, 108, 144 b) 10, 20, 30, 40 c) 12, 24, 36, 48 d) 60, 120, 180, 240

3. a) 4 b) 25 c) None. d) 12

4. Answers may vary. 7, 14

5. Aleem. The prime factors for 72 are always 2 and 3.

6. Answers may vary. 6, 8. Yes, there is more than one solution.

7. 1 month

8. every 15 days

9. the120th customer

10. 32, 56

1.5 Order of Operations

1. a) 41 b) 11 c) 6 d) 3

2. 4 + 8  (9 – 1) – 24  12

= 4 + 8  8 – 24  12

= 4 + 1 – 2

= 3

3. a) brackets; 5 b) multiplication; 5 d) brackets; 12 e) brackets; 12

4. a) 3  (8 + 4)  2 – 12 = 6 b) (3  72) + 2 – 100 = 49

c) (4 2 + 32) –19= 16 d) 22  (6 + 1 + 22) + 5 = 7

5. a) + b) , + c) , +, – d) +, –

6. 7  12 + 2  9; $102

7. a) 9.15  (5  3 + 7  2); $265.35 b) $155.55 c) $109.80

8. 5  80 + 6  100; 1000 km

9. a) In the first step he multiplied 3  4 before he evaluated 42. b) 17

Review

1. a) GCF: 9, LCM: 45 b) GCF: 2, LCM: 120

2. a) 145 b) 15 c) 7 d) 16 e) 7

3. (9 + 5)2 = 142 = 196 but 92 + 52 = 81 + 25 = 106.

4. 9  8 + 65  1.10; $143.50

5. a) 9.1  106b) 7.3  105c) 1.23  108d) 4.2  105

6. a) 2  105+ 2  103+ 1  102+ 9  101+ 2  100b) 1  106+ 5  105+ 9  103+ 9  100

7. 2  10.95 + 2  6.95 + 2  6.5 + 3.95; $52.75

8. 1.989  107, 1  107 + 9  106+ 8  105, 1 989 000

9. a) 20 b) 23

Practice Test

1. B

2. C

3. A

4. D

5. C

6. C

7. a) 16 b) 216 c) 121

8. a) 60 b) 10 c) 5 d) 2

9. a) 2 b) 2, 4 c) 2, 3, 5, 6, 9, 10

10. No. 20 bracelets.

11. 1135calories