Lesson 1.3 Common Factors and Multiples · Lesson 1.3 Common Factors and Multiples Find the common...

Lesson 1.3 Common Factors and Multiples

Find the common factors of each pair of numbers.

1. 28 and 40 2. 45 and 63

3. 35 and 60 4. 56 and 70

Find the greatest common factor of each pair of numbers.

5. 18 and 48 6. 40 and 64

7. 42 and 70 8. 30 and 75

Express the sum of each pair of numbers as a product of the greatest common factor of the numbers and another sum.

9. 42 ! 105 10. 54 ! 90

Find the fi rst three common multiples of each pair of numbers.

11. 3 and 8 12. 4 and 9

13. 9 and 21 14. 12 and 28

Find the least common multiple of each pair of numbers.

15. 16 and 24 16. 15 and 24

17. 18 and 30 18. 25 and 20

Find the greatest common factor of each set of numbers.

19. 15, 45, and 60 20. 28, 42, and 70

21. 63, 84, and 105 22. 56, 78, and 130

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Extra Practice Course 1A 7

MIF_EP6_Ch01.indd 7 4/21/11 4:23:32 PM

Name :Teacher : Date :

Score :

Fractions WorksheetsMath-Aids.Com

Subtracting Mixed Numbers

Subtracting Mixed Numbers

1 ) 7 210 - 1 2

3 =

2 ) 7 12 - 1 1

5 =

3 ) 8 25 - 1 1

2 =

4 ) 6 610 - 1 2

4 =

5 ) 5 15 - 3 1

3 =

6 ) 9 12 - 4 6

10 =

7 ) 7 12 - 2 6

10 =

8 ) 7 12 - 2 3

10 =

9 ) 6 24 - 1 2

5 =

10 ) 9 110 - 3 3

4 =

http://www.math-aids.com/Fractions/

http://www.math-aids.com/

Find each quotient. Express your answer in its simplest form.

13. 8 ! 25

" 14. 10 ! 47

"

15. 3 ! 45

" 16. 7 ! 23

"

17. 23

! 112

" 18. 23

! 159

"

19. 45

! 128

" 20. 34

! 12

"

21. 38

! 16

" 22. 5 12

! 1 13

"

23. 4 29

! 3 16

" 24. 2 58

! 3 34

"

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22 Chapter 3 Lesson 3.1

MIF_EP6_Ch03.indd 22 4/21/11 3:51:46 PM

11. 0.8 ! 0.4 " 12. 0.8 ! 0.8 "

13. 0.4 ! 0.7 " 14. 0.9 ! 0.9 "

Multiply mentally.

15. 0.7 ! 7 " 16. 0.9 ! 0.8 "

17. 0.26 ! 3 " 18. 0.36 ! 4 "

19. 0.064 ! 8 " 20. 0.059 ! 6 "

Write in vertical form. Then multiply.

21. 0.78 ! 3.6 " 22. 2.8 ! 8.4 "

23. 0.49 ! 5.7 " 24. 19.3 ! 2.4 "

25. 6.5 ! 0.608 " 26. 0.31 ! 0.45 "

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MIF_EP6_Ch03.indd 25 4/21/11 3:51:46 PM

Divide.

11. 18 ! 0.18 " 12. 48 ! 0.24 "

13. 54 ! 0.12 " 14. 125 ! 0.25 "

15. 243 ! 0.27 " 16. 972 ! 0.48 "

17. 0.35 ! 0.07 " 18. 0.52 ! 0.02 "

19. 0.96 ! 0.08 " 20. 0.56 ! 0.04 "

21. 0.66 ! 0.6 " 22. 0.81 ! 0.9 "

23. 0.75 ! 0.5 " 24. 0.63 ! 0.7 "

25. 0.504 ! 0.18 " 26. 0.836 ! 0.44 "

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MIF_EP6_Ch03.indd 27 4/21/11 3:51:46 PM

Cumulative Practicefor Chapters 1 to 3

Draw a horizontal number line to represent each set of numbers.

1. Prime numbers less than 25

2. Mixed numbers between !6 and !7 with an interval of 15

between each pair

of mixed numbers

Arrange the following numbers from least to greatest.

3. 13, !5, !8, 2, !10, 6, !20, 0

least greatest

Arrange the following numbers from greatest to least.

4. !12, 7, 20, !16, !4, 25, 0, !30

least greatest

Complete each inequality using ! or ".

5. !36 2 6. 778

!779

7. 8 !10 8. !12 !25

9. !2163 !!81 10. 33 24

11. !!80 ! !!100 ! 12. !600 ! !!700 !

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34 Cumulative Practice for Chapters 1 to 3

(M)IF_P6(EP)_CP_34-38.indd 34 4/21/11 6:58:48 PM

Express each number as a product of its prime factors.

13. 56 14. 180

Find the greatest common factor of each set of numbers.

15. 36 and 42 16. 24, 48, and 84

Find the least common multiple of each set of numbers.

17. 6 and 14 18. 21, 28, and 42

Find the value of each of the following.

19. The square of 14 20. The cube of 30

21. The square root of 324 22. The cube root of 1,728

23. 10! ! !7293 " 24. !5123 # !64 $ !3433 "

25. 225

$ 34

" 26. 156

# 49

"

27. 3.7 $ 2.5 " 28. 18.5 # 2.5 "

Solve. Show your work.

29. The mass of a bag of fl our is 7 kg 500 g. Joyce repacks the fl our into 12 small packs of equal mass. What is the mass, in kilograms, of each small pack of fl our? (1 kg " 1,000 g)

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(M)IF_P6(EP)_CP_34-38.indd 35 4/21/11 6:58:48 PM

Lesson 4.2 Equivalent Ratios

Express the ratio in simplest form.

1. 36 : 20 2. 24 : 64 3. 45 : 90

4. 9 yards : 9 feet 5. 20 weeks : 14 days 6. 32 ounces : 8 pints

State whether each pair of ratios are equivalent.

7. 13 : 15 and 30 : 26 8. 54 : 18 and 18 : 6

Find the missing term of each pair of equivalent ratios.

9. 9 : 13 ! 27 : 10. 6 : 11 ! 42 :

11. 12 : 7 ! : 56 12. 3 : 8 ! : 72

13. 84 : 36 ! : 3 14. 76 : 48 ! : 12

15. 96 : 160 ! 3 : 16. 65 : 90 ! : 18

Find the equivalent ratios.

17. Use division to fi nd all the whole number ratios equivalent to 56 : 24.

18. Use multiplication to fi nd three ratios equivalent to 5 : 11.

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MIF_EP6_Ch04.indd 41 4/21/11 3:53:42 PM

Lesson 6.2 Fractions, Decimals, and Percents

Express each fraction as a percent.

1. 45 2.

58

3. 815 4. 1

34

5. 3710 6. 2

920

Express each decimal as a percent.

7. 0.08 8. 0.56

9. 0.9 10. 1.07

11. 2.75 12. 3.5

Express each percent as a fraction in simplest form.

13. 8.25% 14. 30.5%

15. 3313% 16. 41

23%

17. 5614% 18. 87

12%

Express each fraction as a percent. Round your answer to the nearest whole number.

19. 108250 20.

72125

21. 132216 22.

178450

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MIF_EP6_Ch06.indd 57 4/21/11 4:01:22 PM

7CHAPTER

Algebraic Expressions

Lesson 7.1 Writing Algebraic Expressions

Write an algebraic expression for each of the following.

1. The sum of k and 8. 2. The difference ”y less than 10”.

3. The product of g and 7. 4. The quotient of h and 8.

5. Subtract 6 from 5w. 6. Add 10 to the product of z and 7.

7. Subtract 10 from the 8. Add 5 to the quotient of s and 9.

product of 4 and h.

9. Multiply y by 6, then 10. Subtract the quotient of h and 3,

divide the product by 7. from 4 multiplied by 4.

11. Janet has p stickers. a) Amy has 10 fewer stickers than Janet. How many stickers does Amy

have in terms of p?

b) Bernie has 3 times as many stickers as Janet. How many stickers does Bernie have in terms of p?

c) Catherine has 6 more stickers than Janet. How many stickers does Catherine have in terms of p?

d) Dina has 25

as many stickers as Janet. How many stickers does Dina have

in terms of p?

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MIF_EP6_Ch07.indd 70 4/26/11 12:14:16 PM

Lesson 7.2 Evaluating Algebraic Expressions

Evaluate each expression for the given value of the variable.

1. 6x ! 7 when x " 5 2. 9y # 10 when y " 3

" "

3. 14g # 98 ! 3g when g " 7 4. 6h ! 25 # 5h4

when h " 8

" "

5. 50 # 7w3

! 4w when w " 6 6. 10p # 3p # 24

! 5 when p " 10

" "

Evaluate each expression when p " 4.

7. 3(5p # 1) # 4(3p # 7) 8. 3(5p # 6) ! 4(20 # 3p)

" "

Evaluate each expression when r " 9.

9. 5(10r ! 3) # 7r 10. 4(5r # 3) # 2(6r # 7)

" "


11. 6p ! 4

7 ! 5p # 6

2 # 3p4 when p " 4 12.

3(y # 2)4 !

4(2y # 3)5 when y = 6

" "

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MIF_EP6_Ch07.indd 72 4/21/11 4:21:49 PM

Lesson 7.3 Simplifying Algebraic Expressions

Simplify each expression. Then state the coeffi cient of the variable in each expression.

1. x ! x ! 3 ! 4 2. k " k ! k " 3

# #

Simplify each expression.

3. 6g – 3g ! 8g " g 4. 10u ! 4u " 8u " 3u

# #

5. 9m ! 4m " 5m ! 3m 6. 12x " 4x ! 3x ! 5x

# #

State whether each pair of expressions are equivalent.

7. 8z ! 2z and 3z ! 4z ! 3z 8. 9y and 9 ! y

9. 7n " 2 and 2 " 7n 10. 5g " 2g and 18g6


11. 12 " 8 ! 5d ! 4d " 6d 12. 20 ! 7k " 12 " 5k ! 8k

# #

13. 9m ! 11 " 8m " 6 ! 5m 14. 18 ! 4n " 9 ! 8n " 11n

# #

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MIF_EP6_Ch07.indd 74 4/21/11 4:21:49 PM

Lesson 7.4 Expanding and Factoring Algebraic Expressions

Expand each expression.

1. 3(4w ! 5) 2. 5(6 " 3y)

# #

3. 7(2a " 7) 4. 9(3p ! 5)

# #

5. 10(3 " 4d) 6. 8(5r ! 3)

# #

Factor each expression.

7. 7y ! 21 8. 12 " 4k

# #

9. 18 " 12h 10. 20w ! 15

# #

11. 14 " 8x 12. 24p " 15

# #

State whether each pair of expressions are equivalent.

13. 8(3 " 5m) and 24 " 5m 14. 9(2k ! 3) and 18k ! 27

15. 5(3 ! 5b) and 25b ! 15 16. 3(7z " 4) and 12 " 21z

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MIF_EP6_Ch07.indd 77 4/21/11 4:21:49 PM

Expand each expression. Then simplify the expression.

17. 3(3x ! 7) ! 4(5x " 2) 18. 9(5k ! 2) ! 4(7 " 10k)

# #

19. 7(5 ! 4w) ! 6(8w " 3) 20. 4(6 ! 5g) ! 7(3 " g)

# #

Simplify each expression. Then factor the expression.

21. 12p " 8 ! 6p ! 14 22. 20 ! 15x " 6 " 9x

# #

23. 9h ! 30 ! 12h " 2 24. 20k ! 7 " 2k ! 8

# #

Solve.

25. Expand and simplify the expression 3(y " 3) ! 2(5 ! 3y) ! 24(2y " 5) ! 6(5 " y).

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MIF_EP6_Ch07.indd 78 4/21/11 4:21:49 PM

Cumulative Practicefor Chapters 4 to 7

Find the missing term in each pair of equivalent ratios.

1. 7 : 15 ! 63 : 2. : 13 ! 48 : 104

Write each ratio in simplest form.

3. 36 : 90 4. 56 : 91

5. 60 inches : 3 feet 6. 2 pounds : 24 ounces

Express each decimal as a percent.

7. 0.76 8. 1.09

Express each fraction as a percent.

9. 1320

10. 712

Express each percent as a decimal.

11. 9% 12. 150%

Express each percent as a fraction in simplest form.

13. 88% 14. 120%

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(M)IF_P6(EP)_CP_85-90.indd 85 4/25/11 12:32:53 PM

Find the quantity represented by each percent.

15. 45% of 96 quarts 16. 60% of 60 minutes


17. 9x ! 29 if x " 6 18. 7y ! 10 if y " 4

19. 2(3x # 6) ! 5x ! 4

2 if x " 10 20. 10 # 4y ! 63

# 5y ! 4

3 if y " 5


21. 9w # 8 ! 6w ! 3 # 4w 22. 7 # 8y ! 3 # 3y # 5 ! 6y

Expand each expression.

23. 4(6q ! 3) 24. 7(5 # 7y ) # 3(y # 1)

Factor each expression.

25. 12g # 4g # 4 26. 40 ! 10h # 9 ! 4h

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86 Cumulative Practice for Chapters 4 to 7

(M)IF_P6(EP)_CP_85-90.indd 86 4/21/11 7:51:59 PM

CHAPTER

Equations and Inequalities8Lesson 8.1 Solving Algebraic Equations

Solve each equation using the substitution method.

1. x ! 8 " 14 2. y ! 6 " 20

x " y "

3. p # 9 " 7 4. k # 15 " 20

p " k "

5. 6w " 72 6. 15q " 60

w " q "

7. 18

e " 7 8. 110 g " 12

e " g "

Solve each equation using the concept of balancing.

9. a ! 14 " 20 10. b ! 18 " 34

a " b "

11. 18 " s # 12 12. h # 15 " 9

s " h "

13. 7k " 84 14. m6

" 16

k " m "

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Extra Practice Course 1B 1

Name: Date:

Solve each equation using the concept of balancing. Write all fractional answers in its simplest form.

15. x ! 16

" 56

16. y # 25

" 35

x " y "

17. 8k " 49

18. 10g " 46

k " g "

19. 35

p " 310

20. 23

w " 56

p " w "

21. x ! 1.8 " 3.4 22. p ! 6.3 " 9.1

x " p "

23. y # 3.5 " 2.9 24. k # 8.5 " 2.7

y " k "

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25. 3x ! 2.5 " 6.1 26. 4y # 6.2 " 13

x " y "

27. 3.2k " 40 28. 2.4p " 36

k " p "

29. w ! 23

" 2 56

30. d # 25

" 1 310

w " d "

31. 3y4

" 15 32. 37

k " 6

y " k "

Solve.

33. Find three whole numbers, such that when inserted into the equation below, the value of x " 6.

ax ! b " c

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Extra Practice Course 1B 3

CHAPTER

The Coordinate Plane9Lesson 9.1 Points on the Coordinate Plane

Use the coordinate plane below.

1. Give the coordinates of each point.

P

R

S

Q

T

U

W

V

x

2

3

1

!2

!3

!4

!1!2!3 !1!4!5!6!7!8 4 5 6 7 83210

y

Plot the points on the coordinate plane below. In which quadrant is each point located?

2. S (3, 2), T (0, !1), U (!4, !2), V (4, 0), W (!2, 1), and Z (2, !2)

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Worksheet by Kuta Software LLC

Algebra 1

Assignment

Name___________________________________ ID: 1

Date________________ Period____

Evaluate each expression.

1) (−13) + 50 − 14 2) (−13) − (−32) + 34

3) 9 − 44 + (−43) 4) 37 − 13 − 45

5) (−24) + (−35) − (−20) 6) (−13) − (−24) − 30

7) 49 − (−2) − 48 8) (−2) + (−32) − (−43)

9) (−40) + (−25) + (−20) 10) (−30) + 47 − (−27)

Find each quotient.

11) 0

−312)

0

6

13) 5

−514)

−21

−7

15) 6

−316)

8

−4

17) 32

818)

0

−6

Find each product.

19) −17 ⋅ −6 20) −16 ⋅ 17

21) −18 ⋅ 11 22) −13 ⋅ −16

23) −2 ⋅ −1 24) −16 ⋅ −16

25) −13 ⋅ −8 26) 4 ⋅ −5

Lesson 1.3 Common Factors and Multiples · Lesson 1.3 Common Factors and Multiples Find the common...

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