# Prime factorization, fraction operations and word problems

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10. List the factors of each of the following number for 66.

Using the following list of numbers for exercises 13 and 14:

0, 1, 15, 19, 23, 49, 55, 59, 87, 91, 97, 103, 105,

14. Which of the given numbers are composite?

16. List all the prime numbers between 55 and 75.

22. Social Science. Dr. Mento has a class of 80 students. For a group project, she wants to divide the students into groups of 6, 8, or 10. Is this possible? Explain your answers.

Find the prime factorization of each number?

20. 330

24. Find two factors of 28 with a sum of 11.

Find the greatest common factor for each of the following groups of numbers:

42. 36, 72, and 144

8. What fraction names the shaded part of each of the following figures?

The shaded part is three and the unshaded part is four

18. Business and finance. At lunch, 5 people out of a group of 9 had hamburgers. What fraction names the part of the group who had hamburgers? What fraction names the part who did not have hamburgers?

42. Change to a mixed or whole number: 48/7

60. 13 2/5

14. Statistics. Jeff Bagwell of the Houston Astros has 104 hits in 325 times at bat. Matt Williams of the Arizona Diamond backs has 88 hits in 275 times at bat. Do they have the same batting average?

Write each faction in simplest form:

30. 17/51

42. 42/55

12. 5/21 x 14/25

37. 4 1/5 x 10/21 x 9/20

Evaluate the following. Be sure to use the proper units.

4. 51b/ft x 3ft

26. 3/4 divided 9

38. 5 1/3 divided 2 2/5

46. Business and finance. A piece of land measures 3 3/4 acres and is for sale at $60,000. What is the price per acre?

54. Crafts. Evette has 41 ½ ft of string. She wants to cut it into pieces 3 ¾ ft long. How many pieces of string will she have? How much string remains, if any?

28. Science and medicine. A computer can execute 36 instructions per microsecond. How many instructions can it execute in 4 minutes?

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Forty six questions related to finding factors, prime numbers, Greatest common factor, Least common factor, fractions, mathematical operations, solving linear equations, coordinate geometry, graphing, slope intercept form of graphs, inequality graphs, solving a system of equations and word problems.

Complete and please show all the work.

Please see attached file for full problem description.

1. List all the factors of 45.

2. Which number is prime?

A) 1

B) 12

C) 31

D) 99

3. List all the prime numbers between 25 and 60.

4. Find the GCF for 68, 85, and 153.

5. Find the LCM for 18 and 27.

6. Multiply and write the result in simplest form.

A)

B)

C)

D)

7. Add.

8. Subtract. -

9. Evaluate. (3 ? 2 + 1)2

10. Evaluate. (15 - 5) ÷ [(12 ÷ 2 ? 2) - 2]

A) 10

B) 1

C)

D) 8

11. Evaluate. | -48 |

12. Write the following phrase using symbols. Use the variable x to represent the number.

A number decreased by by 6

13. Subtract. -11 - 20

A) 31

B) -9

C) 9

D) -31

14. Divide.

A) -6

B) 0

C) undefined

D) 1

15. Combine like terms.

2r + 10s + 4r

A) 6r + 10s

B) 16rs

C) 12r + 4s

D) 16r + s

16. Divide.

A) m2n3

B) m4n4

C) m2n4

D) m4n3

17. Multiply.

a7 a5

18. Solve. x - 9 = -6

19. Solve. 10x - = 9x +

A)

B)

C)

D)

20. Solve. 8x - 11 = 2x + 1

21. Translate the following statement into an algebraic equaion. Let x represent the number.

3 more than 9 times a number is 4 times that same number.

22. Solve. 8 - (4x - 3) = 19

23. Tickets for a play at the community theater cost $14 for an adult and $2 for a child. If 270 tickets were sold and the total receipts were $2340, how many of each type of ticket were sold?

24. Graph the solution set of x  -1.

A)

-1 0

B)

-1 0

C)

-1 0

D)

-1 0

25. Solve and graph the solution set. 3x  7x + 20

A)

-5 0

B)

-5 0

C)

0 5

D)

0 5

26. Which of the ordered pairs is a solution for the equation 4x - 3y = 12?

A) (0, 4)

B) (-3, 0)

C) (-3, -4)

D) (0, -4)

27. Plot the point with coordinates (-4, 3).

A)

B)

C)

D)

28.

Graph 3x + y = 3.

29. Graph y = 4.

30. Find the slope of the line passing through the points (0, 2) and (-10, 9).

A)

B)

C)

D)

31. Find the slope of the line passing through the points (-2, 2) and (-2, -3).

A) 0

B) 1

C) -5

D) Undefined

32. Find the slope of the graphed line.

A) 2

B) -2

C)

D) -

33. The following pie chart represents the eye color of students in a certain class.

What percentage of students in the class had blue or brown eyes?

34. The line graph below shows the number of trees in a certain seaside town.

(a) Which year had the fewest trees?

(b) Between which two years did the greatest increase in the number of trees occur?

35. Find the slope and y-intercept.

-9x - 8y = -64

36. Find the slope.

7x + 2y = -11

37. Match the graph with one of the equations.

A)

B)

C) y = -3x + 1

D) y = 3x + 1

38. A roof rises 2.75 ft over a horizontal distance of 10.69 ft. What is the slope of the roof to the nearest hundredth?

A) 3.89

B) 0.26

C) 1.60

D) 2.77

39. Determine which two equations represent parallel lines.

(a) y = 5x - 10 (b) y = -5x + 10 (c) y = 5x + 5 (d) y = x - 10

40. Graph the inequality.

y  3x

41. Rewrite the equation 2x - 3y = -6 as a function of x

A)

B)

C)

D)

42. Solve the system by graphing.

x - 2y = 8

x + y = -1

43. Solve the system by addition.

x + y = 1

x - y = 9

44. Solve the system by addition.

-4x + 5y = 5

x - 2y = -2

45. The sum of two numbers is 43. The second is 1 more than 2 times the first. What are the two numbers?

46. Solve the following system of linear inequalities by graphing.

x + 2y  3

2x - 3y  6

A)

B)

C)

D)