Class 1 Handout - Brookdale Community College



Class 1 Handout

Review Activity for Chapters 1 and 2

Section 1.1

1. Write each of the following in words.

a) 267

b) 34,100

c) 101,276

2. Consider the number 39,268

a) What number is in the hundred’s place?

b) What number is in the ten-thousand’s place?

c) What number is in the ones place?

3. Write each number in standard notation:

a) Three thousand seven hundred thirty-seven

b) Nine hundred thirty

c) Eighty-six thousand twelve

Section 1.2

4. What property of addition is shown by each of the following:

a) 4+8 = 8+4

b) (2+7)+3 = 2+(7+3)

5. Find the perimeter of the following rectangle:

32 feet

12 feet

6. For a 17 mile trip, Joe paid the taxi driver a total of $23. If $5 was a tip, how much

was the fare?[pic]

Section 1.3

7. Write 5+5+5+5 as a multiplication.

8. A cook worked 12 hours at $11 an hour. How much did she earn?

9. Perform the indicated operation, showing remainders when necessary:

a) 25[pic]3 d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

10. The members of a marching band need to make 6 foot banners. They have 50 feet of

material to work with.

a) How many banners can be made?

b) How many feet of material will be left over?

11. a) Estimate the sum of 456 and 19,643 using front end estimation.

Show the values you are using and then find the sum.

b) Find the exact sum of 456 and 19,643.

Section 1.4

12. a) List all the factors of 24.

b) Find the prime factorization of 24.

13. a) Find all the prime factors of 20.

b) Find all the prime factors of 35.

c) What prime factors do they have in common?

14. a) Evaluate the following exponential expression: [pic]

b) Write [pic]in exponential notation.

15. For [pic]: a) What is the base?

b) What is the exponent?

c) Evaluate.

Section 1.5

16. Evaluate each expression, using the following steps:

i) List all the operations in each problem as they appear from left to right.

ii) Give the first operation to be performed.

iii) Evaluate. Show all steps.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

17. At the supermarket, Carlos has 2 cases of soda, 4 bags of potato chips, and 2 cans of

dip in his cart. Each case of soda costs $6, each bag of chips costs $2, and each can

of dip costs $1. Find the total cost of the groceries.

18. Explain the difference in the steps used to evaluate the following expressions:

Expression 1: [pic]

Expression 2: [pic]

Section 1.6

19. Determine whether each statement is an equation:

a) [pic] c) [pic]

b) [pic] d) [pic]

20. Solve each equation. Show all steps. Write the complete check of the solution.

a) [pic] c) [pic]

b) [pic] d) [pic]

21. A man needs $345 for a new set of golf clubs. You want to find how much more

money he needs if he now has $317.

a) Define your variable: X =

b) Set up your equation:

c) Solve your equation:

d) Answer: He needs more.

Section 1.7

22. Name the steps in solving each of the following equations:

a) [pic] c) [pic]

b) [pic] d) [pic]

23. Solve each equation. Show all steps. Write the complete check of the solution.

a) [pic] c) [pic]

b) [pic] d) [pic]

24. A high school PE teacher had the students in her class form three-person teams for a

basketball tournament. Eight teams participated in the tournament. How many

students were in the PE class?

a) Define your variable: Let K =

b) Set up your equation:

c) Solve your equation:

d) Answer: There were kids in the PE class.

Section 2.1

25. If a number is less than 0, what type of number must it be?

26. Use , or = to compare the following sets of numbers, then graph both numbers on

a number line to verify.

a) [pic]6 5 d) 3 [pic]3

b) 0 [pic]7 e) [pic]8 [pic]12

c) [pic] [pic] f) [pic] [pic]

27. Simplify each expression:

a) [pic] c) [pic]

b) [pic] d) [pic]

Section 2.2

28. Explain why the expression [pic] is not written correctly. How should it be

written?

29. Find each sum without a calculator:

a) [pic] c) [pic]

b) [pic] d) [pic]

30. The maintenance costs, utilities, and taxes on a duplex are $900 a month. The owner

of the apartments receives monthly rental payments of $450 and $380. Does this

investment produce a positive amount of money?

Section 2.3

31. To subtract two integers, change the subtraction sign to an addition sign and add the

_______________ of the second number. For example, [pic].

32. Evaluate each expression without a calculator:

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

33. A diver jumps from his boat into the water and descends 50 feet. He pauses to check

his equipment and then descends an additional 70 feet. Use a signed number to

represent the diver’s final depth.

Section 2.4

34. a) The product of two integers with like signs is _______________.

b) The product of two integers with unlike signs is _______________.

35. Evaluate each expression without a calculator:

a) [pic] c) [pic]

b) [pic] d) [pic]

36. A levee, which is an embankment designed to prevent the flooding of a river,

protects a town in a low-lying area. According to geologists, the banks of the levee are eroding at a rate of 2 feet per year. If something isn’t done to correct the problem, what signed number indicates the distance from the levee’s current location to where it will be in 10 years?

Section 2.5

37. How do the rules for dividing integers compare with the rules for multiplying

integers?

38. Evaluate each expression without a calculator:

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

39. Over a week’s time, engineers at a city water reservoir released enough water to

lower the water level 35 feet. Use a signed number to indicate how much the water level changed each day during this period, on average?

Section 2.6

40. Use front end estimation for each of the following.

Show the numbers you are using.

a) [pic] c) [pic]

b) [pic] d) [pic]

41. Explain the difference between [pic] and [pic], then evaluate each one.

42. Evaluate each expression, using the following instructions:

i) List all the operations in each problem as they appear from left to right.

ii) Give the first operation to be performed.

iii) Evaluate. Show all steps.

a) [pic] c) [pic]

b) [pic] d) [pic]

Section 2.7

43. Solve each equation. Show all steps. Write the complete check of the solution.

a) [pic] f) [pic]

b) [pic] g) [pic]

c) [pic] h) [pic]

d) [pic] i) [pic]

e) [pic] j) [pic]

Class 1 Handout Answer Key

1. a) Two hundred sixty-seven

b) Thirty-four thousand, one hundred

c) One hundred one thousand, two hundred seventy-six

2. a) 2

b) 3

c) 8

3. a) 3737

b) 930

c) 86,012

4. a) Commutative property of addition

b) Associative property of addition

5. 88 ft

6. $18

7. [pic]

8. $132

9. a) 8 R 1 d) 0

b) 84 e) undefined

c) 12 f) 8 R 25

10. a) 8 banners

b) 2 feet

11. a) 20500

b) 20099

12. a) 1,2,3,4,6,8,12,24

b) [pic]

13. a) 2,5

b) 5,7

c) 5

14. a) 14,400

b) [pic]

15. a) 7

b) 3

c) 343

16. a) i) addition, multiplication ii) multiplication iii) 27

b) i) subtraction, multiplication, exponent ii) exponent iii) 18

c) i) multiplication, subtraction, exponent ii) multiplication

iii) 64

d) i) addition, multiplication,

subtraction, addition

ii) subtraction

iii) 18

e) i) division, multiplication

ii) division

iii) 25

f) i) subtraction, multiplication,

division

ii) multiplication

iii) 3

17. $22

18. For expression 1, the exponent is done first, followed by the multiplication.

For expression 2, the multiplication is done first, followed by the exponent.

19. a) yes c) no

b) no d) yes

20. a) x = 10 c) b = 3

b) x = 206 d) x = 4793

21. a) x = Amount of additional money he needs

b) 345 = 317 + x

c) x = $28

d) He needs $28 more.

22. a) Subtract 5 from both sides of the equation.

b) Add 5 to both sides of the equation.

c) Divide both sides of the equation by 5.

d) Multiply both sides of the equation by 5.

23. a) x = 1 c) x = 147

c) d = 1100 d) t = 3

24. a) K = The number of students in the class.

b) K = [pic]

c) K = 24

d) There were 24 kids in the PE class.

25. A negative number.

26. a) < d) >

b) > e) >

c) > f) =

27. a) 14 c) [pic]

b) [pic] d) 5

28. The [pic]5 should be in parentheses

29. a) [pic] c) [pic]

b) 10 d) [pic]

30. No, costs are greater than payments. 900 > 830

31. Opposite, ([pic])

32. a) 9 d) [pic]

b)[pic] e) 3

c) 5 f) 9

33. [pic]feet

34. a) Positive

b) Negative

35. a) 0 c) [pic]

b) 7 d) 0

36. [pic] feet

37. The are the same, except that you can multiply by 0, but you can’t divide by 0.

38. a) 9 d) [pic]

b) 1 e) [pic]12

c) undefined f) 0

39. [pic] feet per day

40. a) [pic]

b) [pic]

c) [pic]

d) [pic]

41. For[pic], the base is 3 whereas for[pic], the base is [pic]

[pic] and [pic]

42. a) i) addition, multiplication,

subtraction

ii) multiplication

iii) [pic]

b) i) subtraction, exponent,

subtraction, subtraction,

exponent

ii) subtraction

iii) [pic]

c) i) multiplication, subtraction,

multiplication

ii) multiplication

iii) 50

d) i) exponent, subtraction,

exponent, division, addition

ii) exponent

iii) [pic]254

43. a) h = [pic] f) a = 5

b) r = 0 g) x = [pic]

c) s = [pic] h) y = [pic]

d) x = [pic] i) x = 7

e) x = 4 j) x = [pic]

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