Basic Algebra

This review provides you with an opportunity to test your own skills before you come to SUNY Sullivan for Placement Testing. Work out the problems first on your own and then check to see if you got the right answer. The steps to work out the problem to get the correct answer are given.

  1. Simplify -2.5 + 1.4
    Check
    -1.1

    Follow the sign rules when adding and subtracting:

    If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract the numbers and keep the sign of the larger number.


  2. Simplify −5 + 2 × 7
    Check
    9

    Follow the Order of Operations at all times. You can remember the Order of Operations by the phrase “Please Excuse My Deal Aunt Sally”. For a more detailed explanation visit http://media.tripod.lycos.com/1782282/1373792.pdf.

    Parentheses
    Exponents
    Multiplication / Division – starting at the left and moving to the right
    Addition
    Subtraction


  3. Simplify 3(1-5)2-8+22
    Check
    41

    Order of Operations was used to evaluate the expression.

    3(1-5)2-8+22
    3(-4)2-8+22
    3(15)-8+4
    45-8+4
    49-8
    41
    Do what is inside parentheses first and rewrite the problem. Next do the exponents and rewrite the problem. Next is multiplication, followed by addition and subtraction.

    For more examples, visit http://sradai.tripod.com/webonmediacontents/Order%20of%20Operations%20Examples.pdf




  4. Simplify
    3-52
    6-2x32
    (NOTE: Answer should be written as a fraction.)

    Check
    11
    6


    Follow the Order of Operations
    3-52
    6-2x32
    =
    3-25
    6-2x9
    =
    -22
    6-18
    =
    -22
    -12
    =
    11
    6


  5. Translate the following statement into symbols: The sum of six and three is less than ten.
    Check
    The problem states to “translate” the statement. It does not say to simplify. If it asked you to simplify, you would get 9 < 10.


  6. Insert <, >, or = in the blank to make the following statement true: −3 __ −4
    Check
    >

    As negative numbers become larger, they are getting smaller.


  7. Evaluate 2xy2 for x = −2 and y = 3
    Check
    -36

    Follow the sign rules for multiplying signed numbers. For more information, visit http://sradai.tripod.com/webonmediacontents/Basic%20Rules%20to%20Remember.pdf.

    2xy2 = 2(-2)(3)2 = 2(-2)(9) = -4(9) = -36


  8. Simplify the expression 3(x–5)+11
    Check
    3x-4

    3(x-5)+11
    3x-15+11
    3x-4


  9. Solve x-11 = 2
    Check
    x = 13

    To get x by itself, add the opposite of -11 to both sides.


  10. Solve −4x + 7 = −21
    Check
    x = 7

    -4x + 7 = -21
    -4x = -28
    x = 7


  11. Solve 34x - 5 = -7 (NOTE: Answer should be written as a fraction.)
    Check
    x = -83

    First we add the opposite of -5 to both sides to get the fraction and x by itself. Then multiply both sides by the reciprocal of the fraction.

    34x - 5 = -7
    34x = -2
    (43)(34)x = -21(43)
    x = -83


  12. Solve −3(x – 6) = 5x − 12 + 2x
    Check
    Order of Operations was used to evaluate the expression.

    −3(x – 6) = 5x − 12 + 2x
    −3x + 18 = 5x − 12 + 2x
    −3x + 18 = 7x − 12
    30 = 10x
    3 = x
    To learn more about solving linear equations, visit http://media.tripod.lycos.com/1782282/1668263.pdf


  13. Solve -0.3(x - 3) + x = 0.5(3 - x)
    Check
    -0.3(x - 3) + x = 0.5(3 - x)
    0.7x + 1.2 = 1.5 - 0.5x
    1.2x = 0.3
    x = 4
    To learn more about solving linear equations, visit http://media.tripod.lycos.com/1782282/1668263.pdf


  14. An item is put on sale with a 30% discount off the original price. The sale price is $49. What was the original price?
    Check
    x = $70
    Original price-30% discount of original price=sale price
    x-0.30x=49
    x - 0.30x = 49
    0.70x = 49
    x = 70


  15. Jane has $8 more than three times the money that Joe has. Together, Jane and Joe have $80. How much money does Joe have and how much money does Jane have?
    Check
    x = 18
    Joe = x
    Jane = 3x + 8

    Equation
    x + 3x + 8 = 80
    4x + 8 = 80
    4x = 72
    x = 18


  16. Calculate and give your answer in lowest terms:
    3 + 5
    12 - (-12)

    Check
    824 = 13

    Add the numerator together to get 8. Next add the denominator to get 24. The fraction is 824 = 13. Note: A negative outside parentheses is changed to addition and sign of everything inside parentheses changes to its opposite sign.


  17. Of the following, which is the largest? 23, 0.66, 0.666, 0.6
    Check
    23

    Change the fraction into a decimal by dividing the numerator by the denominator. You will get 0.66666 which is larger than the other decimals given.


  18. A store receives 16,500 cans of Split Pea Soup in 300 cartons. How many cans of Split Pea Soup were in each carton?
    Check
    55 cans

    Divide 16500 by 300 to find the total number of cans in each carton.


  19. A student who takes out loans totaling $10,000 will have to pay back the loan over a period of ten years. If payments amount to $105 per month, how much will the student have to pay back the lender?
    Check
    $12,600

    First we need the total number of months the loan will need to be paid: 10 years x 12 months = 120 months. Now multiply 120 months x 105 each month.


  20. Mark attends classes on Monday and Wednesday from 9:30 AM to 11:00 AM and from 12:30 PM to 4:00 PM. How many hours a week does Mark attend class?
    Check
    10 hours

    He attends class a total of 5 hours on both Monday and Wednesday for a total of 10 hours in class.


  21. If 7x = 43, then x = ? (NOTE: Your answer should be given as an improper fraction.)
    Check
    214

    Since two fractions are set equal to each other you can cross multiply to get 21 = 4x. To get x by itself, you would then divide both sides by 4 to get the answer.


  22. Divide: 412 ÷ 38
    Check
    12

    412 ÷ 38 = 92 X 83 = 726 = 12

    When dividing fractions, think of the phrase “keep change flip.” Keep the first fraction the way it is, change the division sign to multiplication, and take the reciprocal of the second fraction and multiply and reduce.


  23. If 6 = 8 + 4x, then x = ? (NOTE: Your answer should be stated as a fraction.)
    Check
    -12

    6 = 8 + 4x

    -2 = 4x

    -12 = x


  24. City College plans to have 15 computers for every 60 students. How many computers would be needed for 3600 students?
    Check
    900 computers

    1560 = x3600

    60x = 54,000

    x = 900

    Again, with two fractions set equal to each other you will cross multiply to get a new equation and solve the equation.


  25. Find the increase in megawatt usage during the four-year period from 1988 to 1992.
    Check

    1000 megawatts

    Each horizontal line represents 200 megawatts. In the year 1992, 2600 megawatts was used and in 1988, 1600 megawatts was used. Subtract the two amounts to find the difference.


  26. The length of a rectangle is 32 feet and the width is 14 feet. What is the perimeter?
    Check
    92 feet

    The formula to find the perimeter of a rectangle is P = 2L + 2W. Substitute in the values for the length and width and evaluate the expression.

    P = 2(32) + 2(14)

    P = 64 + 28

    P = 92


  27. A babysitter earns $1.50 per hour up to 6:00 PM and $2 per hour after 6:00 PM. How much will the sitter earn on a day they babysat from 10:00 AM to 9:30 PM?
    Check
    $19

    Babysitter worked 8 hours at $1.50 and 3.5 hours at $2.00.

    8(1.5) + 3.5(2)

    12 + 7

    19


  28. Bill receives a 6% salary increase. If Bill’s salary was $12,000 before the raise, what is his new salary?
    Check
    $12,720

    Multiply 12,000 times .06 to get 720. Add 12,000 and 720 to get his new salary of $12,720.


  29. Calculate 434 + 212 (NOTE: Your answer should be given as a mixed number.)
    Check
    714

    To add fractions, you must have common denominators. Both must be changed into that denominator. The common denominator is 4 so we do not need to change the first fraction. The second fraction becomes 224. Now they can be added together.