### Algebra Questionbook - Questions    © '03, A. Azzolino

 4. Write the word name for the SUM of fouteen tens, thirty-three ones, two hundred sixty-three millions, and one hundred fifty-six billions.

 5."Four divided by eight" may be rewritten using the "÷" symbol, the "/" symbol (either in fraction form or on one line in text), or using the good old ")" with an inclusion bar. Rewrite "four divided by eight" using each of these four notations.

 6.What's an exponent? How is it used? (Include examples with your written description.)

 7. State (using notes taken in class, or by visiting the tutorial) the Order of Operations or Mathematical Syntax as outlined in the phrase "Finally, Please, Readily Excuse, My Dear, Aunt Sally." Remember to include notations such as "leftmost first" or "innermost first" where necessary.

 8. & 9. & 10. 1st: Write your birth date. 2nd: Write the four digits of your birth year [ex. 1949]. 3rd: Using the digits of your birth year as 4 numbers, and using any operation you wish [+, -, X, ÷, , and exponents (using only these digits)] and as many parenthesis as you wish, write expressions for the numbers from 1 to 10. Ex: 0 = ( 9 - 9)x(4 - 1). Complete: 0 = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 =

 11.Find one number which is divisible by 4, and also by 5, and also by 9, and also by 7. (Perhaps see Divisibility Test.) What's the smallest this number could be? Why is this the smallest number?

 12.a. List the prime numbers from 42 to 60. ____________________________________ b. Natural numbers, 1, 2, 3, 4, 5, ..., may be grouped into three groups. The list in each of three groups had been started for you. 1st: Name each group. 2nd: Add more numbers to the list until either the list is complete or you have listed the next 25 numbers. ```Name List unity 1 __________ 2, 3, 5, 7, 11, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___ __________ 4, 6, 8, 9, 10, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___, ___ ```

 13.A fraction is a number. The number is written as a ratio. This ratio compares the numator to the denominator. 1st: What does the numerator indicate? 2nd: What does the denominator indicate?

 14. Use this rectangle.       Using vertical lines, divide the rectangle into thirds and shade one of the thirds.       Next, using horizontal lines, divide the rectangle into fifths and shade four of these fifths.       You have set the rectangle up to give you the result of the computation "1/3 x 4/5."       Count the number of small rectangles which have been shaded twice and use this number as the numerator. Count the number of small rectangles in the original rectangle and use this number as the denominator. Write this fraction.

 15.a. Why is it better to reduce before multiplying rather than after multiplying when completing a problem involving multiplication of fractions? b. What additional step(s) must be performed in order to subtract 34 3/5 from 42 2/5 rather than subtracting 34 3/5 from 42 4/5? You MUST complete each of these computations as part of your answer.

 16. Use these 3 numbers: the square root of one-fourth, three-fourths cubed, two-thirds. 1st: Write these numbers using symbols and numerals. 2nd: Write simpler fractions equivalent to each. 3rd: List them from smallest to largest.

17. It is important to recognize certain fractions when they are written in decimal form.
1st: Use a calculator [particularly the ÷ button and the 1/x button], mental work, or pencil-and- paper computation, to write decimal equaivalents for each fraction in the list.
2nd: For each one of these groups describe any patterns you see.
 1/8 = _____ 2/8 = 1/4 = _____ 3/8 = _____ 4/8 = 2/4 = 1/2 = _____ 5/8 = _____ 6/8 = 3/4 = _____ 7/8 = _____ 8/8 = 4/4 = 2/2 = _____

 1/9 = _____ 2/9 = _____ 3/9 = 1/3 = _____ 4/9 = _____ 5/9 = _____ 6/9 = 2/3 = _____ 7/9 = _____ 8/9 = _____ 9/9 = 3/3 = _____

 1/10 = _____ 2/10 = 1/5 = _____ 3/10 = _____ 4/10 = 2/5 = _____ 5/10 = 1/2 = _____ 6/10 = 3/5 = _____ 7/10 = _____ 8/10 = 4/5 = _____ 9/10 = _____ 10/10 = 5/5 = _____

 18. Complete by writing a list of instructions for each: a)To add fractions with like denominators, __. b)To add fractions which do not have like denominators, __________. c)To multiply fractions, ______. d)To divide fractions, _______.

 19. What's the difference in procedure, or what are the extra steps needed, to divide 4.3 by 0.02 rather than divide 4.3 by 2? Include paper and pencil computation of each of these division problems.

 20. Review Questions 1. Simplify the following: 15 + 5 x 2 - 25 + 6 ÷ 3 2. Find the perimeter. 3. One gallon of paint will be enough to paint 240 square feet of wall. How many gallons will be needed to paint 1440 sq. ft.?

 21. Review Questions 1. Mary's checking account has \$898 in it. If she has to withdraw three car payments of \$127 each, what will her new balance be?   2. State the prime factorization of 192.  3. How many five-eighths pound cans of peanuts can be filled with ten pounds of peanuts?  4. Charlie drove 360 miles on 14.6 gallons of gas. How many miles per gallon did he get? Round to the nearest tenth.  5. Round 487.2583 to the nearest tenth, ten, hundred, hundredth:

 22.Review Assignment: Evaluate showing pencil and paper computation. 1)(525 4/9) - (188 1/3) 2) 1000 - 49.009 3) two-fifths cubed 4) three-fourths of sixty 5) 121 6) 1.96

 23.1) Write 4.0057 as a fraction. 2) Write 4.0057 in words. 3) Write 4.125 as a reduced fraction. 4) Write 4.125 in words.

 24. 1) Write 0.25 as a reduced fraction. 2) Write 0.25 as a percent. 3) Write 0.3333333... as a reduced fraction. 4) Write 0.333... as a percent.

 25.Write then solve a word problem involving a proportion. If you use a problem in the text as a model, remember to cite the source.

 26. Explain the term "unit price". Use at least 2 examples in addition to your written explanation.

 27.Explain how to mentally find the following. 1st: 50% of 40 2nd: 150% of 40 3rd: 75% of 40

 28.Explain how to mentally compute the following. 1st: 40 out of 50 is what percent? 2nd: 60 out of 30 is what percent? 3rd: 15 is 50% of what number? 4th: 30 is 150% of what number?

 29.If you're given a marked price and a discount, 1st: how could you find the rate of discount? 2nd: How could you find the sale price?

 30. BEFORE MIDTERM BREAK! Write a letter to your instructor giving a status report of how things are going in the course.

 31. Complete: 1. To multiply a number by 100, ______. 2. To divide a number by 100, ___.

 32. 1st: Write each of the following percents as decimals. 2nd: Explain the general procedure for doing this computation. a.) 12 ½ %, b.) 10 ¼ %, c.) 8.5 %, d.) 13 %, e.) 33 1/3 %, f.) 66 2/3 %

 33. In a problem involving percent increase or percent decrease, what should be used as the base?

 34. Review Questions 1. Find the value of x in 10/15 = 6/x. 2. Find the value of z in z is to twenty-one as six is to eight. 3. If 50 cookies require 1 1/4 cups of flour, how many cookies can be made with 4 coups of flour?

 35. Review 1. If you put \$1200 in a savings account at 9% simple interest, how much will it be worth after 3 years?   2. The value of a house went from \$144,000 to \$180,000 in 3 years. Find the percent increase.

 36. Answer and Show Work: To get an "A" in Math, a student must maintain a 90 average. If the student's test scores on the first four tests were 88, 89, 95, and 94, what must the fifth test score be to guarantee receiving an "A" in the course?

 37. Humorously complete using the proper metric prefix, customary unit, or constant. 1.) 10 cards is 1 ___cards 2.) The insect with 100 feet is really not a ___pede but a ___pede. 3.) One tenth of a bell is a ___ bell. 4.) Ratio of an igloo's circumference to its diameter: Eskimo ___ 5.) 2000 pounds of Chinese soup: Won ___ 6.) 1,000 aches: 1 ___hurtz 7.) 1 million bicycles: 2 ____cycles 8.) 2000 mockingbirds: Two _____mockingbirds 9.) 1000 cubic centimeters of wet socks: 1 ____hosen 10.) 10 rations: 1 ____ration

 38. a.) Define perimeter. b.) Define area. c.) Give an example of the use of the perimeter of something. d.) Give an example of the use of the area of something.

 39. A useful formula involving a trapezoid is A = h(a + b)/2. a.) Label the figure with the appropriate variables

 40. Explain in general how to compute the shaded area. Write and complete your own problem using different shapes.

 41. A unit fraction is a fraction equal to one but having different but equivalent measurements in the numerator and the denominator. Unit fractions are used to convert one unit to another.   1st: Write three other unit fractions. 2nd: Show another example of how a unit fractions may be used in computation to change one unit to another.

 42. Chapters 9 and 10Write a review or cheat sheet for these chapters. You may include formulas, examples, pictures. You will not be able to use it to take the department-written test. Make your rewiew fit on one side of an 8 ½" by 11" sheet of paper.

 43. Review a.) Complete: Any number to the zero power, other than zero, is ________. b.) Complete: Any number to the first power is _____.

 44. End of Semester Letter Write me, Aggie, the instructor, a letter. Tell me how you've changed this semester and how you are the same as you were in the beginning of the semester. Tell me what you've learned about yourself and about math. So far, what was the best part of the course and what was the worst part of the course?

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