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Notes for Algebra

Learn how to solve algebraic problems using a four-step plan: understanding the problem, planning the solution, solving the problem, and checking the solution.

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Notes for Algebra

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  1. Notes for Algebra Chapter 0

  2. 0-1 Plan for Problem Solving

  3. Four-step problem-solving plan • Understand the Problem (Read the problem and directions carefully) a. Identify what information is given. b. Identify what you need to find. • Plan the solution (choose a variable to represent the unknown, and write an equation.) • Solve the problem. • Check the solution. a. Does your answer make sense? b. Does you answer fit the information in the problem?

  4. Example 1 pg. P5 Use the four-step plan LAWNS: Mr. Nunez’s lawn is 50 feet long and 35 feet wide. He paid a lawn service $350 to aerate and reseed his lawn. What did the lawn service charge per square foot?

  5. Example 1 pg. P5 Use the four-step plan LAWNS: Mr. Nunez’s lawn is 50 feet long and 35 feet wide. He paid a lawn service $350 to aerate and reseed his lawn. What did the lawn service charge per square foot? $0.20 per square foot

  6. Example 2 pg. P6 Use the Four-Step Plan A used book store had a sale on all paperbacks for $0.45 each. The store had $72.45 in sales. How many books did the store sell?

  7. Example 2 pg. P6 Use the Four-Step Plan A used book store had a sale on all paperbacks for $0.45 each. The store had $72.45 in sales. How many books did the store sell? 161 books

  8. 0-6 pg. P6 1-6

  9. 0-2 Real Numbers

  10. Positive numbers The numbers listed to the right of zero on a number line.

  11. Negative Numbers The numbers listed to the left of the zero on a number line.

  12. Natural numbers Counting numbers

  13. Whole numbers Zero and the counting numbers

  14. Integers Zero and all positive and negative whole numbers

  15. Rational numbers All integers and numbers that can be expressed as a fraction or a terminating or repeating decimal.

  16. Irrational numbers Numbers that can not be expressed as terminating or repeating decimals on in the form of a fraction.

  17. Square root One of two equal factors of a number (the principal square root is the positive square root of a number)

  18. Perfect Square A number with a rational number as its square root.

  19. Example 1 pg. P7 Classify Real numbers Name the set or sets of numbers to which each real number belongs. 1.) 2.) 3.)

  20. Example 1 pg. P7 Classify Real numbers Name the set or sets of numbers to which each real number belongs. 1.) rational number 2.) natural number, whole number, integer, rational number 3.) irrational number

  21. Graph To draw, or plot the points named by those numbers on a number line.

  22. Coordinate The number that corresponds to a point on a number line.

  23. Example 2 pg. P8 Graph and Order Real Numbers Graph each set of numbers on a number line. 1.) 2.) , 3.)

  24. Example 2 pg. P8 Graph and Order Real Numbers Graph each set of numbers on a number line. 1.) -1 0 1 2.) , 0 1 2 3 4 5 3.) -2.5 -2 -1.5 -1 0.5

  25. Example 3 pg. P8 Write Repeating Decimals as Fractions Write as a fraction in simplest form.

  26. Example 3 pg. P8 Write Repeating Decimals as Fractions Write as a fraction in simplest form.

  27. Example 4 pg. P9 Simplify Roots Simplify each square root 1.) 2.)

  28. Example 4 pg. P9 Simplify Roots Simplify each square root 1.) 2 2.)

  29. Example 5 pg. P9 Estimate Roots Estimate each square root to the nearest whole number. 1.) 2.)

  30. Example 5 pg. P9 Estimate Roots Estimate each square root to the nearest whole number. 1.) 2.)

  31. 0-2 pg. P10 1-35

  32. 0-3 Operations with Integers

  33. Example 1 pg. P11 Add Integers with the same sign Use the number line to find .

  34. Example 1 pg. P11 Add Integers with the same sign Use the number line to find . 1 -5 -4 -3 -2 -1 0 1 2 3 4 5

  35. Absolute Value The distance a number is from zero on the number line.

  36. Rules for adding integers Integers with the same sign ( or )Add the numbers and keep the sign. Integers with different signs (or ) Subtract the smaller value from the larger value and take the sign of the largest value

  37. Example 2 pg. P11 Add integers using absolute value Find .

  38. Example 2 pg. P11 Add integers using absolute value Find .

  39. Opposites Every positive integer has an opposite negative integer

  40. Additive Inverse (used when subtracting) A number and its opposites are additive inverses. Subtraction means to “add the opposite”

  41. Example 3 pg. P11 Subtract Positive Integers Find .

  42. Example 3 pg. P11 Subtract Positive Integers Find .

  43. Rules for multiplying integers Integers with the same sign ( or )The product will always be a positive answer Integers with different signs (or ) The product will always be a negative answer

  44. Example 4 pg. P12 Multiply and divide Integers Find each product or quotient. 1.) 2.) 3.) 4.)

  45. Example 4 pg. P12 Multiply and divide Integers Find each product or quotient. 1.) 2.) 14 3.) 121 4.)

  46. 0-3 pg. P12 1-23

  47. 0-4 Adding and Subtracting Rational Numbers

  48. Example 1 pg. P13 Compare Rational Numbers Replace ___ with or to make ___ a true statement.

  49. Example 1 pg. P13 Compare Rational Numbers Replace ___ with or to make a true statement.

  50. Example 2 pg. P13 Order Rational Numbers Order and from least to greatest.

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