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Mastering Algebraic Expressions and Real Numbers

Learn operations with real numbers, simplify algebraic expressions, and follow order of operations. Understand variables, constants, powers, and roots.

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Mastering Algebraic Expressions and Real Numbers

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  1. Math 71A 1.1 – Algebraic Expressions and Real Numbers 1.2 – Operations with Real Numbers and Simplifying Algebraic Expressions

  2. Order of Operations • 1. Parentheses(in general, grouping symbols: , , , , ) • 2. Exponents(and roots and absolute values) • 3. Multiplication/division(from left to right) • 4. Addition/subtraction(from left to right)

  3. ex:

  4. ex: Evaluate for .

  5. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex:

  6. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex: variable

  7. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex: variable

  8. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex: variable constant

  9. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex: variable constant # of months in a year

  10. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex: variable constant # of months in a year

  11. A letter used to represent various numbers is called a _________________. ex: A letter used to represent a particular number is called a _________________. ex: variable constant # of months in a year

  12. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex:

  13. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex: algebraic expression

  14. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex: algebraic expression , ,

  15. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex: algebraic expression , , equation

  16. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex: algebraic expression , , equation

  17. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex: algebraic expression , , equation

  18. The combination of variables, constants, numbers, , , , , powers, roots, etc. is called an _____________________________. • ex: • Two algebraic expressions with an equal sign in between is called an ________________________. • ex: algebraic expression , , equation

  19. Absolute Value The absolute value bars make the number inside positive. ex:

  20. Absolute Value The absolute value bars make the number inside positive. ex:

  21. Absolute Value The absolute value bars make the number inside positive. ex:

  22. Absolute Value The absolute value bars make the number inside positive. ex:

  23. Absolute Value The absolute value bars make the number inside positive. ex:

  24. Addition When adding same signs, we ___________, and when adding opposite signs, we ____________. ex:

  25. Addition When adding same signs, we ___________, and when adding opposite signs, we ____________. ex: add

  26. Addition When adding same signs, we ___________, and when adding opposite signs, we ____________. ex: add subtract

  27. Addition When adding same signs, we ___________, and when adding opposite signs, we ____________. ex: add subtract Keep same sign

  28. Addition When adding same signs, we ___________, and when adding opposite signs, we ____________. ex: add subtract Keep same sign Keep sign of

  29. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if .

  30. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if . additive inverses

  31. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if . additive inverses

  32. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if . additive inverses

  33. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if . additive inverses

  34. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if . additive inverses

  35. Addition Properties 1. 2. Note: and are called ___________________. ex: The additive inverse of is __________. ex: The additive inverse of is ___________. ex: Find if . additive inverses

  36. Subtracting We can define subtraction in terms of addition: ex:

  37. Subtracting We can define subtraction in terms of addition: ex:

  38. Subtracting We can define subtraction in terms of addition: ex:

  39. Subtracting We can define subtraction in terms of addition: ex:

  40. Subtracting We can define subtraction in terms of addition: ex:

  41. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex:

  42. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same

  43. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive

  44. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite

  45. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative

  46. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative

  47. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative

  48. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative

  49. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative

  50. Multiplying When multiplying ___________signs, the result is _________________. When multiplying ___________ signs, the result is _________________. ex: same positive opposite negative

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