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Chapter 1

Chapter 1. Sets of Numbers. The set of Natural Numbers is {1,2,3,…} The set of Whole Numbers is {0,1,2,3,…}. Using a Number Line. Ordering Numbers. a >b if a lies to the right of b on the number line. a < b if a lies to the left of b on the number line.

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Chapter 1

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  1. Chapter 1

  2. Sets of Numbers • The set of Natural Numbers is {1,2,3,…} • The set of Whole Numbers is {0,1,2,3,…}

  3. Using a Number Line

  4. Ordering Numbers • a >b if a lies to the right of b on the number line. • a < b if a lies to the left of b on the number line.

  5. Reading Bar Graphs

  6. Reading Line Graphs

  7. Rounding Whole Numbers • Locate the digit in the place you are rounding to (called the rounding digit). • Look at the digit to the right of the rounding digit (called the test digit). • If the test digit is 5 or greater, round up by adding 1 to the rounding digit and changing all the digits to the right of the rounding digit to 0. • If the test digit is less than 5, round down by keeping the rounding digit the same and changing all of the digits to the right of the rounding digit to 0.

  8. Examples • Round 63,427 to the nearest hundred. • Round 76,003 to the nearest ten thousand. • Round 1,259,561 to the nearest thousand.

  9. Definition A variable is a letter that is used to stand for a number.

  10. Important Properties of Addition • Commutative Property of Addition. If a and b are numbers, then a + b = b + a • Associative Property of Addition. If a, b, and c are numbers, then (a + b) + c = a + (b + c) • Addition Property of 0. If a is any number then a + 0 = a.

  11. Notation

  12. Interpreting Bar GraphsWhat is the total annual rainfall?

  13. Notation

  14. Definition The change in going from a to b is given by b - a

  15. Interpreting Line GraphsWhat was the change in the value of the Dow Jones Average for the day?

  16. Geometry • A square is a four-sided figure whose sides are equal and meet at right angles. • The perimeter of a square is the total sum of the lengths of the four sides. P = s + s + s + s • A rectangle is a four-sided figure whose opposite sides are equal and meet at right angles. • The perimeter of a rectangle is the total sum of the two lengths and two widths. P = l + l + w + w

  17. Examples • Find the perimeter of a square whose side is 4 inches. • Find the perimeter of a rectangle whose length is 6 feet and width is 3 feet.

  18. Examples Suppose you want to put a redwood border around your rectangular garden. If the length of the garden is 25 feet and the width is 12 feet, what is the minimum length of redwood edging that you need to buy?

  19. The Meaning of Multiplication

  20. Notation

  21. Important Properties of Multiplication • Commutative Property of Multiplication. If a and b are numbers, then a x b = b x a • Associative Property of Multiplication. If a, b, and c are numbers, then (a x b) x c = a x (b x c)

  22. Important Properties of Multiplication • Multiplication Property of 0. If a is any number, then a x0 = 0 • Multiplication Property of 1. If a is any number, then a x 1 = a

  23. The Meaning of Division

  24. Notation

  25. Multiplication and Division

  26. Important Properties of Division

  27. Important Properties of Division

  28. Division by Zero

  29. Definition An exponent is used to indicate repeated multiplication. The exponent tells how many times the base is used as a factor.

  30. Definition

  31. Geometry The AREA of a square whose side is s is given by the formula

  32. Geometry The AREA of a rectangle whose length is L and width is W is given by the formula A = L W

  33. Examples Find the area of a square whose side is 6 feet. Find the area of a rectangle whose length is 5 feet and width is 4 feet.

  34. Estimation Estimation is used to find an approximate answer to a problem. One method of estimating a solution is to use Front End Rounding. In this case each number is rounded to its largest place value.

  35. Example Use Front End Rounding to estimate the sum 3,714 + 2,489 + 781 + 5,500 + 303.

  36. Definition Numbers that are used in a multiplication are called FACTORS.

  37. Definition To Factor a number means to rewrite the number as a product of other numbers.

  38. Definition A Prime Number is a whole number greater than 1 that can only be divided by 1 and the number itself. What are the first ten prime numbers?

  39. Definition Any whole number greater than 1 that is not a prime number is called a composite number.

  40. Definitions Any whole number that is divisible by two is an even number. Any whole number that is not divisible by two is an odd number.

  41. Definition To find the PRIME FACTORIZATION of a number means to write the number as a product of prime numbers. Example: Find the prime factorization of 36

  42. BIG DEAL The Fundamental Theorem of Arithmetic: Any composite number has exactly one set of prime factors. This factorization is unique.

  43. Factor the following into a product of prime numbers

  44. Bob said Paul is tall. Bob, said Paul, is tall

  45. Order of Operations AgreementPEMDAS • Parentheses first. • Exponents • Multiplication or • Division • Addition or • Subtraction • Similar operations are done from left to right.

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