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Representing Multiplying Fractions

Representing Multiplying Fractions. 7.2E Simplify numerical expressions involving order of operations and exponents. Mr. Brewer’s 7 th Grade Math October 26-30, 2009. 7.2A Represent multiplication and division situations involving fractions with models, pictures, words, and numbers.

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Representing Multiplying Fractions

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  1. Representing Multiplying Fractions 7.2E Simplify numerical expressions involving order of operations and exponents. Mr. Brewer’s 7th Grade Math October 26-30, 2009 7.2A Represent multiplication and division situations involving fractions with models, pictures, words, and numbers. Order of Operations

  2. Use a rectangle to graphically multiply two fractions. 1 1 2 First, shade in of the rows. 3 X 3 5

  3. Use a rectangle to graphically multiply two fractions. 2 1 2 Next, shade in of the columns. 5 X 3 5 Now find the intersection.

  4. Use a rectangle to graphically multiply two fractions. Now, write the fraction for the intersecting squares. 1 2 X 3 5 2 15

  5. Use a rectangle to graphically multiply two fractions. 1 First, shade in of the rows. 1 1 4 X 4 2

  6. Use a rectangle to graphically multiply two fractions. 1 Next, shade in of the columns. 1 1 2 X 4 2 Now find the intersection.

  7. Use a rectangle to graphically multiply two fractions. Now, write the fraction for the intersecting squares. 1 1 X 4 2 2 1 = 16 8

  8. Which model best represents this expression: 2 1 X 3 2

  9. 1 ÷ 4 Which model best represents this expression: 3

  10. Which model best represents this expression: 3 3 X 4 5

  11. 1 1 Which model best represents this expression: X 5 3

  12. Order of Operations A standard way to simplify mathematical expressions and equations. For example: 8 + 3 X 4 = 11 X 4 = 44 …or does it equal 8 + 3 X 4 = 8 X 12 = 20

  13. Order of Operations • Simplify within Grouping Symbols ( ), { }, [ ], | |, Fraction Bars • Simplify Exponents • Complete Multiplication and Division from Left to Right • Complete Addition and Subtraction from Left to Right

  14. 8 + 3 - 5

  15. 5 X 8 – 3 X 4

  16. 5 + 8 ÷ 2 X 4

  17. 12 ÷ 3 + 4 x 6 – 4 x 3

  18. 6 6 ÷ 6 + 6 ÷ 6

  19. Representing Squares & Square Roots 7.2E Simplify numerical expressions involving order of operations and exponents. Mr. Brewer’s 7th Grade Math October 26-30, 2009 7.1C Represent squares and square roots using geometric models. Order of Operations

  20. Squares and Square Roots The square of a number is the product of a number and itself. Ex. The square of 4 is 16, because 4 X 4 = 16. The square of 4 can be written as 4 = 16. This expression is read “Four squared equals 16. 2 The square root of a number is the is the number that you can square to get the original number. Ex. A square root of 36 is 6, because 6 X 6 = 36. The symbol for square root is . The square root of 36 is written as 36 and is read “the square root of 36.”

  21. You can use grids to model the square and square root of a number. This grid represents 5 = 25 2

  22. Which grid represents 4 = 16? 2

  23. Look for the square! Which group of objects represents a square?

  24. What does each grid represent?

  25. Which square root is represented by one side of the model below?

  26. Which square root is represented models below?

  27. Order of Operations • Simplify within Grouping Symbols ( ), { }, [ ], | |, Fraction Bars • Simplify Exponents • Complete Multiplication and Division from Left to Right • Complete Addition and Subtraction from Left to Right

  28. What is are Grouping Symbols? • Grouping symbols are symbols that separate parts of an equation from other parts of an equation. 5(3 – 3 x 3) x 4 5 + 3 – 3 x {3 x 4} 5 + [3 – 3 x 3] x 4

  29. What is an Exponent? • An exponent is a little number high and to the right of a regular or base number. Exponent 3 4 Base

  30. What an Exponent Represents • An exponent tells how many times a number is multiplied by itself. 4 = 3 x 3 x 3 x 3 3

  31. Reading Exponents • This exponent is read three to the 3rd power or three cubed. Exponent 3 3 Base

  32. Read These Exponents 3 2 6 5 2 7 3 4

  33. What is the Exponent? 2 x 2 x 2 = 2

  34. What is the Exponent? 5 x 5 x 5 x 5 = 5

  35. What is the Base and the Exponent? 3 x 3 =

  36. What is the Base and the Exponent? 9 x 9 =

  37. What is the Expanded Form? 8 = 4

  38. What is the Expanded Form? 7 = 5

  39. Multiplying Exponents Out 4 3 = 3 x 3 x 3 x 3 9 27 81

  40. 2 8 x (5 - 3)

  41. 5(8 – 3) x 4

  42. (4 + 8) ÷ (2 + 2)

  43. 12 ÷ 3 + 4 6 – 4 3

  44. 2 4(6-3)

  45. 2 8 x (3 + 5)

  46. 2 5(3 – 3 x 3) x 4

  47. 2 + 3 + 3 + 25 ÷ 5 2

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