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1.6

Multiplying Whole Numbers and Area. 1.6. Multiplying Whole Numbers. Multiplication is repeated addition but with different notation. 6 + 6 + 6 + 6 + 6 = The  is called a multiplication sign. Properties. Multiplication Property of 0 The product of 0 and any number is 0. For example,

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1.6

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  1. Multiplying Whole Numbers and Area 1.6

  2. Multiplying Whole Numbers Multiplication is repeated addition but with different notation. 6 + 6 + 6 + 6 + 6 = The  is called a multiplication sign.

  3. Properties Multiplication Property of 0 The product of 0 and any number is 0. For example, 5  0 = 0 and 0  8 = 0. Multiplication Property of 1 The product of 1 and any number is that same number. For example, 1  9 = 9 and 7  1 = 7.

  4. Properties Commutative Property of Multiplication Changing the order of two factors does not change their product. For example, 4  3 = 12 and 3  4 = 12. Associative Property of Multiplication Changing the grouping of factors does not change their product. For example, (2  3)  4 = 2  (3  4).

  5. Properties Distributive Property Multiplication distributes over addition. For example, 2(3 + 4) = 2 3 + 2  4 Rewrite 4(5 + 6) using the distributive property. 4(5 + 6) =44 = 4 5 + 4  6

  6. Multiplying Whole Numbers Example: Use the distributive property to multiply 3 and 79. Write 79 in expanded form. Apply the Distributive Property. Multiply. Add.

  7. Multiplying Whole Numbers Example: Multiply 624 by 3.

  8. Multiplying Whole Numbers Practice Problem 3 Multiply. Carry the two. a. 4(3) = 12 and 12 + 2 = 14 b. Carry the two. Carry the one. 9(3) = 7 and 7 + 1 = 8 9(1) = 9 and 9 + 2 = 11 p. 50

  9. Multiplying Whole Numbers Example: Multiply 91 by 72.

  10. Multiplying Whole Numbers Practice Problem 4 Multiply. a. 2(594) = 1188 7(594) = 4158 Add. b. 1(306) = 306 8(306) = 2448 Add. p. 50

  11. Multiplying Whole Numbers Ending in Zero(s) Example: Multiply 3 by 9000. 3  9000 = 3  9 1000 = (27)  1000 = 27,000

  12. 12 inches 4 inches Finding the Area of a Rectangle EXAMPLE Find the area of the following rectangle. SOLUTION inches inches square inches

  13. Solving Problems by Multiplying

  14. Example A particular color printer can print 21 pages per minute. How many pages can it print in 25 minutes? Pages per minute  Number of minutes = 21  25

  15. Dividing Whole Numbers 1.7

  16. Dividing Whole Numbers The process of separating a quantity into equal parts is called division.

  17. Properties of 1 Division Properties of 1 The quotient of any number (except 0) and that same number is 1. For example, The quotient of any number and 1 is that same number. For example,

  18. Properties of 0 The quotient of 0 and any number (except 0) is 0. For example, The quotient of any number and 0 is not a number. We say that are undefined.

  19. Example Divide: 3705 ÷ 5

  20. Solving Problems by Dividing Example Find the quotient of 78 and 5.

  21. Solving Problems by Dividing Example Practice Problem 4 a Practice Problem 5 a Practice Problem 6 a Practice Problem 6 b Practice Problem 8 Practice Problem 9 p. 63-66

  22. Example Divide: 51,600 ÷ 403 = 128 R 16

  23. Solving Problems by Dividing

  24. Example Books are being packed 12 to a box. If there are 1344 books to be packed how many boxes will be used? = 1344 ÷ 12 = 112 boxes will be used

  25. Solving Problems by Dividing Example Marina, Manual, and Min bought 120 high-density computer diskettes to share equally. How many diskettes did each person get? Calculators can be packed 24 to a box. If 497 calculators are to be packed but only full boxes are shipped, how many full boxes will be shipped? How many calculators are left over and not shipped? p. 67-68

  26. Finding Averages The average of a list of numbers is the sum of the numbers divided by the number of numbers.

  27. An Introduction to Problem Solving 1.8

  28. Addition, Subtraction, Multiplication, or Division

  29. Problem-Solving Steps

  30. Example There are 24 hours in a day. How many hours are in a week? TRANSLATE the problem. 24  7 = 168 hours Lets see if our answer is reasonable by estimating. 20  10 = 210 hours The answer is reasonable since 168 is close to our estimated answer of 210. There are 168 hours in a week.

  31. Example Practice Problem 1 1. UNDERSTAND the problem. The Bank of America Building is the second-tallest building in San Francisco, California, at 779 feet. The tallest building in San Francisco is the Transamerica Pyramid, which is 74 feet taller than the Bank of America Building. How tall is the Transamerica Pyramid? SOLUTION 2. TRANSLATE the problem. 3. SOLVE the problem. CHECK Subtract the difference of 74 from the solution of 853. • INTERPRET the results. • The tallest building is 853 feet. p. 75

  32. Example Practice Problem 2 1. UNDERSTAND the problem. Four friends bought a lottery ticket and won $65,000. If each person is to receive the same amount of money, how much does each person receive? SOLUTION 2. TRANSLATE the problem. 3. SOLVE the problem. CHECK Multiply the solution by 4. • INTERPRET the results. • Each of the four friends will receive $16,250 p.76

  33. Example Practice Problem 3 1. UNDERSTAND the problem. The director of the learning lab also needs to include in the budget a line for 425 blank CDs at a cost of $4 each What is this total cost for the blank CDs? SOLUTION 2. TRANSLATE the problem. CHECK Divide the solution by 4. • INTERPRET the results. • The budget needs a line for CDs for $1,700. p.77

  34. Example Practice Problem 4 1. UNDERSTAND the problem. In 2008, the average salary of a public school teacher in Alaska was $56,758. For the same year, the average salary for a public school teacher in Hawaii was $3358 less than this. What was the average public school teacher’s salary in Hawaii? SOLUTION 2. TRANSLATE the problem. CHECK Add $3,358 to the solution. • INTERPRET the results. • The average public school teacher’s salary in Hawaii is $53,400. p.77

  35. Using More Than One Operation Find the total cost of 10 computers at $2100 each and 7 boxes of diskettes at $12 each. Example: The total cost is $21,084.

  36. Using More Than One Operation Practice Problem 5 1. UNDERSTAND the problem.A gardener is trying to decide how much fertilizer to buy for his yard. He knows that his lot is in the shape of a rectangle that measures 90 feet by 120 feet. He also knows that the floor of his house is in the shape of a rectangle that measures 45 feet by 65 feet. How much area of the lot is not covered by the house? SOLUTION 2. TRANSLATE the problem. 3. SOLVE the problem. 4. INTERPRET the problem. Needs to buy fertilizer for 7875 sq ft. p.79

  37. Exponents, Square Roots, and Order of Operations 1.9

  38. Using Exponential Notation 85 In the product 3  3  3  3  3, notice that 3 is a factor several times. The exponent, 5, indicates how many times the base, 3 is a factor.

  39. Using Exponential Notation 85 “three to the second power” or “three squared.” “three to the third power” or “three cubed” “three to the fourth power”

  40. Examples p 85 Evaluate. 1. 92 2. 45 3. 5  32 = 9  9 = 81 = 4  4  4  4  4 = 1024 = 45 = 5  3  3

  41. Examples Write using exponential notation. Practice Problem 1 Practice Problem 2 Practice Problem 3 Practice Problem 4 Evaluate. Practice Problem 5 Practice Problem 6 Practice Problem 7 Practice Problem 8 p. 85

  42. Evaluating Square Roots 86 A square root of a number is one of two identical factors of the number.

  43. Examples 86 Find each square root. 1. 2. 3.

  44. Examples Find each square root. Practice Problem 9 Practice Problem 10 Practice Problem 11 p.86

  45. Using the Order of Operations 87 Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars or square roots, starting with the innermost set. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right.

  46. Example Simplify: p 87

  47. Example Practice Problem 12 Evaluate . SOLUTION Multiply 9 by 3 Divide 8 by 4 Subtract 2 from 27 p 87

  48. Example Simplify: p 88

  49. Example Simplify: p 88

  50. Example Practice Problem 13 Evaluate . SOLUTION Write 22 as 4 Divide 48 by 3 Multiply 16 by 4 p 88

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