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1.1 Whole Number Operations

1.1 Whole Number Operations. See handout. Addition/Subtraction – On Your Own. Find the value of the expression. Use estimation to check your answer. Multiplication – On Your Own. Find the value of the expression. Use estimation to check your answer. Division – On Your Own.

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1.1 Whole Number Operations

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  1. 1.1 Whole Number Operations • See handout

  2. Addition/Subtraction – On Your Own • Find the value of the expression. Use estimation to check your answer.

  3. Multiplication – On Your Own • Find the value of the expression. Use estimation to check your answer.

  4. Division – On Your Own • Find the value of the expression. Use estimation to check your answer.

  5. Division – On Your Own • Find the value of the expression. Use estimation to check your answer.

  6. Division – On Your Own Find groups means divide!

  7. 1.2 Powers and Exponents

  8. Power – On Your Own • Power: a product of repeated factors Write the product as a power:

  9. Base and Exponent – On Your Own • Base of a power: the repeated factor • Exponent of a power: the number of times the base is used as a factor Find the value of the power:

  10. Perfect Square – On Your Own • Perfect square: the square of a whole number 9 = 32, so 9 is a perfect square. Determine whether the number is a perfect square:

  11. 1.3 Order of Operations • Numerical expression: an expression that contains only numbers and operations • Evaluate: to find the value • Order of Operations: • Parentheses • Exponents • Multiplication and Division left to right • Addition and Subtraction left to right 1.3 Notes

  12. Using Order of Operations to Evaluate a Numerical Expression 1.1

  13. 1.4 Prime Factorization • Factor tree: a diagram that splits whole numbers into factor pairs until all factors are prime Factor tree for 60 • Draw a factor tree for 24

  14. Factor Pairs - On Your Own • Factor pair: a pair of numbers that are factors of a product Factor pairs for 12: 1, 12 (1 x 12 = 12) 2, 6 (2 x 6 = 12) 3, 4 (3 x 4 = 12) List the factor pairs of the number:

  15. Prime Factorization - On Your Own • Prime factorization: a composite number written as a product of its prime factors The prime factorization of 60: Write the prime factorization of the number:

  16. Prime Factorization - On Your Own What is the greatest perfect square that is a factor of 1575?

  17. 1.5 Greatest Common Factor • Common factors: factors that are shared by two or more numbers • Greatest common factor: the greatest of the common factors Find the GCF of 24 and 40 using common factors:

  18. Finding GCF Using Prime Factorization Find the GCF of 12 and 56 using prime factorization: The GCF is 4.

  19. Using GCF to Find the Greatest Number of Equal-sized Groups • You have 24 roses and 36 tulips. What is the greatest number of identical flower arrangements you can make? 24 = 2 ∙ 2 ∙ 2 ∙ 3 36 = 2 ∙ 2 ∙ 3 ∙ 3 The common factors are 2, 2, and 3. The greatest number of identical arrangements is 2 ∙ 2 ∙ 3 = 12

  20. Notes 1.6: Least Common Multiple • Common multiples: multiples that are shared by two or more numbers List the common multiples of 4 and 6: • Least common multiple: the least of the common multiples

  21. Finding LCM Using Prime Factorization Find the LCM of 16 and 20 Write what they have in common: 2 ∙ 2 Write the remaining prime factors: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 Multiply: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 = 80 80 is the LCM of 16 and 20.

  22. Finding the LCM of Three Numbers Find the LCM of 4, 15, and 18: Write what two or three of the trees have in common: 2 ∙ 3 Write the remaining prime factors: 2 ∙ 3 ∙ 2 ∙ 3 ∙ 5 Multiply. 2 ∙ 3 ∙ 2 ∙ 3 ∙ 5 = 180 180 is the LCM of 4, 15, and 18.

  23. Using LCM to Find When Two Things Happen at Same Time

  24. On Your Own • A traffic light changes every 30 seconds. Another changes every 45 seconds. Both lights change. After how many seconds will both change at the same time? Find LCM of 30 and 45 by listing multiples: 30, 60, 90, … 45, 90, … The lights will change at the same time in 90 seconds (or one and a half minutes).

  25. Finding GCF and LCM using Inverted Division

  26. Notes 1.6 Extension: Adding and Subtracting Fractions • Least common denominator: the LCM of the denominators • To add and subtract fractions with unlike denominators: • Use a common denominator, simplify at end • Use the least common denominator

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