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Pre-Algebra

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  1. Pre-Algebra Chapter 3: Number Theory

  2. Chapter Project – 50 points • You will work in groups of 2. • You will research on the internet 3 baseball players. You will track their abilities, using a provided worksheet. • Due at the end of the chapter: _____NOV 24th __

  3. Schedule of Events

  4. Goals for Learning • To identify divisible numbers • To tell prime numbers from composite numbers • To find the greatest common divisor • To use the distributive property to multiply or factor expressions • To find the least common multiple • To use scientific notation for large and small numbers

  5. Lesson 1 – Divisibility Rules • Vocabulary – • Divisible – able to be divided by a whole number with no remainder • Rules: • Divisibility by 2: if the last digit is an even number:0,2,4,6,8 • Divisibility by 3: the sum of the digits is divisible by 3. • Divisibility by 4: last 2 digits divisible by 4. • Divisibility by 5: the last digit is 0 or 5. • Divisibility by 6: if its divisible by 2 or 3. • Divisibility by 8: last 3 digits divisible by 8. • Divisibility by 9: the sum of the digits is divisible by 9. • Divisibility by 10: last digit is 0.

  6. Practice In the textbook, you will notice that they write the statements just like below. 2|12 - this is asking….is 12 divisible by 2?

  7. Homework • Lesson 1 cont. • Homework: Pg 63 #1-20

  8. Lesson 2 – Prime and Composite Numbers • Vocabulary – • Prime – a whole number greater than one that has only 1 and itself as factors • Composite – a whole number that is not a prime number, or who has more than 2 factors.

  9. More Information… • The numbers 0 and 1 are neither prime nor composite. • All even numbers are divisible by two and so all even numbers greater than two are composite numbers. • All numbers that end in five are divisible by five. Therefore all numbers that end with five and are greater than five are composite numbers.

  10. Finding Prime/Composite Numbers: Using a 1-50 chart.

  11. Finding Prime/Composite Numbers: Using Prime Factorization

  12. Homework • Lesson 2 – Prime and Composite Numbers • Homework: Worksheet 24

  13. Lesson 3 – Greatest Common Factor • Vocabulary – • Common Factor – a number that will divide each of two or more number with no remainder • Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) – the largest factor of two or more numbers or terms

  14. Finding the GCD/GCF • Step 1: Find all of the factors. • Step 2: Circle all of the common factors. • Step 3: Choose the GREATEST common factor. • Example: (9,24) • Example 2: (12x, 60x) • Example 3: (18y, 36)

  15. Homework: • Lesson 3: Greatest Common Factor • Homework: Pg. 67 #1-15

  16. Lesson 4 – Factoring • Vocabulary – • Distributive Property – numbers within parenthesis that can be multiplied by the same factor • Examples: • 2(9+2) = • 4r(2-1) = • 3(a+3b-4c)=

  17. Few more examples: • 2(4+3)= • 2(x+5)= • 8(4m+4)=

  18. Factoring Terms • Step 1: List the factors, and find the GCF. • Step 2: Write the GCF outside the parenthesis. • Step 3: Determine what factors will make the original statement true. • Factor: 4x+6. • Factor: 3x+3y. • Factor: ab+ac. • Factor: 4x+7y.

  19. Few more examples: • 9c+3 = • 12y+20= • 6h+36 = • 14m+28k= • 5s+20 = 5(s+__________) • 2c+22d = _____(c+11d) • 7p+28 = 7(_________+4)

  20. Homework: • Lesson 4: More on Factoring • Pg. 70-71 #2-30 even

  21. Lesson 5 – Least Common Multiple • Vocabulary – • Least Common Multiple (LCM) – the smallest number divisible by all numbers in a group. • Multiples are like counting by numbers… • For Example: 2 - M2 – 2,4,6,8,10,12,14,16,18,20, etc. • What are the M5? • M10? • What is the common multiple of (4,9)?

  22. Cont. • LCM of (3,63) • LCM of (9,6) • LCM of (54,120)

  23. Vocabulary Cont… • Prime Factorization – an expression showing the prime factors of a number • Step 1: Construct a factor tree. (54,120) • Step 2: Identify the greatest power of each prime number. • Step 3: Multiply the greatest primes.

  24. More Examples: • LCM (18, 55, 125)

  25. Cont. • LCM (16, 21, 32)

  26. Homework: • Lesson 5 – Least Common Multiple • Pg. 74 #1-12

  27. Lesson 6 – Scientific Notation • Vocabulary – • Scientific Notation – a number written as the product of a number between 1 and 10 and a power of 10. • What is power of 10? Does anyone remember? • What about exponents?

  28. Rules: • When changing a WHOLE NUMBER to a number between 1 and 10, place the decimal point behind the last digit and move the decimal point to the LEFT. • When changing a DECIMAL NUMBER to a number between 1 and 10, move the decimal point to the RIGHT. • 3,500 • 0.073 • 83,000 • 0.00065 • 0.0078 • 768,000

  29. Writing in Scientific Notation • Step 1: Change you number to a number between 1 and 10. • Step 2: Add the power of 10. • If you added a decimal point, your exponent will be positive. • If you moved a decimal point already present, your exponent will be NEGATIVE. • 24,000 • 606,000,000 • 0.00347 • 517,000,000,000 • 0.000438 • 84,000,000,000 • 0.0000947 • 0.000000346

  30. Homework: • Lesson 6 – Scientific Notation • Pg. 77 #1-25

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