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Lesson 5

Lesson 5. ACT Prep II. Properties of Natural Numbers and Basic Statistics . Assignment. Get out a sheet of paper Record definitions, and complete problems on this paper. SHOW WORK! Turn in at the end of the hour. A. Divisors and Factors.

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Lesson 5

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  1. Lesson 5 ACT Prep II. Properties of Natural Numbers and Basic Statistics

  2. Assignment • Get out a sheet of paper • Record definitions, and complete problems on this paper. SHOW WORK! • Turn in at the end of the hour.

  3. A. Divisors and Factors Divisor – A divisor of a number is any number which will divide it evenly. EX) 10 is a divisor of 30, since 30/10 = 3 Factors – the factors of a number are all the numbers which divide into it evenly EX) The factors of 50 are: 1, 50, 2, 25, 5, 10

  4. A. The Divisor Test

  5. A. The Divisor Test Using the divisor test, determine what number (between 2-9) is a divisor of the given number. Note: some may have more than one divisor, name them all! 1) 1064 2) 1665 3) 1667 4) 3534

  6. B. Prime, Composite, and Unit ACT Definitions: Unit – The number 1 Prime – any number divisible by 1 and itself Composite – numbers with more than 2 factors

  7. 2. Prime Factorization What is prime factorization? Ex) Use a factor tree to determine the prime factorization of 72

  8. Try These Problems • Determine all the factors of 120 • Write the prime factorization of 100 • Find the least common multiple (LCM) of the following. • 12, 32 b) 8, 50, 120 c) d)

  9. C. Basic Probability and Statistics • Probability P = the number of ways it could occur the total number of possible occurrences Ex1) If there are 10 red balls, 3 green balls, and 2 blue balls in a jar, what is the probability that a green ball will be chosen? Ex2) A die has 6 faces numbered 1 to 6. What is the probability of rolling a 4?

  10. 2. The arithmetic mean (average) Ex1) Find the average of 10, 12, and 23 Ex2) A student needs to average 80% on 5 tests to get a B. If the first 4 tests were 70, 75, 86, and 84, what does this student need on the 5th test?

  11. 3. Median and Mode Median – the middle data point when the numbers are arranged from least to greatest. Note: If there are 2 middle points, find the average of those two Mode – the value that occurs the most Hint: MOde = MOst Note: the might be no mode or multiple modes

  12. Median and Mode cont. Find the median and mode of the following set of numbers { 3, 8, 9, 10, 15, 15}

  13. 4. Counting Problems Whenever you have to count how many ways to make a series of choices do the following: • Determine how many choices have to be made and put down a blank for each choice • Fill in each blank with the number of ways that a choice can be made • Multiply the numbers together

  14. 4. Counting Problems Ex2) How many different sandwiches consisting of one cheese, one meat, and one bread can be made from a choice of 4 cheeses, 3 meats, and 5 breads?

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