Lesson 5

ACT PrepII. Properties of Natural Numbers and

Basic Statistics

Assignment

1) Get out a sheet of paper2) Record definitions, and complete problems

on this paper. SHOW WORK!3) Turn in at the end of the hour.

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 evenlyEX) The factors of 50 are: 1, 50, 2, 25, 5, 10

A. The Divisor Test2 Check if it is even

3 Sum of the digits: if the sum is divisible by 3, so is the number

4 The last 2 digits must be divisible by 4

5 Check if the number ends in 0 or 5

6 Apply the 2 and 3 test (if it’s divisible by 2 and 3, it’s divisible by 6)

7 No easy test here

8 The last 3 digits must be divisible by 8

9 Sum of the digits: if the sum is divisible by 9, so is the number

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

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

2. Prime Factorization

What is prime factorization?

Ex) Use a factor tree to determine the prime factorization of 72

Try These Problems

1) Determine all the factors of 120

2) Write the prime factorization of 100

3) Find the least common multiple (LCM) of the following.

a) 12, 32 b) 8, 50, 120

c) d)

C. Basic Probability and Statistics

1. 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?

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?

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

Median and Mode cont.

Find the median and mode of the following set of numbers

{ 3, 8, 9, 10, 15, 15}

4. Counting Problems

Whenever you have to count how many ways to make a series of choices do the following:1. Determine how many choices have to be

made and put down a blank for each choice2. Fill in each blank with the number of ways

that a choice can be made3. Multiply the numbers together

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?