1. Rational Numbers
5-1 to 5-7
Kane Oct 2007

2. Factors

3. Vocab…
Factor
“a” is a factor is of “b” if “a” will divide evenly into “b”
Prime number
Any number with only two factors; 1 and itself.
(Is 1 a prime?) why or why not?
No, the number 1 only has one factor:1*1=1
The first 5 prime numbers are:
Composite number
Any whole number with more than 2 factors.

4. Find all the prime numbers between 1-100
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
11, 12, 13, 14, 15, 16, 17, 18, 19, 20
21, 22, 23, 24, 25, 26, 27, 28, 29, 30
31, 32, 33, 34, 35, 36, 37, 38, 39, 40
41, 42, 43, 44, 45, 46, 47, 48, 49, 50
51, 52, 53, 54, 55, 56, 57, 58, 59, 60
61, 62, 63, 64, 65, 66, 67, 68, 69, 70
71, 72, 73, 74, 75, 76, 77, 78, 79, 80
81, 82, 83, 84, 85, 86, 87, 88, 89, 90
91, 92, 93, 94, 95, 96, 97, 98, 99, 100

5. Practice Tell if each number is prime or composite: Ex1: 36 Ex2: 81

6. Vocab (operations) Prime factorization
Writing a number as the product of prime numbers
ie: the prime factorization of 20 = 2*2*5
Greatest Common Factor (GCF)
The largest factor that any two composite numbers have in common.

7. Examples: Prime Factorization (find the prime factorization of each number)
Ex5: Ex6:

8. Examples: Find the GCF Ex7: Find the GCF of 60 and 72
Find the prime factorization of each number
Find the common factors:
60:
72:
Find the product of the common factors:

9. Rational Numbers
Chapter
5-2

10. Vocabulary Rational Number Simplest form
Any number that can be written as a fraction
Simplest form
When the GCF of the numerator and the denominator is the number 1.

11. Ez-xamples Ex1 write 54/60 in simplest form.
To simplify completely divide both numbers by their GCF
54 = 2*3*3*3
60 = 2*2*3*5
Or just divide by factors that you know.
The GCF is 6

12. Ex2: Change the fraction from a mixed number to an improper fraction.
Step 1: multiply the whole number by
the denominator.
Step 2: Add the numerator to the product
of the whole number and the denominator.
Step 3: Put the new sum over the original
denominator

13. Equivalent Fractions
Ex3: to come up with fractions with equal value multiply the original fraction by any number over itself.

14. Equivalent Fractions and Decimals
The decimal equivalent for these fractions is??
Chapter 5 - 3

15. Vocab! Terminating Decimal Any decimal that ends Repeating Decimal
a decimal that has a repeating pattern.

16. Writing Fractions as Decimals
Ex1: Billy just started playing baseball. After a few games he started to think he was pretty good. In 8 games he got up to bat 20 times. Of those times he got a hit 9 times. What is his batting average?

17. Decimal to Fraction
Ex2: to turn a decimal into a fraction put the number over the place value and simplify
.025 is 25 thousandths or

18. Repeated Decimals
Ex3: The rules are a little different when dealing with repeated decimals. To change a repeated decimal to a fraction use the line-9 rule.
Step 1: figure out how many digits are in the repeated pattern. In this case it is 2.
Step 2: take the repeated pattern and set it as the numerator of a fraction
Step 3: Count the number of decimal places the pattern takes up.
Put the numerator over that many 9s. For example if it just the tenths place
only use one 9, if it is the hundredths use two 9s and so on.
.45 goes to the hundredths place so we will only need two 9s 99
Step 4: simplify!

19. Least Common Multiple
Chapter 5 - 4

20. Vocab…
Multiple:
Any number you can get by multiplying two numbers together.
ie: 5*4 = 20 so 20 is a multiple of both 4 and 5
Least Common Multiple (LCM)
The first multiple that any two numbers have in common.
Least common denominator
The LCM of the denominators, of two or more fractions.

21. Examples!! Ex1: Find the LCM of 36 and 30
-step 1: prime factor each #.
-step 2: select the largest version of each factor.
-step 3: multiply out each of the selected factors
180 is the LCM

22. In order to compare rational numbers (fractions) give them common denominators.
Ex2: put in numerical order
step 1: find the LCM of the denominators
step 2: change both fractions so they have a denominator of 48
and 15 16

23. Ex3: put the numbers .053, .38, and .275 becomes
To compare decimals make sure that they all have the same number of decimal places. Hint: line up decimal points & fill empty spaces with zeros (0s)
Ex3: put the numbers .053, .38, and .275
becomes

24. What if you have a decimal and a fraction??
Ex4: compare 0.32 and 5/16
You have to make them both either fractions or both decimals.
(Hint): It is usually easier to turn the fractions into a decimal.
we compare
Therefore

25. Adding and Subtracting Like Fractions
Chapter 5 - 5

26. What is the rule for adding and subtracting like fractions??
Ex1:
Ex2:

27. Adding and Subtracting Unlike Fractions
Chapter 5 - 6

28. What is the rule for adding and subtracting unlike fractions?
Ex1: -7 12

29. Ex2:

30. Multiplying and Dividing Rational Numbers
Chapter 5-7

31. Multiply: make sure all mixed numbers are changed to improper fractions
Multiply straight across the top and straight across the bottom, then simplify
Ex1: SIMPLIFY

32. Rules for Dividing Step 1: take the reciprocal of the second fraction
Step 2:change division to multiplication
Step 3: multiply across
Ex2: becomes

33. Scientific Notation
Chapter 2
Section 11

34. Vocab… Scientific Notation
When a very large or very small number is written as a product of two factors.
The first number must be greater than or equal to 1 but less than ten.
The second number must be a power of ten (10x)

35. Vocab…
Standard Form
Normal number format. The same as we are used to seeing

36. For these examples change the scientific notation to standard form.
Ex 1: 2.63 X 106
2.63 X 1,000,000
2,630,000
Ex 2: 8.9 X 104
8.9 X 10,000
89,000

37. Examples For these examples change standard notation to scientific notation
Is really
259,000,000.0
To get a number greater than 1 and less than 10 move the decimal left 8 times
2 59,000,000.0
Because we moved the decimal 8
spaces the power of 10 will be 108
2.59 X 108 .