1. Chapter 2 Rational Numbers

2. Terms to Know
Divisible: a number is divisible by a second number if the number can be divided by the second number with a remainder of 0
10 is divisible by 5
5 is not divisible by 10

3. Terms to Know
Factor: an integer that divides another integer with a remainder of 0
5 is a factor of 10
10 is not a factor of 5
10 is divisible by 5, so 5 is a factor of 10

4. Terms to Know
Prime Number: A whole number greater then 1, with exactly 2 factors, 1 and itself
Are the following numbers prime?
(your divisibility rules can help you) 1 37
20724

5. Terms to Know
Composite Number: A whole number greater than 1, with more than two factors
Are the following composite numbers?
(use your divisibility rules to help you) 1 37
2724

6. Explaining why a number is prim or composite
Is prime? Explain. NO
14582 is not prime because it is divisible by 2. The number is composite.

7. Explaining why a number is prim or composite
Is 29 prime?
YES
It can only be divided by 1 and 29, therefor the number 29 is prime

8. Prime Factorization
Prime factorization: A composite number written as a product of prime numbers
To find prime factorization use a factor tree.

9. Write the prime factorization of 54
NOTE: When solved the prime factorization equals 54, the original number 54 27 2 3 9
Prime Factorization :
2·3·3·3 OR
2·33 3 3

10. Finding the GCF
Greatest Common Factor (GCF): The GCF of two or more numbers is the greatest number that is a factor of all of the numbers
Two ways of doing this…
List the factors (works great for smaller numbers)
Prime Factorization (Makes the hard numbers easier to deal with)

11. Finding GCF by Listing Find the GCF of 54 and 63 54: 63:
Greatest factor both numbers share is 9, therefor 9 is the GCF 1 2 6 9 27 54 1 3 7 9 21 63
Greatest factor both numbers share is 9, therefor 9 is the GCF

12. Find the GCF through Prime Factorization
Find the GCF of 54 and 63 54 63
54 = 2 · 3 · 3 · 3
63 = 3 · 3 · 7 9 7 27 2 3 3 3 9
Both P.F. share a 3 and another 3, multiply these together = 9
9 is the GCF of 54 and 63 3 3

13. If you struggle with these topics view your work on page 55

14. Any number that can be written as a fraction
Rational number
Any number that can be written as a fraction
Are the following rational numbers?

15. Between Fractions
Simplifying Fractions

16. Fraction to Decimal
The fraction bar is just a division sign

17. Decimal to Fraction
Don’t forget to simplify!

18. If you are struggling with this look at your work from page 59

19. Comparing Fractions

20. Comparing Decimals
Line up the decimal points (you need to compare the tens place with other tens places etc.)
Digits to the left have greater value
2.345
2.435
1.345
2.34

21. Using these two methods and your know how to change fractions to decimals and vise versa, you can order larger groups of numbers If you struggle with this subject review your work on page 64

22. Adding and Subtracting Rational Numbers
1) Make all mixed numbers improper fractions 2) Find common denominators 3) Add or subtract the numerators 4) Keep the denominator 5) Simplify

23. 3 and 4 1 2 5

24. If you struggle on this topic refer to your work from page 68

25. Multiplying Rational Numbers
1)Make into improper fractions 2) Pre-cancel if you can 3) Multiply numerators 4) Multiply denominators 5) Simplify

26. 3
And 4 1 7 5 2 1

27. Dividing Fractions
1) Make into improper factions 2) Multiply by the reciprocal 3) Simplify

28. 1 3
First fraction stays the same
Division become Multiplication
Second fraction is flipped
See Multiplying Fractions 2

29. If you struggle with this refer to your work on page 75

30. Formulas
You do not need to memorize formulas refer to page 648 in the text Formula: A rule that shows the relationship between two or more quantities It’s an expression you are given to calculate information about certain scenarios. Just plug in and chug out.

31. 4 steps Choose the formula List your known and unknown variables
Substitute values into the formula
Solve the formula based on it’s rules

32. 1. Choose the formula
Make sure you know what the question is asking for and your formula can solve for it.
If I want to find the area for a square, a formula that solves for volume is pretty useless
Copy the formula down and give yourself plenty of room to work

33. 2 list your variable
Read the question carefully and list what you know and what you need to find
I picked random numbers to use as an example. Read carefully, your problems will tell you what goes where. If you have more then 1 unknown, you can not solve.
NOTE: ½ is a constant. It does not change and is part of the rule of the formula

34. 3 Substitute into the formula
NOTE: Use parentheses to keep work neat and clear
NOTE: only replace the variables, keep the rules the same

35. 5 Solve using the rules of the formula
NOTE: Formulas will have units of measure associated with them. Pay attention and include them with your answer
Area will be squared units
Volume will be cubed units

36. Isolating Variables
You pretend you know the other values and solve for the unknown you are asked to isolate Many times you don’t need to do this, you can just use algebra after you substitute in.

37. How to isolate a variable
Determine which variable you want to isolate
Ask yourself what operation is going on (Adding, subtracting, multiplying, dividing, etc.)
Do the opposite of that operation to both sides of the equal sign. This should cancel out the unwanted variables attached to the one you want to isolate

38. Isolate the in the following formula
You are multiplying by (w), so divide each side of the equal sign by (w)
W’s cancel

39. If you are struggling on this topic review your work from page 83

40. Powers and Exponents
Exponent 42
Base

41. Exponents
Be careful with you signs!

42. If you are struggling with this section refer to your work on page 88

43. Scientific Notation
Makes large numbers smaller and easier to work with
Also some calculators can only show so many numbers and they will make use of this with EE instead of a X10

44. Scientific to Standard Notation
You are only moving decimal points and filling in empty stops with zeros
Positive powers of 10 move to the right
Negative powers of 10 move to the left

45. Power of 4, move decimal 4 places to the right
Power of -4, move decimal 4 places to the left

46. Standard to Scientific Notation
First number is always between 1 and 10!
Count the number of places you need to move the decimal to make a number between 1 and 10
The number of places you moved the decimal is your exponent
You are always multiplying by a power of 10

47. Needed to move the decimal 13 places to the left so you multiply by 1013
Needed to move the decimal 11 places to the right so you multiply by 10-11
NOTE: If your number is less then 1 in standard notation, you will have a negative exponent in scientific notation

48. If you are struggling on this topic refer to your work on page 94