1. Numbers and Operations

2. Families of numbers

3. The Numbrella Complex numbers Real Numbers Imaginary Numbers |
Rational Numbers Irrational Numbers
Integers
Whole Numbers
Natural Numbers
a+bi
Has a real and an imaginary component
i—or bi
Can be expressed as a fraction
Can’t be expressed as a fraction
All “non-decimal” values
All positive integers and zero
All positive integers

4. Natural Numbers
Counting Numbers
1, 2, 3, 4, 5, …

5. Counting Numbers & Zero
Whole Numbers
Counting Numbers & Zero
0, 1, 2, 3, 4, 5, …

6. Positive and Negative Numbers and Zero
Integers
Positive and Negative Numbers and Zero
…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

7. Can be expressed as the ratio of 2 integers
Rational Numbers
Can be expressed as the ratio of 2 integers

8. Cannot be expressed as the ratio of 2 integers
Irrational Numbers
Cannot be expressed as the ratio of 2 integers
Non-terminating, non-repeating integers Π

9. Examples:
The approximate value of √7: √4 = 2 √9 = 3 so √7 is approx. 2.6 Determine the approximate value of the point: The point is about 3.4

10. Scientific Notation

11. Significant Digits Rules
1-9 are significant
0’s between digits are significant
0’s at the end suggest rounding and are not significant
Leading 0’s are not significant
0’s at the end of a decimal indicate the level of precision
Every digit in scientific notation is significant

12. Examples 1024 4 Significant Digits 1000 1 Significant Digit
ALWAYS HAVE ONE SIGNIFICANT DIGIT IN FRONT OF THE DECIMAL FOR SCIENTIFIC NOTATION

13. Examples
Expand: 2.15 x x 103 a negative exponent tells you to move the decimal to the left Write in scientific notation: 3,145,062 2,230, move the decimal so that there is only one digit in front and count the number of spaces you have moved—moving left is positive here and right is negative x x x 10-4

14. Examples
Simplify: do the math on the numeric portion as you normally would, use the rules of exponents on the powers of ten, place in standard scientific notation to finish (one digit before the decimal) (2.75 x 102)(4 x 103) 11 x x 106
5 x
10 x 108
.5 x 10-2
5 x 10-1

15. Percent

16. Percentages Convert 20% to a decimal Convert .45 to a percentage
20/100= .2
Convert .45 to a percentage
.45 * 100= 45%
Convert ¾ to a percentage
¾= * 100=75%

17. Examples: What is 7 percent of 50?
.07 * 50 = 3.5
A CD that normally costs $15 is on sale for 20% off. What will you pay
Option 1
.2 * 15 = = 12
Option 2
If it is 20% off you will pay 80%
.8 * 15 = 12

18. Order of Operations

19. PEMDAS A R N T H E S I X P O N E T S M UL T & D I V A D & S U B
From left to right

20. Examples:
30 ÷ 10 • (20 – 15)2 30 ÷ 10 • ÷ 10 • 25 75
Parenthesis
Exponents
then mult and div
From left to right

21. Absolute Value

22. Formal definition
Absolute value is the distance from the origin and distance is always positive.

23. Examples
|6| |-7| |-9-3|
|-12| 12

24. GCF and LCM

25. Examples GCF—greatest common factor 20 35 60 24 5 4 5 7 6 10 3 8
What is the largest number that divides all the given numbers evenly
22* * *3* *3
WHAT DO THEY SHARE?
* 3=12

26. Examples LCM—least common multiple 20 35 60 24 5 4 5 7 6 10 3 8
What is the smallest number that the given number go into evenly
22* * *3* *3
WHAT IS THE LAGEST VALUE SHOWN IN EACH?
22*5*7= *3*5=120

27. Using Proportions

28. What is a proportion and how can you solve a problem with it?
If Sue charges a flat rate each hour to babysit. If she ears $44 for 8 hours. What will she earn for 5 hours?
PRIMARY RULE:
If you put the $ amount in the numerator on one side put the same value in the numerator on the other side. Etc.
cross mult = 8x
27.5= x
Sue will earn $27.50 for 5 hours.

29. Distance and Work Problems

30. Distance problems

31. Example
It took the Smith’s 5 hours to go 275 miles. What was their average rate of speed?
D=rt
275 = r(5)
55 = r
They went about 55 mph

32. Work problems Use the reciprocal of the time for the rate of work
W for 1st person =hours worked * rate of work
W for 2nd person =hours worked * rate of work
Total job always =1
1 = W for 1st person + W for 2nd person

33. Example:
John and Sam decide to build a bird house. John and build the bird house in 5 hours working alone. Sam can do it in 8 hours alone. How long will it take if they work together?
It will take them 3.08 hours to make the bird house.

34. Estimation
What are the critical terms for estimation?

35. The “detail” associated with a measurement
Precision
The “detail” associated with a measurement

36. Calculations with two different levels of precision can only be accurate to the least precise measure.
Add a slide with two examples

37. How correct a measurement is
Accuracy
How correct a measurement is
The smaller the unit of measure the more accurate your measurement

38. The amount of difference between your measurement and the true value
Error
The amount of difference between your measurement and the true value

39. Examples:
Jim bought 3 pounds of nails for $ Which amount is closest to the price per pound? Round off and check above and below 15/3 = 5 and 18/3 = 6 A reasonable values would be between $5 and $6 but closer to $5

40. Conversions

41. Length Conversions 1 inch = 2.54 cm 12 inches = 1 foot 3 feet = 1 yard
5280 feet = 1 mile
How many inches are in 1 yard?
1 yard = 3 feet 1 foot = 12 inches
3x12 =36 inches

42. Fluid Conversions 3 Teaspoons = 1 Tablespoon 2 Tablespoons = 1 ounce
8 ounces = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon

43. Weight Conversions 16 ounces = 1 pound 2.2 pounds = 1 kilogram
2000 pounds = 1 ton

44. milli-
centi-
-meter = distance
-gram = weight
-liter = fluid
kilo-