1. Welcome to SCIE 0900 Instructor: Bernadine Cutsor
current 8/29/08
Welcome to SCIE Instructor: Bernadine Cutsor

2. Why do we study science? Need a basic understanding of science
current 8/29/08
Need a basic understanding of science
Difference between science and technology
Science = process to understand and explain the natural world
Technology = application of scientific principles
Helps us to make informed decisions
Using the Scientific Method to approach a problem and find a reasonable solution.

3. The Learning Pyramid Lecture Study Sessions Lecture Lecture & Lab
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Lecture
Listen
Study Sessions
Read
Lecture
Audiovisual
Lecture & Lab
Demonstration
Study Sessions
Discussion group
Lab
Practice by doing
Study
Sessions
Teach others or immediate use
Lab

4. current 8/29/08
Why SCIE 0900?
To introduce you to skills that will make you more successful in future science classes
Chemistry
Biology
Physics

5. Review of Math Principles
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Review of Math Principles

6. Addition Sum of 2 or more numbers called addends 2 + 4 = 4 + 2
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Addition
Sum of 2 or more numbers called addends
2 + 4 = 4 + 2

7. Addition of numbers w/different signs
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Addition of numbers w/different signs
4 + 2 = 6
-4 + (- 2)= -6
= -2

8. Combine numbers w/same sign
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Combine numbers w/same sign
4 + (-5) + (-3) + 7 +(-9) =
(-5) + (-3) + (-9) = -17
= 11
Finish the problem:
= 6 OR (-17) = -6

9. current 8/29/08
Subtraction
4 – (-2) =
4 + 2 = 6
4 – (+2) =
4 -2 = 2

10. current 8/29/08
-4 – (+2) =
-4 – 2 = -6
-4 – (-2) = -2
= -2

11. 8 x 4 = 32 (positives) (-6) x (-3) = 18 (-2) x 4 = -8 Multiplying
current 8/29/08
Multiplying
8 x 4 = 32 (positives)
(-6) x (-3) = 18
(negative x negative = positive)
(-2) x 4 = -8
negative x positive = negative

12. (-2) x 5 x (-3) x 4 = (-2 x 5) x (-3) x 4 = (-10) x (-3) x 4 =
current 8/29/08
More than one number
(-2) x 5 x (-3) x 4 =
(-2 x 5) x (-3) x 4 =
(-10) x (-3) x 4 =
(-10) x (-12) = 120

13. current 8/29/08
4 x 3 x 7 x (-3) =
12 x 7 x (-3) =
12 x (-21) = - 252

14. Dividing Signed Numbers
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Dividing Signed Numbers
16 ÷ 2 = 8
(-64) ÷ (-8) = 8
Same signs = positive answer

15. different signs = negative answer
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210 ÷ (-42) = -5
(-77) ÷ 11 = -7
different signs = negative answer

16. Fractions Way of representing the division of a “whole” into “parts” 1
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Fractions
Way of representing the division of a “whole” into “parts” 1 2
numerator
denominator

17. Adding and Subtracting Fractions
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Adding and Subtracting Fractions
Denominator must be the same
Usually is the least common denominator
(LCD)
EX:
½ + ¼ =
2 2
2 4 = X = + =

18. Subtracting 1/3 – ¼ = Determine LCD: 1/3 x 4/4 = 4/12 ¼ x 3/3 = 3/12
current 8/29/08
Subtracting
1/3 – ¼ =
Determine LCD:
1/3 x 4/4 = 4/12
¼ x 3/3 = 3/12
Answer:
4/ /12 = 1/12

19. Multiplying Fractions
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Multiplying Fractions
By a whole number: 2 3
2 X 6
3 X 1 12 3 4 = = 6 = X

20. Multiplying Fractions
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Multiplying Fractions
By another fraction: x x X = = =

21. Multiplying fractions with calculator
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Multiplying fractions with calculator
Enter into calculator 2 ways:
245.8 x 24.9 x 12.8 ÷ 3.85 ÷675.9 ÷28.4 = 1.06
245.8 ÷ 3.85 x 24.9 ÷ x 12.8 ÷ 28.4 = 1.06 X X =

22. current 8/29/08
Dividing Fractions 1 1 ÷ = 2 4
becomes 4 1 x = 2 2 1

23. Fractions as Ratios and Proportions
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Fractions as Ratios and Proportions
A "ratio" is just a comparison between two different things.
For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group.
Suppose there are thirty-five people, fifteen of whom are men.  Then the ratio of men to women is 15 to 20.

24. Ratio a:b or a/b or a to b Comparison of two numbers
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Ratio
Comparison of two numbers
Expresses the relative size of two quantities as the quotient of one divided by the other
Written in 3 ways:
a:b or a/b or a to b

25. Ratio of men to women is 15 to 20.
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The order in which the ratio is written is important because it defines the comparison
Ratios should be left in their original form to represent the size of the sample compared
In our example
Ratio of men to women is 15 to 20.
Notice that, in the expression "the ratio of men to women", "men" came first.
This order is very important, and must be respected:  whichever word came first, its number must come first.
If the expression had been "the ratio of women to men", then the ratio would have been "20 to 15"

26. current 8/29/08
Reducing Ratios
Let's return to the 15 men and 20 women in our original group:
We had expressed the ratio as a fraction, namely, 15/20. This fraction reduces to 3/4.
This means that you can also express the ratio of men to women as 3/4, 3 : 4, or "3 to 4".

27. However…
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This points out something important about ratios: the numbers used in the ratio might not be the absolute references.
The ratio "15 to 20" refers to the absolute numbers of men and women, respectively.
But "3 to 4" just tells you that, for every three men, there are four women.
This also tells you that, in any representative set of seven people (3 + 4 = 7) from this group, three will be men.

28. Using Ratios to Solve Word Problems
current 8/29/08
Using Ratios to Solve Word Problems
In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course?
The ratio, "7 to 5" (or 7 : 5 or 7/5), tells you that, of every = 12 students, five failed.
That is, 5/12 of the class flunked.

29. So in a class of 36 students – 5 X 36 = 180 = 15 12 1 12
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So in a class of 36 students –
5 X 36 = = 15
= 15 students failed.

30. Units in Ratios
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Ratios may or may not have units – it depends on what you are comparing
In some cases units may cancel out
Express the ratio in simplest form: $10 to $45
This means that you should write the ratio as a fraction, and you should then reduce the fraction:
10/45 = 2/9
Note that the units "canceled" on the fraction, since the units, "$", were the same on both values.
So there is no unit on the answer

31. current 8/29/08
Ratios and Units
Express the ratio in simplest form: 240 miles to 8 gallons
In this case, you would have
(240 miles)/(8 gallons) = (30 miles)/(1 gallon)
In more common language, 30 miles per gallon.
Properly, this answer should have units on it, since the units, "miles" and "gallons", do not cancel out.

32. Write two equivalent ratios for each ratio
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Write two equivalent ratios for each ratio
11:19 3 17
54 to 24

33. Write each ratio in simplest form.
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Write each ratio in simplest form.
32:20
15:33
14 9
21 48

34. What is a Proportion? A statement that two ratios are equal.
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What is a Proportion?
A statement that two ratios are equal.
A comparison of one fraction to another
For example:
15 = X

35. Solve the Problem Cross Multiply and set up an equation 15 Men = X men
current 8/29/08
Solve the Problem
Cross Multiply and set up an equation
15 Men = X men
30 women women
(15) (100) = (30) X
1500 = 30 X
1500 = X 30
X = 50 men and 100 women

36. Check your answer to see if the equations are equal
current 8/29/08
Check your answer to see if the equations are equal
15 = 50
15/30 = 0.50
50/100 = 0.50
The Proportion is true if the both fractions reduce to the same value.

37. Check your answer to see if the equations are equal
current 8/29/08
Check your answer to see if the equations are equal
15 X 100 = 1500
30 X 50 = 1500
1500
15 = 50
= 1

38. State whether the ratios are proportional. yes or no
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State whether the ratios are proportional. yes or no
= 2
2 =
7 =
40 =

39. current 8/29/08
What are Percentages?
15 Men = men
30 women women
%’s are actually proportions based on 100 as the sample size
15/30 = .5 x 100% = 50%
50/100 = .5 x 100% = 50%