Welcome to SCIE 0900

Instructor: Bernadine Cutsor

Why do we study science?

1. Need a basic understanding of science

2. Difference between science and technologyScience = process to understand and explain the natural world

Technology = application of scientific principles

3. Helps us to make informed decisions

4. Using the Scientific Method to approach a problem and find a reasonable solution.

The Learning Pyramid

Listen

Read

Audiovisual

Demonstration

Discussion group

Practice by doing

Teach others or immediate use

Lecture

Lecture

Lecture & Lab

Lab

Lab

Study Sessions

Study Sessions

Study

Sessions

Why SCIE 0900?

• To introduce you to skills that will make you more successful in future science classes

• Chemistry

• Biology

• Physics

Review of Math Principles

Addition

• Sum of 2 or more numbers called addends

2 + 4 = 4 + 2

Addition of numbers w/different signs

4 + 2 = 6

-4 + (- 2)= -6

-4 + 2 = -2

Combine numbers w/same sign 4 + (-5) + (-3) + 7 +(-9) =

(-5) + (-3) + (-9) = -17 4 + 7 = 11

Finish the problem:-17+11 = 6 OR 11 + (-17) = -6

Subtraction

4 – (-2) = 4 + 2 = 64 – (+2) =4 -2 = 2

-4 – (+2) =

-4 – 2 = -6

-4 – (-2) = -2

-4 + 2 = -2

Multiplying

8 x 4 = 32 (positives)

(-6) x (-3) = 18 (negative x negative = positive)

(-2) x 4 = -8 negative x positive = negative

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

4 x 3 x 7 x (-3) =

12 x 7 x (-3) =

12 x (-21) = - 252

Dividing Signed Numbers

16 ÷ 2 = 8

(-64) ÷ (-8) = 8Same signs = positive answer

210 ÷ (-42) = -5

(-77) ÷ 11 = -7 different signs = negative answer

Fractions

• Way of representing the division of a “whole” into “parts”

1

2

numerator

denominator

Adding and Subtracting Fractions

• Denominator must be the same

• Usually is the least common denominator

(LCD)

• EX:

½ + ¼ =

1 2 2

2 2 4

2 1 2 + 1 3

4 4 4 4

X =

+ = =

Subtracting

1/3 – ¼ =

Determine LCD:

1/3 x 4/4 = 4/12

¼ x 3/3 = 3/12

Answer:

4/12 - 3/12 = 1/12

Multiplying Fractions

By a whole number:

2

3X 6 =

2 X 6

3 X 1

=12

3= 4

Multiplying Fractions

By another fraction:

2 15 2 x 15 30 15

3 16 3 x 16 48 24X = = =

Multiplying fractions with calculator

245.8 24.9 12.8

3.85 675.9 28.4

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 ÷ 675.9 x 12.8 ÷ 28.4 = 1.06

X X =

Dividing Fractions

1 ÷ 1=

2

4

becomes

1

2x

4

1=

2

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.

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

• 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"

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".

However…• 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.

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 7 + 5 = 12 students, five failed.

• That is, 5/12 of the class flunked.

So in a class of 36 students –

5 X 36 = 180 = 15

12 1 12

= 15 students failed.

Units in Ratios– Ratios may or may not have units – it depends on what

you are comparing

– In some cases units may cancel outExpress 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

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.

Write two equivalent ratios for each ratio

3

17

54 to 24

11:19

Write each ratio in simplest form.

32:20 15:33

149

21 48

What is a Proportion?A statement that two ratios are equal.

A comparison of one fraction to another

• For example:

15 = X

40 100

Solve the Problem

• Cross Multiply and set up an equation

15 Men = X men

30 women 100 women

(15) (100) = (30) X

1500 = 30 X

1500 = X

30

X = 50 men and 100 women

Check your answer to see if the equations are equal

15 = 50 30 100

15/30 = 0.50

50/100 = 0.50

The Proportion is true if the both fractions reduce to the same value.

Check your answer to see if the equations are equal

15 X 100 = 1500

30 X 50 = 1500

1500

1500

15 = 50

30 100

= 1

State whether the ratios are proportional. yes or no

8 = 2

7 28

2 = 6

11 33

7 = 30

10 2140 = 4

50 5

What are Percentages?

15 Men = 50 men

30 women 100 women

%’s are actually proportions based on 100 as the sample size

15/30 = .5 x 100% = 50%

50/100 = .5 x 100% = 50%