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

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.

The Learning Pyramid Lecture Study Sessions Lecture Lecture & Lab current 8/29/08 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

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

Review of Math Principles current 8/29/08 Review of Math Principles

Addition Sum of 2 or more numbers called addends 2 + 4 = 4 + 2 current 8/29/08 Addition Sum of 2 or more numbers called addends 2 + 4 = 4 + 2

Addition of numbers w/different signs current 8/29/08 Addition of numbers w/different signs 4 + 2 = 6 -4 + (- 2)= -6 -4 + 2 = -2

Combine numbers w/same sign current 8/29/08 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

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

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

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

(-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

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

Dividing Signed Numbers current 8/29/08 Dividing Signed Numbers 16 ÷ 2 = 8 (-64) ÷ (-8) = 8 Same signs = positive answer

different signs = negative answer current 8/29/08 210 ÷ (-42) = -5 (-77) ÷ 11 = -7 different signs = negative answer

Fractions Way of representing the division of a “whole” into “parts” 1 current 8/29/08 Fractions Way of representing the division of a “whole” into “parts” 1 2 numerator denominator

Adding and Subtracting Fractions current 8/29/08 Adding and Subtracting Fractions Denominator must be the same Usually is the least common denominator (LCD) EX: ½ + ¼ = 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 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 - 3/12 = 1/12

Multiplying Fractions current 8/29/08 Multiplying Fractions By a whole number: 2 3 2 X 6 3 X 1 12 3 4 = = 6 = X

Multiplying Fractions current 8/29/08 Multiplying Fractions By another fraction: 2 15 2 x 15 30 15 3 16 3 x 16 48 24 X = = =

Multiplying fractions with calculator current 8/29/08 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 =

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

Fractions as Ratios and Proportions current 8/29/08 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 a:b or a/b or a to b Comparison of two numbers current 8/29/08 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

Ratio of men to women is 15 to 20. current 8/29/08 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"

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".

However… current 8/29/08 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 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 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 current 8/29/08 So in a class of 36 students – 5 X 36 = 180 = 15 12 1 12 = 15 students failed.

Units in Ratios current 8/29/08 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

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.

Write two equivalent ratios for each ratio current 8/29/08 Write two equivalent ratios for each ratio 11:19 3 17 54 to 24

Write each ratio in simplest form. current 8/29/08 Write each ratio in simplest form. 32:20 15:33 14 9 21 48

What is a Proportion? A statement that two ratios are equal. current 8/29/08 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 current 8/29/08 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 current 8/29/08 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 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 30 100 = 1

State whether the ratios are proportional. yes or no current 8/29/08 State whether the ratios are proportional. yes or no = 2 7 28 2 = 6 11 33 7 = 30 10 21 40 = 4 50 5

current 8/29/08 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%