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1 Fractions, Decimals Name: and Percents Class: Glencoe (p281) Date: 11/1/10 Holt (p304) Percent Ratio that compares a number to % = Percent to Decimal Move the decimal 2 places to the left. 45% = % = % = % = 1.24 Decimal to Percent Move the decimal two places to the right = 0.078% = 1293% = 30450% Percents to Fractions Denominator for any whole # is 100.

2 240% = 240 = 2 40 / 100 = 2 2 / % = 0.7 = Add as many zeroes, to the intial 100, in the denominator as there are decimal places. 1.24% = 1.24 = 124 = Fractions to Decimals Numerator divided by the denominator. 4 / 5 = 4 5 = 0.8 = 80% Fractions to Percents To change any fraction to a percent, first change it to a decimal, then move the decimal two places to the right. 9 / 4 = 9 4 = 2.25 = 225%

3 Using the Percent Name: Proportion Class: Glencoe (p288) Date: 11/2/10 Holt (p316) Percent Proportion part (a) = % (p) base (b) 100 part = is total of Part Base is being compared to the whole or total quantity. is the whole or total quantity. Five is what percent of 8? 5 is the part. 8 is the total or base. Substitute into the percent proportion. part (is) = p total (of) = p Use the steps for solving a proportion. 5 x p = 62.5 So, 5 is 62.5% of 8.

4 What percent of 4 is 7? part (is) = p base (of) = p x p = 175 So, 175% of 4 is 7. 3 is what percent of 4? 3 = p p = 75 What number is 75% of 4? a = a = 3 3 is 75% of what number? 3 = 75 b 100 b = 4

5 What number is 5.5% of 650? a = a = Fifty-two is 40% of what number? 52 = 40 REMEMBER IS / OF! b x b = 130

6 Finding Percents Mentally Date: 11/2/10 REFER TO THE CONVERSION CHART GIVEN TO YOU YESTERDAY! Round to the closest percent. 22% is just a bit more than 20%. 13% is about 12.5% or 1 / 8. Estimate 80% of % is 4 / is about / 5 of 300 is 240. So, 80% of 296 is 240.

7 Using Percent Name: Equations Class: Glencoe (p298) Date: 11/5/10 Holt (p316) Percent Equation Equivalent to the percent proportion. Percent has to be written as a decimal. Formula Part = % (write as a decimal) x base Missing Part What number is 75% of 4? y = 0.75(4) y = 3 Missing Percent 3 is what percent of 4? HINT! part = is base of 3 = y(4) 3 4 = y 0.75 = y 75% = y Missing Base 3 is 75% of what number? 3 = 0.75y = y 4 = y

8 Discount HINT! Step One Step Two Simple Interest (i) The amount for which the regular price of an item is reduced. Mateo wants to buy a skateboard. The regular price of the skateboard is $135. Suppose the skateboard is on sale at a 25% discount. Find the sale price of the skateboard. part = discount = commission = markup base = total = original price y = discounted amount y = 0.25(135) y = $33.75 regular price - discount = sale price $135 - $33.75 = $ The amount of money paid or earned for the use of the money. Interest = Principal x Rate x Time Principal (p) Rate ( r ) Time (t) The amount borrowed or invested. Percent. In years.

9 Suppose Miguel invests $1200 at an annual rate of 6.5%. How long will it take until Miguel earns $195? i = prt $195 = $1200 x x t 195 = 78t = t 2.5 = t Commission Fee paid to a salesperson based on a percent of sales. Suppose a real estate agent earns a 3% sales commission. What commission would be earned for selling a house listed for $130,000. part = percent x base y = 0.03(130,000) y = $3900 Markup Selling an item for more than it was originally paid for. Suppose a store purchases paint brushes for $8 each. Find the markup if the brushes are sold for 15% over the price paid for them.

10 part = percent x base y = 0.15(8) y = $1.20

11 Percent of Change Name: Glencoe (p304) Class: Holt (p324) Date: 11/8/10 Percent of Change The percent an amount has increased or decreased. Step 1 Step 2 Find the percent of change from 56 inches to 63 inches. Subtract to find the amount of change = 7 (new measurement minus old measurement) Write a ratio that compares the amount of change to the original measurement. Formula percent of change = amount of change (new - old) original measurement Percent of Increase = 7 56 = Step 3 = 12.5% (Write the decimal as a %.) The percent of change from 56" to 63" is 12.5%. Percent of Increase When the amount increases.

12 Steps In 1975, the average price per gallon of gasoline was $0.57. In 2010, the average price per gallon is $2.59. Find the percent of change (percent of increase ). 1. Subtract (new - original) 2. Write a ratio (amt of change to original) 3. Rewrite the decimal as a percent = or 354% 0.57 The percent of increase is 354%. Percent of Decrease Negative percent of change, when the amount decreases. Steps One of the largest stock market drops on Wall Street occurred on October 19,1987. On this day, the stock market opened at points and closed at points. What was the percent of change (% of decrease ). 1. new - original (closing - opening) 2. change original (opening) 3. write the decimal as a percent

13 = or -22.6% The percent of decrease is -22.6%.

14 Probability and Predictions Glencoe (p310) Holt (p512) Outcomes Simple Event Probability Name: Class: Date: The number of possible results. One outcome or a collection of outcomes. The chances of an event happening. The probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. Formula P(event) = number of favorable outcomes number of possible outcomes The probability of an event is always between 0 and 1. The closer the probability is to 1, the more likely it is to occur. Suppose a number cube is rolled. What is the probability of rolling a prime number? There are 3 prime #'s (favorable) on a number cube. 2, 3, and 5.

15 There are 6 possible outcomes. 1, 2, 3, 4, 5, and 6 P(prime) = favorable = 3 = 1 possible 6 2 The probability of rolling a prime number is 1 / 2 or 50%. Sample Space The set of all possible outcomes. In the example above, there were 6 possible outcome (1, 2, 3, 4, 5, 6). Theoretical Probability What should occur. The probability in the example above was theoretical. Experimental Probability What actually occurs. Theoretically, if you flip a coin 10 times, you should land on heads 50% of the time. When you actually flip the coin, you get the experimental prob. Prediction Educated guess (conjecture) based on information given previously or what you already know. Using the % part = % Proportion total 100

16 Express each probability as a fraction and as a percent. There are 2 red marbles, 4 blue marbles, 7 green marbles, and 5 yellow marbles in a bag. Suppose one marble is selected at random. Find the probability of each outcome. P(not blue or red) = 12 = = p = % or 66 2 / 3 %

17 Similar Figures and Proportions Similar Figures Corresponding Sides Corresponding Angles Proportional Name: Class: Date: 11/22/10 Have the same shape, but not necessarily the same size. The matching sides of two or more polygons. PROPORTIONAL. The matching angles of two or more polygons. EQUAL. If two figures are similar, then the measures of the corresponding angles are equal and the corresponding sides are proportional. Cross-multiply to find out if the ratios are a proportion (equivalent). Y Q X Z P R x = p What other angles are equal to one another? Add the answers to your notes. XY corresponds to QP.

18 Write the other corresponding sides in your notes. Are the two shapes similar? 15 ft ft 20 ft 8 ft 4 ft ft Set up a proportion using corresponding sides. 15 = = = = 60 OR 15 = 20 = ALL REDUCE TO: 5 = 5 =

19 Indirect Measurement Used to find measurements that are difficult to measure directly. 10 cm? cm 5 cm 6 cm 3 cm 4 cm 10 =? x 4 5 = 8

20 Measures of Central Name: Tendency Class: Date: 11/30/10 Measures of Central Tendency Mean Median Mode One or more numbers that represent a whole set of numbers. The sum of the data divided by the number of items in the data set. The middle number of the ordered (least to greatest) data or the mean of the middle two numbers. The number or numbers that appear most often (2 or more times). It is possible to have no mode. Line Plot numbers total. 2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,6,6, 7,7,7,8,8,8,9,9,10,11 Find the mean? 5.7 The median? 5 The mode? 4 and 5

21 Extremes or Outliers Really small or large numbers that mess up the data. Vegetable Calories Vegetable Calories Asparagus 14 Cauliflower 10 Beans 30 Celery 17 Bell pepper 20 Corn 66 Broccoli 25 Lettuce 9 Cabbage 17 Spinach 9 Carrots 28 Zucchini 17 Identify an extreme value and describe how it affects the mean. 66 Calculate the mean with the extreme value and without the extreme value. With = Without =

22 Measures of Variation Range Quartiles Median Name: Class: Date: 12/1/10 The difference between the biggest and the smallest number. It describes how a set of data varies. The values that divide the data into four equal parts. Divides the data set in half. It's very important to list the data from least to greatest median Lower Quartile (LQ) The median of the lower half of the data set Lower Quartile Upper Quartile (UQ) The median of the upper half of the data set Upper Quartile

23 Interquartile Range (IQR) The difference between the upper quartile and the lower quartile. Find the interquartile range for the data set UQ = = 6 LQ = 4 Interquartile Range = 6

Stem and Leaf Plot Name: Class: Date: 12/2/10 Stem and Leaf Numerical data is listed in ascending (1-10) Plots or descending (10-1) order. Stem Leaves Interpretation The greatest place value.

24 Stem and Leaf Plot Name: Class: Date: 12/2/10 Stem and Leaf Numerical data is listed in ascending (1-10) Plots or descending (10-1) order. Stem Leaves Interpretation The greatest place value. The next greatest place value(s). If you were asked to interpret the data using a given stem and leaf plot, you would have to write all of the numbers out in order first. 22, 26, 27, 31, 33, 35, 42, 44, 46, 57, 58, 59, 61, 63, 64, 65, 67 What is the lowest score? What is the highest score? What is the mean? What is the median? What is the mode?

Histograms Histogram Name: Class: Date: 12/2/10 Uses bars to display numerical data that has been organized into equal intervals. There is no space between the bars.

25 Histograms Histogram Name: Class: Date: 12/2/10 Uses bars to display numerical data that has been organized into equal intervals. There is no space between the bars. To make a Histogram you start with a frequency table which uses tally marks. Once you add up your tally marks, you must decide which intervals to use, (ex. 50, 100, 150 ). III Grade 0-20 IIIIIIIII Grade Grade IIIIIIIIIIIIIIIIIIII Grade IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIII Grade IIIIIIIIIIIIIIIIIIIII

26 Box and Name: Whisker Plots Class: Glencoe; p617 Date: 12/6/10 Holt; p28 Box-and Whisker Plot Outliers OR Extremes Lower Extreme (LE) Upper Extreme (UE) Median OR 2nd Quartile Lower Quartile OR 1st Quartile Upper Quartile OR 3rd Quartile Diagram Divides a set of data into four parts using the median and quartiles (medians of the 1st half and 2nd half of the data). Lowest, extreme value and the highest, extreme value. Lowest, smallest number in the set, not the smallest on the number line. Highest, biggest number in the set, not the biggest on the number line. Of the entire set of data put in order from least to greatest. Has to be found 1st. Once the data has been divided in half by finding the median, the lower quartile is the median of the first half of the data. The median of the 2nd half of the data. Starts with a number line. You cannot skip units on the number lines. Intervals have to be the same.

27 1st 2nd 3rd Every Box-and-Whisker is divided into four parts. Each part represents 25% of the data. Make sure you label each value on the box-and whisker.

28 Area: Parallelograms, Name: Triangles, and Class: Trapezoids Date: 1/4/11 Glencoe; p520 Holt; p Area of a Rectangle Multiply the length times the width. A = lw Length Area of a Parallelogram Area of a Triangle Multiply the base of the parallelogram by the height. A = bh THE HEIGHT FORMS A RIGHT ANGLE WITH THE BASE. Width Height Base Multiply the base of the triangle by the height of the same triangle, then divide the answer by 2. A = bh / 2 OR A = 1 / 2 bh Height Base THE HEIGHT ALWAYS FORMS A RIGHT ANGLE WITH THE BASE.

29 Area of a Add (base 1 + base 2 ) times it by the Trapezoid height and then divide by 2. A = (b 1 + b 2 )h / 2 OR A = 1 / 2 (b 1 + b 2 )h THE PARALLEL LINES OF THE TRAPEZOID ARE THE BASES. Base 1 Height Base 2 s You find the answers. Find the area. Triangle: base, 8 in.; height, 7in. Trapezoid: height, 2cm; bases, 3cm, 6cm Parallelogram: base, 3.8yd; height, 6yd Find the height. If the area of a trapezoid is 54ft 2, and the bases measure 16 feet and 8 feet. Find the base. If the parallelogram has an area of 36.8m 2, and a height of 9.2 meters.

30 Polygons Name: Glencoe; p527 Class: Holt; p382 Date: 1/6/11 Polygon Is a simple closed figure formed by three or more line segments. Has no curved sides. No overlapping sides. Sides / Edges Vertices Diagonal Are line segments that meet only at Side their endpoints. Vertice The endpoints where the sides of a polygon meet. A line segment in a polygon that joins two nonconsecutive vertices. Pick one vertex and join it to all of the other vertices. Interior Angles Are inside the polygon. Exterior Angles Are outside the polygon. Formed when the sides of the polygon are extended. Regular Polygon A polygon that is equilateral - all sides are congruent.

31 How many degrees are in the polygon? 4 triangles x 180 = 720 Number of sides = 6 (6-2)180 = 720 The number of triangles formed by the diagonals x 180 = the number of degrees in the polygon; OR Where the number of sides = n; (n - 2)180 = the number of degrees in the polygon. Find the measure of one interior angle of a pentagon. (n - 2)180 = the sum of the degrees of all the interior angles (5-2)180 = 540 Divide 540 by 5 (because there are 5 interior angles). One interior angle in a pentagon = 108

32 Circumference Name: and Area: Circles Class: Perimeter Date: 1/7/11 Glencoe; p533 Holt; p438 Circle Diameter Circumference Radius Pi (π) Area of a Circle The set of all points in a plane that are the same distance from a given point. The distance across the circle through its center. Distance around the circle. C = πd or 2πr Distance from the center to any point on the circle. Stands for the number π 3.14 The area of a circle is equal to π times the square of its radius. A = πr 2 or πrr Find the circumference. Round to the nearest tenth. C = 2πr 3.2 ft C = 2(3.14)(3.2) C 20.1 ft

33 The circumference of a tree is 14 inches. What is the diameter, rounded to the nearest tenth? 1. Write the formula. (C = πd) 2. Substitute. (14 = 3.14d) 3. Solve algebraically. ( = d) d 4.5 inches Find the area. Round to the nearest tenth. A = πr 2 31 m A = π(15.5) 2 A = 3.14(240) 15.5 X 15.5 = 240 A m 2 DIAMETER HAS TO BE DIVIDED IN HALF! Find the radius of a circle if its area is square meters. 1. Write the formula. (A = πr 2 ) 2. Substitute. (132.7 = 3.14r 2 ) 3. Solve algebraically. ( = r 2 ) = r r THE INVERSE OPERATION FOR A NUMBER SQUARED, IS FINDING THE SQUARE ROOT OF THE

34 Central Angle An angle whose vertex is the center of the circle. Chord Inscribed Angle A segment of a circle whose endpoints are on the circle. Has its vertex on the circle and sides that are chords. Arc Part of the circle (curved). Perimeter The distance around a geometric figure. l (length) Of a Rectangle P = 2l + 2w w (width) a = or 2(7) + 2(7) = 28 b = or 2(3) + 2(3) = 12 a + b = = 40 P = 40

half of a circle rectangle triangle Idaho rectangle There can be more than one way to separate an irregular

35 Area: Name: Irregular Class: Figures Date: 1/7/11 Glencoe; p539 Holt; p457 Area To find the area of an irregular figure, separate the irregular figure into figures that you recognize. half of a circle rectangle triangle Idaho rectangle There can be more than one way to separate an irregular figure. rectangles triangle rectangle trapezoid Find the area of the regular polygon to the nearest tenth. 6 ft rectangle trapezoids 1.5 ft 8 ft

36 Remember to divide the irregular figure into smaller, recognizable shapes. LOOK BACK AT YOUR NOTES TO FIND THE FORMULAS YOU NEED.

Three- Name: Dimensional Class: Figures Date: 1/18/11 Glencoe; p556 Holt; p472 Perspective Nets Plane Solids Point of view; different views of the same figure.

37 Three- Name: Dimensional Class: Figures Date: 1/18/11 Glencoe; p556 Holt; p472 Perspective Nets Plane Solids Point of view; different views of the same figure. Two-dimensional patterns for threedimensionals figures. Two-dimensional flat surface that extends in all directions. Intersecting planes that form 3D figures. Polyhedron Face Edge Vertex A solid with flat surfaces that are polygons. Flat surface (sides) of a solid. Prisms have rectangular faces. Pyramids have triangular faces. Where two faces (planes) meet (intersect). The solid and dotted lines on the figure. Where three or more edges (planes) intersect in a point.

38 Base Prism Pyramid The face that is used to classify a solid. Prism has 2 and pyramid has 1. A polyhedron with two parallel, congruent bases, can be any polygon. All of the other faces are parallelograms. A polyhedron with one base that can be any polygon. All of the other faces are triangles. Rectangular Prism Triangular Pyramid Edge Face Vertex Edge PRISMS AND PYRAMIDS ARE NAMED BY THE SHAPE OF THEIR BASE(S). THE SOLIDs ABOVE ARE A RECTANGULAR PRISM AND A TRIANGULAR PYRAMID. Triangular Prism Base - names the solid Vertex - point Face - sides Edge - lines Square Prism -6 Faces -12 Edges -8 Vertices

39 Triangular Pyramid -4 Faces -6 Edges -4 Vertices Rectangular Pyramid? Faces? Edges? Vertices Cone Cylinder

40 Volume: Name: Prisms and Class: Cylinders Date: 1/19/11 Glencoe; p563 Volume Formula (MAIN) Is the measure of space occupied by a solid region. The volume (V) of a prism is the area of the base (B) times the height (h) of the prism. V = Bh (BASIC FORMULA FOR ALL VOLUME) Find the volume of the rectangular prism that has a l = 7.5 in., w = 2 in., and h = 4 in. (Area of the Base of a Rect. Prism = B = I x w) V = Bh Rectangular Prism V = (l x w) x h V = (7.5 x 2) x 4 V =? in 3 Find the volume of the triangular prism where the triangle has a base = 4 cm, height = 3 cm, and the height of the prism = 6 cm. Height of the Triangle REMEMBER THE HEIGHT OF ANY POLYGON (2D SHAPE) ALWAYS FORMS A RIGHT ANGLE WITH THE BASE. Base of the Triangle Height of the Prism

41 V = BH Triangular Prism V = ( bh / 2 ) x H or V = ( 4 x 3 / 2 ) x 6 V =? cm 3 lwh / 2 h = height of the triangle (base) H = Height of the entire prism Height of the Prism The distance between the two bases. Line that connects (touches) the two bases. Cylinder The volume of a cylinder with radius r is the area of the base B times the height h. (Area of the base is π x radius x radius) V = Bh Cylinder Formula V = πr 2 h or πrrh Find the volume of the cylinder to the nearest tenth. Use 3.14 for π. The diameter of the base is 16.4 mm. The height of the cylinder is 20 mm. V = πr 2 h V = 3.14 x 8.2 x 8.2 x 20 V =? mm 3 Height Width Length = 6 units Width = 4 units Height = 2 units V =? Length

42 Volume: Name: Pyramids, Class: Cones, and Spheres Date: 1/20/11 Glencoe; p568 Holt; p480 Pyramid The volume V of a pyramid is one-third the area of the base B time the height h. MAIN FORMULA FOR A PYRAMID V = 1 / 3 Bh OR V = Bh / 3 Height of the Pyramid/Cone Touches the center of the base and the point of the pyramid/cone. Forms a right angle with the base. Find the volume of the following triangular pyramid: base of the triangle = 8ft height of the triangle = 6ft height of the pyramid = 20ft V = Bh/3 V = (bh/2)h / 3 V = [(8x6) / 2]20 3 V =? ft 3 Find the volume of the following rectangular pyramid: 8.3 cm 7 cm 5 cm

43 V = Bh/3 V = lwh / 3 V = (7 x 5 x 8.3) / 3 V =? cm 3 Cone The volume V of a cone with radius r is one-third the area of the base B time the height h. V = Bh/3 V = (πrrh) / 3 Find the volume of the following cone: Diameter = 9 cm height of the cone = 10 cm V = Bh/3 V = (πrrh) / 3 V = (3.14 x 4.5 x 4.5 x 10) / 3 V? cm 3 Find the volume. 5 cm 12 cm V = Bh/3 V = (πrrh) / 3 V = 3.14 x 5 x 5 x 12 / 3 V? cm 3

44 Sphere The volume of a sphere is 4 / 3 times π times the radius cubed. V = 4 / 3 π r 3 OR 4 / 3 π r r r Find the volume of the sphere to the nearest tenth. Use 3.14 for π. 9 yds V = 4 / 3 π r 3 V = 4 / 3 x 3.14 x 9 x 9 x 9 V =?

45 Surface Area: Name: Prisms, Class: Cylinders, and Spheres Date: 1/25/11 Glencoe; p573 Holt; p486 Net Surface Area Rectangular Prism Formula The surface of a 3D figure laid out flat. The sum of the areas of these surfaces. Surface area (S) = area of the top + area of the bottom + area of the front + area of the back + area of the left + area of the right S = 2lw + 2lh + 2wh 14 in. 20 in. 10 in. S = 2lw + 2lh + 2wh S = 2(20)(14) + 2(20)(10) + 2(14)(10) S =? in 2 Triangular Prism How to solve: Area of the 2 bases (triangles) + the area of the 3 rectangular faces. BASE = A = bh/2 BASE = A = bh/2 LEFT = A = lw RIGHT = A = lw BOTTOM = A = lw

46 4 cm 5 cm 6 cm 3 cm BASE = A = bh/2 = 3(4) / 2 =? BASE = A = bh/2 = 3(4) / 2 =? LEFT = A = lw = 6(5) =? RIGHT = A = lw = 6(5) =? BOTTOM = A = lw = 6(3) =? S =? cm 2 ADD THEM UP! Cylinder Formula Area of the 2 bases + the area of the curved (lateral) surface. S = 2πrr + 2πrh 1 m 3 m S = 2πrr + 2πrh S = 2 x 3.14 x 1 x x 3.14 x 1 x 3 S =? m 2 Sphere Formula Four times pi time the radius *r* squared. S = 4πrr Find the surface area of the sphere to the nearest tenth.

47 6 m S = 4πrr S = 4 x 3.14 x 6 x 6 S =?

Volume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth.

Volume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth. Volume of Cylinders As with prisms, the area of the base of a cylinder tells the number of cubic units in one layer. The height tells how many layers there are in the cylinder. The volume V of a cylinder