Fractions. 7th Grade Math. Review of 6th Grade. Slide 1 / 306 Slide 2 / 306. Slide 4 / 306. Slide 3 / 306. Slide 5 / 306.

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1 Slide 1 / 06 Slide 2 / 06 7th Grade Math Review of 6th Grade Slide / 06 Table of Contents Click on the topic to go to that section Slide 4 / 06 Fractions Decimal Computation Statistics Number System Epressions Equations and Inequalities Geometry Ratios and Proportions Fractions Return to Table of Contents Slide 5 / 06 List what you remember about fractions. Slide 6 / 06 Greatest Common Factor Hint We can use prime factorization to find the greatest common factor (GCF). 1. Factor the given numbers into primes. 2. Circle the factors that are common.. Multiply the common factors together to find the greatest common factor.

2 1 Find the GCF of 18 and 44. Slide 7 / 06 2 Find the GCF of 72 and 75. Slide 8 / 06 Slide 9 / 06 Slide 10 / 06 Find the GCF of 52 and 78. A multiple of a whole number is the product of the number and any nonzero whole number. A multiple that is shared by two or more numbers is a common multiple. Multiples of 6: 6,, 18, 24, 0, 6, 42, 48,... Multiples of 14: 14, 28, 42, 56, 70, 84,... The least of the common multiples of two or more numbers is the least common multiple (LCM). The LCM of 6 and 14 is 42. Slide 11 / 06 Slide / 06 There are 2 ways to find the LCM: 1. List the multiples of each number until you find the first one they have in common. 2. Write the prime factorization of each number. Multiply all factors together. Use common factors only once (in other words, use the highest eponent for a repeated factor). EXAMPLE: 6 and 8 Multiples of 6: 6,, 18, 24, 0 Multiples of 8: 8, 16, 24 LCM = 24 Prime Factorization: LCM: 2 = 8 = 24

3 Slide 1 / 06 Slide 14 / 06 4 Find the least common multiple 5 Find the least common multiple of 10 and 14. of 6 and 14. A 2 A 10 B 20 B 0 C 70 C 42 D 140 D 150 Slide 15 / 06 Slide 16 / 06 6 Find the LCM of 24 and 60. Which is easier to solve? (4 + 6) Do they both have the same answer? You can rewrite an epression by removing a common factor. This is called the Distributive Property. Slide 17 / 06 Slide 18 / 06 The Distributive Property allows you to: 1. Rewrite an epression by factoring out the GCF. 2. Rewrite an epression by multiplying by the GCF. 7 In order to rewrite this epression using the Distributive Property, what GCF will you factor? EXAMPLE Rewrite by factoring out the GCF: (9 + 16) 7(4 + 9) Rewrite by multiplying by the GCF: ( + 7) 8(4 + 1)

4 Slide 19 / 06 Slide 20 / 06 8 In order to rewrite this epression using the Distributive Property, what GCF will you factor? Use the distributive property to rewrite this epression: A ( + 28) B 4(9 + 21) C 2( ) D ( + 7) Slide 21 / 06 Slide 22 / Use the distributive property to rewrite this epression: Adding Fractions A 4(22 + 8) B 8(11 + 4) 1. Rewrite the fractions with a common denominator. 2. Add the numerators.. Leave the denominator the same. 4. Simplify your answer. C 2( ) D 11(8 + ) Adding Mied Numbers Add the fractions (see above steps). 2. Add the whole numbers.. Simplify your answer. (you may need to rename the fraction) Link Back to List Slide 2 / 06 Slide 24 /

5 Slide 25 / 06 Slide 26 / 06 1 Find the sum. 14 Is the equation below true or false? True 1 8 False Click For reminder Don't forget to regroup to the whole number if you end up with the numerator larger than the denominator. A quick way to find LCDs... Slide 27 / 06 List multiples of the larger denominator and stop when you find a common multiple for the smaller denominator. Slide 28 / 06 Common Denominators Another way to find a common denominator is to multiply the two denominators together. 1 2 E: and 5 = E: and 5 Multiples of 5: 5, 10, E: and Multiples of 9: 9, 18, 27, 6 Slide 29 / 06 Slide 0 /

6 Slide 1 / 06 Slide 2 / = A 7 16 C 8 1 B 8 4 D Slide / 06 Slide 4 / = = A C 7 8 A C B D 8 7 B 5 5 D 6 5 Slide 5 / 06 Slide 6 / 06 Subtracting Fractions Rewrite the fractions with a common denominator. 2. Subtract the numerators.. Leave the denominator the same. 4. Simplify your answer Subtracting Mied Numbers Subtract the fractions (see above steps..). (you may need to borrow from the whole number) 2. Subtract the whole numbers.. Simplify your answer. (you may need to simplify the fraction) Link Back to List

7 Slide 7 / 06 Slide 8 / Slide 9 / 06 Slide 40 / Is the equation below true or false? 25 Is the equation below true or false? True False True False Slide 41 / 06 Slide 42 / Find the difference

8 Slide 4 / 06 Slide 44 / 06 A Regrouping Review When you regroup for subtracting, you take one of your whole numbers and change it into a fraction with the same denominator as the fraction in the mied number. 5 = = Don't forget to add the fraction you regrouped from your whole number to the fraction already given in the problem Slide 45 / 06 Slide 46 / Do you need to regroup in order 29 Do you need to regroup in order to complete this problem? to complete this problem? Yes or No Yes or No Slide 47 / 06 Slide 48 / 06 0 What does 17 become 10 when regrouping? 1 5 What does 21 become when regrouping? 8

9 Slide 49 / 06 Slide 50 / = = A 2 1 C 1 11 A 8 C B D 1 1 B 1 21 D Slide 51 / 06 Slide 52 / = 1. Multiply the numerators. 2. Multiply the denominators.. Simplify your answer. Multiplying Fractions... A B 7 5 C D 6 2 Multiplying Mied Numbers Rewrite the Mied Number(s) as an improper fraction. (write whole numbers / 1) 2. Multiply the fractions.. Simplify your answer. Link Back to List Slide 5 / 06 Slide 54 / = =

10 Slide 55 / 06 Slide 56 / ( 8) = 8 1 = True False Slide 57 / 06 Slide 58 / = A 21 C True False B 7 D 5 7 Slide 59 / 06 Slide 60 / ( ) A ( ) C 20 8 Dividing Fractions Leave the first fraction the same. 2. Multiply the first fraction by the reciprocal of the second fraction.. Simplify your answer. Dividing Mied Numbers... B D Rewrite the Mied Number(s) as an improper fraction(s). (write whole numbers / 1) 2. Divide the fractions.. Simplify your answer.

11 Slide 61 / 06 Slide 62 / 06 To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Make sure you simplify your answer! = Some people use the saying "Keep Change Flip" to help them remember the process. True False = = = = = = 2 5 Slide 6 / 06 Slide 64 / = = True False A B C Slide 65 / 06 Slide 66 / To divide fractions with whole or mied numbers, write the numbers as an improper fractions. Then divide the two fractions by using the rule (multiply the first fraction by the reciprocal of the second). Make sure you write your answer in simplest form = = = = = 2 = = 4 1

12 Slide 67 / 06 Slide 68 / = = Slide 69 / 06 Slide 70 / = Decimal Computation Return to Table of Contents Slide 71 / 06 List what you remember about decimals. Slide 72 / 06 Some division terms to remember... The number to be divided into is known as the dividend The number which divides the other number is known as the divisor The answer to a division problem is called the quotient 4 quotient 20 5 = 4 divisor 5 20 dividend 20 5 = 4

13 Slide 7 / 06 Slide 74 / 06 When we are dividing, we are breaking apart into equal groups EXAMPLE 1 Find 12 EXAMPLE 2 (change pages to see each step) Step 1 : Can go into 1, no so can go into 1, yes Step 2 : Bring down the 2. Can go into, yes = 1 - = 1 Compare 1 < 4 = - = 0 Compare 0 < Step 1: Can 15 go into, no so can 15 go into 5, yes = = 5 Compare 5 < 15 EXAMPLE 2 (change pages to see each step) Slide 75 / 06 EXAMPLE 2 (change pages to see each step) Slide 76 / 06 Step 2 : Bring down the 7. Can 25 go into 207, yes = = Compare < 15 Step : You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division = = 0 Compare 0 < 15 Slide 77 / 06 Slide 78 / Compute. 50 Compute.

14 Slide 79 / 06 Slide 80 / Compute. If you know how to add whole numbers then you can add decimals. Just follow these few steps. Step 1: Put the numbers in a vertical column, aligning the decimal points. Step 2: Add each column of digits, starting on the right and working to the left. Step : Place the decimal point in the answer directly below the decimal points that you lined up in Step 1. Slide 81 / 06 Slide 82 / Add the following: 5 Find the sum = = A 6.1 B C 1.15 D 0.16 C click click Slide 8 / 06 Slide 84 / Find the sum: = click What do we do if there aren't enough decimal places when we subtract? Don't forget...line Them Up! What goes here?

15 Slide 85 / 06 Slide 86 / = click = click Slide 87 / 06 Slide 88 / = click =.992 click Slide 89 / 06 Slide 90 / 06 If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step 1: Ignore the decimal points. Step 2: Multiply the numbers using the same rules as whole numbers. EXAMPLE } Step : Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer. There are a total of three digits to the right of the decimal points. There must be three digits to the right of the decimal point in the answer.

16 Slide 91 / Multiply click Slide 92 / Multiply click Slide 9 / 06 Slide 94 / Multiply Divide by Decimals Step 1: Change the divisor to a whole number by multiplying by a power of 10. Step 2: Multiply the dividend by the same power of 10. Step : Step 4: Use long division. Bring the decimal point up into the quotient. Divisor Quotient Dividend Slide 95 / 06 Slide 96 / 06 Try rewriting these problems so you are ready to divide! 62 Divide = click 9 Multiply by 10, so that 15.6 becomes must also be multiplied by Multiply by 1000, so that.24 becomes must also be multiplied by 1000

17 Slide 97 / 06 Slide 98 / divided by 0.25 = click = click Slide 99 / 06 There are two types of decimals - terminating and repeating. Eamples: Slide 100 / 06 A terminating decimal is a decimal that ends. All of the eamples we have completed so far are terminating. A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern. To denote a repeating decimal, a line is drawn above the numbers that repeat. However, with a calculator, the last digit is rounded Slide 101 / 06 Slide 102 / click

18 Slide 10 / 06 Slide 104 / click Statistics Return to Table of Contents Slide 105 / 06 List what you remember about statistics. Slide 106 / 06 Measures of Center Vocabulary: Mean - The sum of the data values divided by the number of items; average Median - The middle data value when the values are written in numerical order Mode - The data value that occurs the most often Slide 107 / 06 Slide 108 / 06

19 Slide 109 / 06 Slide 110 / 06 Slide 111 / 06 Measures of Variation Vocabulary: Slide 1 / 06 Minimum- The smallest value in a set of data Maimum- The largest value in a set of data Range - The difference between the greatest data value and the least data value Quartiles - are the values that divide the data in four equal parts. Lower (1st) Quartile (Q1) - The median of the lower half of the data Upper (rd) Quartile (Q) - The median of the upper half of the data. Interquartile Range - The difference of the upper quartile and the lower quartile. (Q - Q1) Outliers - Numbers that are significantly larger or much smaller than the rest of the data Slide 11 / 06 Slide 114 / 06 Quartiles There are three quartiles for every set of data. Lower Half Upper Half 10, 14, 17, 18, 21, 25, 27, 28 Q1 Q2 Q The lower quartile (Q1) is the median of the lower half of the data which is The upper quartile (Q) is the median of the upper half of the data which is 26. The second quartile (Q2) is the median of the entire data set which is The interquartile range is Q - Q1 which is equal to 10.5.

20 Slide 115 / 06 Slide 116 / 06 Slide 117 / 06 Slide 118 / 06 Slide 119 / 06 Slide 0 / 06

21 Slide 1 / 06 Slide 2 / 06 Slide / 06 Slide 4 / 06 The mean absolute deviation of a set of data is the average distance between each data value and the mean. Steps 1. Find the mean. 2. Find the distance between each data value and the mean. That is, find the absolute value of the difference between each data value and the mean.. Find the average of those differences. *HINT: Use a table to help you organize your data. Slide 5 / 06 Let's continue with the "Phone Usage" eample. Step 1 - We already found the mean of the data is 56. Step 2 - Now create a table to find the differences. Slide 6 / 06 Step - Find the average of those differences. Data Value Absolute Value of the Difference Data Value - Mean = The mean absolute deviation is.75. The average distance between each data value and the mean is.75 minutes. This means that the number of minutes each friend talks on the phone varies.75 minutes from the mean of 56 minutes.

22 Slide 7 / 06 Slide 8 / 06 SAMPLES: TEST SCORES Slide 9 / 06 Grade Tally Frequency 0-9 I I IIII IIII III III F 8 R E 6 Q U 4 E N 2 C Y GRADE Slide 10 / 06 A bo and whisker plot is a data display that organizes data into four groups Data Frequency Table Histogram The median divides the data into an upper and lower half TEST SCORES Grade Tally Frequency II III II I IIII 7II II 2 F 8 R E 6 Q U 4 E N 2 C Y GRADE The median of the lower half is the lower quartile. The median of the upper half is the upper quartile. The least data value is the minimum. The greatest data value is the maimum. Slide 11 / 06 Slide 12 / 06 25% 25% 25% 25% median The entire bo represents 50% of the data. 25% of the data lie in the bo on each side of the median Each whisker represents 25% of the data

23 Slide 1 / 06 Slide 14 / 06 Slide 15 / 06 Slide 16 / 06 Slide 17 / 06 Slide 18 / 06 A dot plot (line plot) is a number line with marks that show the frequency of data. A dot plot helps you see where data cluster. Eample: Test Scores The count of "" marks above each score represents the number of students who received that score.

24 Slide 19 / 06 Slide 140 / 06 Slide 141 / 06 Slide 142 / 06 Slide 14 / 06 Slide 144 / 06 List what you remember about the number system. Number System Return to Table of Contents

25 Slide 145 / 06 Define Integer Slide 146 / 06 Integers on the number line Definition of Integer: The set of natural numbers, their opposites, and zero. Negative Integers Zero Positive Integers Eamples of Integers: {...-6, -5, -4, -, -2, -1, 0, 1, 2,, 4, 5, 6, 7...} Numbers to the Numbers to the left of zero are Zero is neither right of zero are less than zero positive or negative greater than zero ` Slide 147 / 06 Slide 148 / 06 Slide 149 / 06 Slide 150 / 06

26 Slide 151 / 06 Absolute Value of Integers Slide 152 / 06 The absolute value is the distance a number is from zero on the number line, regardless of direction. Distance and absolute value are always nonnegative (positive or zero) What is the distance from 0 to 5? Slide 15 / 06 Slide 154 / 06 Slide 155 / 06 Slide 156 / 06 Use the Number Line To compare integers, plot points on the number line. The numbers farther to the right are greater. The numbers farther to the left are smaller

27 Slide 157 / 06 Slide 158 / 06 Slide 159 / 06 Slide 160 / 06 Slide 161 / 06 Slide 162 / 06 Comparing Rational Numbers Sometimes you will be given fractions and decimals that you need to compare. It is usually easier to convert all fractions to decimals in order to compare them on a number line. To convert a fraction to a decimal, divide the numerator by the denominator

28 Slide 16 / 06 Slide 164 / 06 Slide 165 / 06 Slide 166 / 06 (-, +) (+, +) y - ais origin 0 - ais (-, -) (+, -) The coordinate plane is divided into four sections called quadrants. The quadrants are formed by two intersecting number lines called aes. The horizontal line is the -ais. The vertical line is the y-ais. Slide 167 / 06 The point of intersection is called the origin. (0,0) Slide 168 / 06 To graph an ordered pair, such as (,2): start at the origin (0,0) move left or right on the -ais depending on the first number then move up or down from there depending on the second number plot the point (,2)

29 Slide 169 / 06 Slide 170 / 06 Slide 171 / 06 Slide 172 / 06 Slide 17 / 06 Slide 174 / 06 Epressions Return to Table of Contents

30 Slide 175 / 06 List what you remember about epressions. Slide 176 / 06 Eponents Eponents, or Powers, are a quick way to write repeated multiplication, just as multiplication was a quick way to write repeated addition. These are all equivalent: 2 4 Eponential Form Epanded Form 16 Standard Form In this eample 2 is raised to the 4 th power. That means that 2 is multiplied by itself 4 times. Slide 177 / 06 Powers of Integers Slide 178 / 06 Bases and Eponents When "raising a number to a power", The number we start with is called the base, the number we raise it to is called the eponent. The entire epression is called a power. 2 4 You read this as "two to the fourth power." Slide 179 / 06 Slide 180 / 06

31 Slide 181 / 06 Slide 182 / 06 Slide 18 / 06 Slide 184 / 06 What does P E M/D A/S stand for? What does "Order of Operations" mean? The Order of Operations is an agreed upon set of rules that tells us in which "order" to solve a problem. The P stands for Parentheses : Usually represented by ( ). Other grouping symbols are [ ] and { }. Eamples: (5 + 6); [5 + 6]; {5 + 6}/2 The E stands for Eponents : The small raised number net to the larger number. Eponents mean to the power (2nd, rd, 4th, etc.) Eample: 2 means 2 to the third power or 2(2)(2) The M/D stands for Multiplication or Division : From left to right. Eample: 4() or The A/S stands for Addition or Subtraction : From left to right. Eample: 4 + or 4 - Slide 185 / 06 Watch Out! Slide 186 / 06 When you have a problem that looks like a fraction but has an operation in the numerator, denominator, or both, you must solve everything in the numerator or denominator before dividing. 45 (7-2) 45 (5) 45 15

32 Slide 187 / 06 Slide 188 / 06 Slide 189 / 06 Slide 190 / 06 Slide 191 / 06 Slide 192 / 06 Let's try another problem. What happens if there is more than one set of grouping symbols? [ 6 + ( 2 8 ) + ( ) 7 ] When there are more than 1 set of grouping symbols, start inside and work out following the Order of Operations. [ 6 + ( 2 8 ) + ( ) 7 ] [ 6 + ( 16 ) + ( 16-9 ) 7 ] [ 6 + ( 16 ) + ( 7 ) 7 ] [ 6 + ( 16 ) + 1 ] [ ] [ 2 ] 69

33 Slide 19 / 06 Slide 194 / 06 Slide 195 / 06 Slide 196 / 06 Slide 197 / 06 What is a Constant? A constant is a fied value, a number on its own, whose value does not change. A constant may either be positive or negative. Eample: In this epression 2 is a constant. click to reveal Eample: 11m - 7 Slide 198 / 06 What is a Variable? A variable is any letter or symbol that represents a changeable or unknown value. Eample: In this epression is a variable. click to reveal In this epression -7 is a constant. click to reveal

34 Slide 199 / 06 What is a Coefficient? A coefficient is the number multiplied by the variable. It is located in front of the variable. Slide 200 / 06 If a variable contains no visible coefficient, the coefficient is 1. Eample 1: + 4 is the same as Eample: In this epression 4 is a coefficient. click to reveal Eample 2: Eample : is the same as has a coefficient of Slide 201 / 06 Slide 202 / 06 Slide 20 / 06 Slide 204 / 06

35 Slide 205 / 06 Slide 206 / 06 Slide 207 / 06 Slide 208 / 06 Slide 209 / 06 Slide 210 / 06

36 Slide 211 / 06 Slide 2 / 06 Equations and Inequalities Return to Table of Contents Slide 21 / 06 List what you remember about equations and inequalities. Slide 214 / 06 Determining the Solutions of Equations A solution to an equation is a number that makes the equation true. In order to determine if a number is a solution, replace the variable with the number and evaluate the equation. If the number makes the equation true, it is a solution. If the number makes the equation false, it is not a solution. Slide 215 / 06 Slide 216 / 06

37 Slide 217 / 06 Slide 218 / 06 Why are we moving on to Solving Equations? First we evaluated epressions where we were given the value of the variable and had which solution made the equation true. Now, we are told what the epression equals and we need to find the value of the variable. When solving equations, the goal is to isolate the variable on one side of the equation in order to determine its value (the value that makes the equation true). This will eliminate the guess & check of testing possible solutions. Slide 219 / 06 Slide 220 / 06 Slide 221 / 06 Slide 222 / 06

38 Slide 22 / 06 Slide 224 / 06 To solve equations, you must use inverse operations in order to isolate the variable on one side of the equation. Whatever you do to one side of an equation, you MUST do to the other side! Slide 225 / 06 Slide 226 / 06 Slide 227 / 06 Slide 228 / 06

39 Slide 229 / 06 Slide 20 / 06 Slide 21 / 06 Slide 22 / 06 Slide 2 / 06 Slide 24 / 06 An inequality is a statement that two quantities are not equal. The quantities are compared by using one of the following signs: Symbol Epression Words < A < B A is less than B > A > B A is greater than B < A < B > A > B A is less than or equal to B A is greater than or equal to B

40 Slide 25 / 06 Slide 26 / 06 Slide 27 / 06 Slide 28 / 06 Solution Sets Remember: Equations have one solution. Solutions to inequalities are NOT single numbers. Instead, inequalities will have more than one value for a solution This would be read as, "The solution set is all numbers greater than or equal to negative 5." Slide 29 / 06 Slide 240 / 06 Let's name the numbers that are solutions to the given inequality. r > 10 Which of the following are solutions? {5, 10, 15, 20} 5 > 10 is not true So, 5 is not a solution 10 > 10 is not true So, 10 is not a solution 15 > 10 is true So, 15 is a solution 20 > 10 is true So, 20 is a solution Answer: {15, 20} are solutions to the inequality r > 10

41 Slide 241 / 06 Slide 242 / 06 Slide 24 / 06 Since inequalities have more than one solution, we show the solution two ways. The first is to write the inequality. The second is to graph the inequality on a number line. In order to graph an inequality, you need to do two things: 1. Draw a circle (open or closed) on the number that is your boundary. 2. Etend the line in the proper direction. Slide 244 / 06 Remember! Closed circle means the solution set includes that number and is used to represent or. Open circle means that number is not included in the solution set and is used to represent < or >. Etend your line to the right when your number is larger than the variable. # > variable variable < # Etend your line to the left when your number is smaller than the variable. # < variable variable > # Slide 245 / 06 Slide 246 / 06

42 Slide 247 / 06 Slide 248 / 06 Slide 249 / 06 Slide 250 / 06 List what you remember about geometry. Geometry Return to Table of Contents Slide 251 / 06 The Area (A) of a rectangle is found by using the formula: A = length(width) A = lw Slide 252 / What is the Area (A) of the figure? 1 ft The Area (A) of a square is found by using the formula: 7 ft A = side(side) A = s 2

43 Slide 25 / 06 Slide 254 / Find the area of the figure below. 8 The Area (A) of a parallelogram is found by using the formula: A = base(height) A = bh Note: The base & height always form a right angle! Slide 255 / 06 Slide 256 / Find the area. 171 Find the area. 8 m 10 ft 9 ft 1 m 1 m m 11 ft 8 m Slide 257 / 06 Slide 258 / Find the area. The Area (A) of a triangle is found by using the formula: 1 cm cm 7 cm Note: The base & height always form a right angle!

44 Slide 259 / 06 Slide 260 / Find the area. 174 Find the area 10 in 8 in 9 in 10 m m 9 m 6 in 14 m Slide 261 / 06 Slide 262 / 06 The Area (A) of a trapezoid is also found by using the formula: 175 Find the area of the trapezoid by drawing a diagonal. 9 m Note: The base & height always form a right angle! 10 in 5 in 8.5 m 11 m in 176 Find the area of the trapezoid using the formula. Slide 26 / 06 Slide 264 / 06 Area of Irregular Figures 20 cm 1 cm cm 1. Divide the figure into smaller figures (that you know how to find the area of) 2. Label each small figure and label the new lengths and widths of each shape. Find the area of each shape 4. Add the areas 5. Label your answer

45 Slide 265 / 06 Slide 266 / 06 Eample: Find the area of the figure. 4 m 2 m m 8 m 177 Find the area. ' 4' 4 m 2 m #1 #2 m 2 m 6 m 2' 5' 1' 10' 8' Slide 267 / 06 Slide 268 / Find the area. 179 Find the area. 8 cm 18 cm cm 25 Slide 269 / 06 Slide 270 / 06 Area of a Shaded Region 1. Find area of whole figure. 2. Find area of unshaded figure(s). Eample Find the area of the shaded region. 10 ft Area Whole Rectangle. Subtract unshaded area from whole figure. 4. Label answer with units 2. ft ft 8 ft Area Unshaded Square Area Shaded Region

46 Slide 271 / Find the area of the shaded region. Slide 272 / Find the area of the shaded region. 11' ' 4' 16" 15" 7" 5" 8' 17" Slide 27 / 06 -Dimensional Solids Categories & Characteristics of -D Solids: Prisms 1. Have 2 congruent, polygon bases which are parallel to one another 2. Sides are rectangular (parallelograms). Named by the shape of their base Pyramids 1. Have 1 polygon base with a verte opposite it 2. Sides are triangular. Named by the shape of their base Cylinders 1. Have 2 congruent, circular bases which are parallel to one another 2. Sides are curved Cones 1. Have 1 circular bases with a verte opposite it 2. Sides are curved Slide 275 / 06 Slide 274 / 06 -Dimensional Solids Vocabulary Words for -D Solids: Polyhedron A -D figure whose faces are all polygons (Prisms & Pyramids) Face Flat surface of a Polyhedron Edge Line segment formed where 2 faces meet Verte (Vertices) Point where or more faces/edges meet Solid a -D figure Net a 2-D drawing of a -D figure (what a -D figure would look like if it were unfolded) Slide 276 / Name the figure. A rectangular prism B triangular prism C triangular D pyramid cylinder E cone F square pyramid 18 Name the figure. A rectangular prism B triangular prism C triangular D pyramid cylinder E cone F square pyramid

47 Slide 277 / 06 Slide 278 / Name the figure. 185 Name the figure. A B C D E F rectangular prism triangular prism triangular pyramid pentagonal prism cone square pyramid A B C D E F rectangular prism triangular prism triangular pyramid pentagonal prism cone square pyramid Slide 279 / 06 Slide 280 / Name the figure. A rectangular prism B cylinder C triangular D pyramid pentagonal prism E cone F square pyramid 187 How many faces does a cube have? Slide 281 / 06 Slide 282 / How many vertices does a triangular prism have? 189 How many edges does a square pyramid have?

48 Slide 28 / 06 Surface Area Eample Slide 284 / 06 The sum of the areas of all outside faces of a -D figure. To find surface area, you must find the area of each face of the figure then add them together. 7 in 2 in 6 in A net is helpful in calculating surface area. #1 6 in #2 # #4 6 in #5 #6 7 in 2 in 2 in #1 6 in #2 # #4 2 in 6 in #5 #6 2 in 7 in #1 #2 # #4 #5 #6 Simply label each section and find the area of each. Slide 285 / 06 Slide 286 / Find the surface area of the figure given its net. 191 Find the surface area of the figure given its net. 7 yd 7 yd cm 9 cm 7 yd 25 cm 7 yd Since all of the faces are the What same, pattern you can did find you the notice area while of one finding face and the multiply surface area it of by a 6 cube? to calculate the surface area of a cube. Slide 287 / 06 Volume Formulas Formula 1 V= lwh, where l = length, w = width, h = height Multiply the length, width, and height of the rectangular prism. Formula 2 Eample Slide 288 / 06 Each of the small cubes in the prism shown have a length, width and height of 1/4 inch. The formula for volume is lwh. Therefore the volume of one of the small cubes is: V=Bh, where B = area of base, h = height Find the area of the rectangular prism's base and multiply it by the height. Multiply the numerators Forget how to multiply together, then multiply the fractions? denominators. In other words, multiply across.

49 192 Find the volume of the given figure. Slide 289 / Find the volume of the given figure. Slide 290 / 06 Slide 291 / 06 Slide 292 / Find the volume of the given figure. Ratios and Proportions Return to Table of Contents Slide 29 / 06 Slide 294 / 06 List what you remember about the ratios and proportions. Ratio- A comparison of two numbers by division Ratios can be written three different ways: a to b a : b a b Each is read, "the ratio of a to b." Each ratio should be in simplest form.

50 Slide 295 / 06 Slide 296 / There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of vanilla cupcakes to strawberry cupcakes? 196 There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of chocolate & strawberry cupcakes to vanilla & chocolate cupcakes? A 7 : 9 B 7 27 C 7 11 D 1 : A B 11 7 C 5 4 D Slide 297 / 06 Slide 298 / There are 27 cupcakes. 9 are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of total cupcakes to vanilla cupcakes? Equivalent ratios have the same value A 27 to 9 : 2 is equivalent to 6: 4 B 7 to 27 1 to is equivalent to 9 to 27 C 27 to 7 D 11 to is equivalent to Slide 299 / 06 There are two ways to determine if ratios are equivalent Since the numerator and denominator were multiplied by the same value, the ratios are equivalent is equivalent to True False Slide 00 / Cross Products Since the cross products are equal, the ratios are equivalent = 5 60 = 60

51 199 5 is equivalent to True False Slide 01 / 06 Slide 02 / 06 Rate: a ratio of two quantities measured in different units Eamples of rates: 4 participants/2 teams 5 gallons/ rooms 8 burgers/2 tomatoes Unit rate: Rate with a denominator of one Often epressed with the word "per" Eamples of unit rates: 4 miles/gallon 2 cookies per person 62 words/minute Slide 0 / 06 Finding a Unit Rate Si friends have pizza together. The bill is $6. What is the cost per person? Slide 04 / Sity cupcakes are at a party for twenty children. How many cupcakes per person? Hint: Since the question asks for cost per person, the cost should be first, or in the numerator. $6 6 people Since unit rates always have a denominator of one, rewrite the rate so that the denominator is one. $6 6 6 people 6 $ person The cost of pizza is $10.50 per person Slide 05 / 06 Slide 06 / John's car can travel 94.5 miles on gallons of gas. How many miles per gallon can the car travel? 202 The snake can slither 24 feet in half a day. How many feet can the snake move in an hour?