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This is a 7 th review:

This is a 7 th review:. This is for you to study on. Please take notes and answer the questions as you go. There are over 90 Slides. This should take you more than today’s class to finish….take your time and work out each question. There are purple hints… Just like this one through out

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This is a 7 th review:

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  1. This is a 7th review: This is for you to study on. Please take notes and answer the questions as you go. There are over 90 Slides. This should take you more than today’s class to finish….take your time and work out each question.

  2. There are purple hints… Just like this one through out The slide. Write them down and bring them to Mr. Todd for a prize on Friday

  3. 4 n • Try These-look them up if you forgot • The product of four and a number is decreased by ten and increase by a different number. • 2. The sum of two different numbers is decreased by two • 3. The difference of two different numbers is increased three. 4x – 10 + y x + y – 2 x – y + 3 C. the difference of 3 times a number and 7 3x – 7 D. the quotient of 4 and a number, increased by 10 + 10

  4. Solve for X – Don’t forget the cookie! • 15 + x = 25 • 2. x - 15 = 25 • 3. 15x = 30 • 4. x - 5= 35 -15 -15 X= 10 +15 +15 X = 40 15 15 X = 2 40 X =

  5. Insert Lesson Title Here Lesson Quiz 12 24 1 2 1. Write a fraction equivalent to . 2. Write as a mixed number. 3. Write 4 as an improper fraction. 4. A carpenter is building a stairway. Each stair has to be 12 in. wide. The carpenter’s ruler is marked in sixteenths. What length should he measure? 1 8 17 8 2 3 7 31 7 7 8 14 16 in. 12

  6. • • • • • –5 –4 –3 –2 –1 0 1 2 3 4 5 Compare. Use <, >, or =. 1. –32 32 2. 26 |–26| 3. –8–12 4. Graph the numbers –2, 3, –4, 5, and –1 on a number line. Then list the numbers in order from least to greatest. < = > –4, –2, –1, 3, 5

  7. 3-3 Adding Integers Course 2 Insert Lesson Title Here Lesson Quiz Add. 1. –7 + (–6) 2. –15 + 24 + (–9) 3. –24 + 7 + (–3) 4. Evaluate x + y for x = –2 and y = –15. –13 0 –20 –17 5. The math club’s income from a bake sale was $217. Advertising expenses were $32. What is the club’s total profit or loss? $185 profit

  8. 3-4 Subtracting Integers Course 2 Insert Lesson Title Here Lesson Quiz Subtract. 1. 3 – 9 2. –7 – 4 3. –3 – (–5) 4. Evaluate x – y – z for x = –4, y = 5, and z = –10. –6 –11 2 1 5. On January 1, 2002, the high temperature was 81˚F in Kona, Hawaii. The low temperature was –29˚F in Barrow, Alaska. What was the difference between the two temperatures? 110˚F

  9. 3-5 Multiplying and Dividing Integers Course 2 Insert Lesson Title Here Lesson Quiz Find each product or quotient. 1. –8 · 12 2. –3 · 5 · (–2) 3. –75 ÷ 5 4. –110 ÷ (–2) 5. The temperature at Bar Harbor, Maine, was –3°F. It then dropped during the night to be 4 times as cold. What was the temperature then? –96 30 –15 55 –12˚F

  10. Exponents with negative bases Find each value. 1. -23 3. -32 -8 2. -53 -125 9 4. -52 25

  11. 3-2 The Coordinate Plane 5 y 4 3 2 1 0 x 2 –1 –4 –2 1 –3 3 5 4 –5 –1 –2 –3 –4 –5 Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 Give the coordinates of each point and identify the quadrant that contains each point A 1.A (–2, 4); II C 2.B (3, –2); IV 3.C (2, 3); I Plot each point on a coordinate plane. E B 4.D (2, –3) D 5.E (–4, –2)

  12. Frequency Tables and Stem-and-Leaf Plots 1-3 English Exam Grades Cumulative Frequency Grades Frequency Course 2 Try This: Example 1 The list shows the grades received on an English exam. Make a cumulative frequency table of the data. 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96 Step 1: Look at the range to choose equal intervals for the data. 60–69 70–79 80–89 90–99

  13. Frequency Tables and Stem-and-Leaf Plots 1-3 English Exam Grades Cumulative Frequency Grades Frequency 60–69 70–79 80–89 90–99 Course 2 Try This: Example 1 Continued The list shows the grades received on an English exam. Make a cumulative frequency table of the data. 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96 Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column. 4 4 6 6

  14. Frequency Tables and Stem-and-Leaf Plots 1-3 English Exam Grades Cumulative Frequency Grades Frequency 4 60–69 4 70–79 80–89 6 6 90–99 Course 2 Try This: Example 1 Continued The list shows the grades received on an English exam. Make a cumulative frequency table of the data. 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96 Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row. 4 8 14 20

  15. Don’t tell anyone else Hint: Full of energy Remember you must wait till Friday

  16. Frequency Tables and Stem-and-Leaf Plots 1-3 Stems Leaves Course 2 Additional Example 2 Continued The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 3: List the leaves for each stem from least to greatest. The stems are the tens digits. The leaves are the ones digits. 8 5 5 7 7 2 1 2 3 4 0 3 2 3 9 1 3 3 0

  17. 1-4 Bar Graphs and Histograms Pet Class A Class B Dog 12 14 Cat 9 8 Bird 2 3 Course 2 Try This: Example 2 The table shows the number of pets owned by students in two classes. Step 1: Choose a scale and interval for the vertical axis. 16 12 8 4 0

  18. 1-4 Bar Graphs and Histograms 16 12 8 4 0 Pet Class A Class B Dog 12 14 Cat 9 8 Bird 2 3 Course 2 Try This: Example 2 Step 2: Draw a pair of bars for each pet’s data. Use different colors to show class A and class B.

  19. 1-4 Bar Graphs and Histograms 16 12 8 4 0 Pet Class A Class B Dog 12 14 Cat 9 8 Bird 2 3 Course 2 Try This: Example 2 Step 3: Label the axes and give the graph a title. Pets Owned in Two Classes Number of pets Cat Bird Dog

  20. 1-4 Bar Graphs and Histograms 16 12 8 4 0 Pet Class A Class B Dog 12 14 Cat 9 8 Bird 2 3 Course 2 Try This: Example 2 Step 4: Make a key to show what each bar represents. Pets Owned in Two Classes Number of pets Cat Bird Dog Class A Class B

  21. 1-4 Bar Graphs and Histograms Frequency Number of Hats Owned Course 2 Try This: Example 3 Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap. 30 25 20 15 10 5 0 1–3 12 18 4–6 7–9 24

  22. 1-4 Bar Graphs and Histograms Frequency Number of Hats Owned Course 2 Try This: Example 3 Number of Hats Owned Step 4: Label the axes and give the graph a title. 30 25 20 15 10 5 0 Frequency 1–3 12 18 4–6 7–9 24 7–9 1–3 4–6 Number of Hats

  23. Reading and Interpreting Circle Graphs 1-5 Course 2 Additional Example 2B: Interpreting Circle Graphs Leon surveyed 30 people about whether they own pets. The circle graph shows his results. Use the graph to answer each question. B. If 60 people were surveyed and 12 people said they own dogs only, how many people own both cats and dogs? Since 20% is 12 people, 10% is 6 people. Six people own both cats and dogs.

  24. Reading and Interpreting Circle Graphs 1-5 Course 2 Try This: Example 2A Fifty students were asked which instrument they could play. The circle graph shows the responses. Use the graph to answer each question. flute 10% drum 20% A. How many students do not play an instrument? The circle graph shows that 50%, or one-half, of the students play no instrument. One-half of 50 is 25, so twenty-five students do not play an instrument. no instrument 50% piano 20%

  25. Reading and Interpreting Circle Graphs 1-5 Course 2 Try This: Example 2B Fifty students were asked which instrument they could play. The circle graph shows the responses. Use the graph to answer each question. flute 10% drum 20% B. Ten students said they play the piano. How many play the flute? Since 20% is 10 students, 10% is 5 students. Five students play the flute. no instrument 50% piano 20%

  26. 1-8 Scatter Plots Course 2 There are three ways to describe data displayed in a scatter plot. Positive Correlation Negative Correlation No Correlation The values in both data sets increase at the same time. The values in one data set increase as the values in the other set decrease. The values in both data sets show no pattern.

  27. Are you writing any of this down?

  28. 1-9 Misleading Graphs Course 2 Lesson Quiz: Part 1 Explain why each graph could be misleading and why. The vertical scale on the graph is not small enough to show the changes, so it appears to be unchanging and flat.

  29. 1-9 Misleading Graphs Course 2 Lesson Quiz: Part 2 Explain why each graph could be misleading and why. The scale does not start at 0, so it emphasizes the differences in bar heights more.

  30. Best laugh ever!

  31. Chapter 2 Evaluate 1.18 ÷ 3 + 7 2. 102 ÷ (8 - 4) 3. 10 + {23 – (8 + 7)} 4. 8(2 + 3) + 24 5. 81 ÷ 92 3 + 15 13 25 18 64 18

  32. Helpful Hint When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set. 1. Perform operations within grouping symbols. 2. Evaluate powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.

  33. 2-4 Prime Factorization Course 2 A composite number is a whole number that has more than two factors. Six is a composite number because it has more than two factors—1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite. A composite number can be written as the product of its prime factors. This is called the prime factorization of the number. You can use a factor tree to find the prime factors of a composite number.

  34. Did you actually read the last slide?

  35. 2-4 Prime Factorization Course 2 Additional Example 1A: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. A. 24 Write 24 as the product of two factors. 24 8 · 3 Continue factoring until all factors are prime. 4 · 2 · 3 2 · 2 · 2 · 3 The prime factorization of 24 is 2 · 2 · 2 · 3. Using exponents, you can write this as 23 · 3.

  36. Insert Lesson Title Here Lesson Quiz Use a factor tree to find the prime factorization. 1. 27 2. 36 3. 28 Use a step diagram to find the prime factorization. 4. 132 5. 52 6. 108 33 22 · 32 22 · 7 22 · 3 · 11 22 · 13 22 · 33

  37. 2-5 Greatest Common Factor Course 2 Warm Up Write the prime factorization of each number. SHOW YOUR WORK 1.20 2. 100 3. 30 4. 128 5. 70 22 · 5 22 · 52 2 · 3 · 5 27 2 · 5 · 7

  38. Its all over his walls at mr. Todd’s house.. Well at least his babies room

  39. 2-5 Greatest Common Factor Course 2 The greatest common factor (GCF) of two or more whole numbers is the greatest whole number that divides evenly into each number. One way to find the GCF of two or more numbers is to list all the factors of each number. The GCF is the greatest factor that appears in all the lists.

  40. 2-5 Greatest Common Factor Course 2 Additional Example 1:Using a List to Find the GCF Find the greatest common factor (GCF). 12, 36, 54 List all of the factors of each number. 12: 1, 2, 3, 4, 6, 12 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Circle the greatest factor that is in all the lists. 54: 1, 2, 3, 6, 9, 18, 27, 54 The GCF is 6.

  41. 2-5 Greatest Common Factor Course 2 Additional Example 2A: Using Prime Factorization to Find the GCF Find the greatest common factor (GCF). A. 40, 56 Write the prime factorization of each number and circle the common factors. 40 = 2 · 2 · 2 · 5 56 = 2 · 2 · 2 · 7 2 · 2 · 2 = 8 Multiply the common prime factors. The GFC is 8.

  42. 2-5 Greatest Common Factor Course 2 Additional Example 2B: Using Prime Factorization to Find the GCF Find the greatest common factor (GCF). B. 252, 180, 96, 60 Write the prime factorization of each number and circle the common prime factors. 252 = 2 · 2 · 3 · 3 · 7 180 = 2 · 2 · 3 · 3 · 5 96 = 2 · 2 · 2 · 2 · 2 · 3 60 = 2 · 2 · 3 · 5 2 · 2 · 3 = 12 Multiply the common prime factors. The GCF is 12.

  43. 2-5 Greatest Common Factor Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 Find the greatest common factor (GCF). 1. 28, 40 2. 24, 56 3. 54, 99 4. 20, 35, 70 4 8 9 5

  44. 2-6 Least Common Multiple Course 2 A multiple of a number is a product of that number and a whole number. Some multiples of 7,500 and 5,000 are as follows: 7,500: 7,500, 15,000, 22,500, 30,000, 37,500, 45,000, . . . 5,000: 5,000, 10,000, 15,000, 20,000, 25,000, 30,000, . . . A common multiple of two or more numbers is a number that is a multiple of each of the given numbers. So 15,000 and 30,000 are common multiples of 7,500 and 5,000.

  45. 2-6 Least Common Multiple Course 2 The least common multiple (LCM) of two or more numbers is the common multiple with the least value. The LCM of 7,500 and 5,000 is 15,000. This is the lowest mileage at which both services are due at the same time.

  46. 2-6 Least Common Multiple Course 2 Additional Example 2A: Using Prime Factorization to Find the LCM Find the least common multiple (LCM). A. 60, 130 60 = 2 · 2 · 3 · 5 Write the prime factorization of each number. 130 = 2 · 5 · 13 Circle the common prime factors. List the prime factors, using the circled factors only once. 2, 2, 3, 5, 13 2 · 2 · 3 · 5 · 13 Multiply the factors in the list. The LCM is 780.

  47. 2-6 Least Common Multiple Course 2 Additional Example 2B: Using Prime Factorization to Find the LCM Find the least common multiple (LCM). B. 14, 35, 49 Write the prime factorization of each number. 14 = 2 · 7 35 = 5 · 7 Circle the common prime factors. 49 = 7 · 7 List the prime factors, using the circled factors only once. 2, 5, 7, 7 Multiply the factors in the list. 2 · 5 · 7 · 7 The LCM is 490.

  48. 2-6 Least Common Multiple Course 2 Insert Lesson Title Here Try This: Example 2A Find the least common multiple (LCM). A. 50, 130 Write the prime factorization of each number. 50 = 2 · 5 · 5 Circle the common prime factors. 130 = 2 · 5 · 13 List the prime factors, using the circled factors only once. 2, 5, 5, 13 2 · 5 · 5 · 13 Multiply the factors in the list. The LCM is 650.

  49. Vocabulary A variable is a symbol, normally a letter of the alphabet, that represents one or more numerical values. It takes the place of a number! Variable = ?Some Unknown Number? A constant is a quantity that does not change.

  50. • add 3 to a number • a number plus 3 + • the sum of a number and 3 n + 3 • 3 more than a number • a number increased by 3 • subtract 12 from a number • a number minus 12 • the difference of a number and 12 - x – 12 • 12 less than a number • a number decreased by 12 • take away 12 from a number • a number less than 12

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