Using Proportions to Solve Percent Problems (page 562)

LESSON Name 81 Using Proportions to Solve Percent Problems (page 562) Percent problems can be solved using proportions. Make and complete a percent box. (The total is always 100.) 1. Write in the known facts. 2. Write a letter in each unknown box. Write a proportion using only two rows. Use the row that answers the question asked. Use the row that is complete with two numbers. Solve the proportion. 1. Cross-multiply. 2. Divide by the known factor. Practice Set (page 565) Example: Thirty percent of the class passed the test. If 21 students did not pass the test, how many students were in the class? did not pass total 100 130 70 70 100 = 21 t 70 t = 100 21 70t = 2100 t = 2100 70 t = 30 students Twenty-one of the 70 acres were planted with alfalf What percent of the acres was not planted with alfalfa? 70 21 not total n 100 = 70 Lori still has 60% of the book to read. If she has read 120 pages, how many pages does she still have to read? 100 160 has read still to read = s pages c. Dewayne missed four of the 30 problems on the problem set. What percent of the problems did Dewayne answer correctly? 30 34 d. Tell whether you found a part, a whole, or a percent to solve each of problems a through c. c. Saxon Math Course 2 L81-325 Adaptations Lesson 81

Written Practice (page 565) 1. A(2, 1), B(5, 1), C(5, 3) Reflect across the x-axis. 2. 3. 70, 80, 80, 80, 85, 85, 85, 85, 85, 90, 90, 90, 90, 95, 100 A (, ), B (, ), C (, ) 4. The most common number is the. He typed 5. 6 ft 1 in. 5 ft 6 1 2 in. five times, more than any other number. range: 6. 7. x < 4 x 2 8. 48 is 4 of the invitations 5 is of? sent not sent 9. Think in 1_ 8 s. AC = in. 1 of AC = in. 2 Saxon Math Course 2 L81-326 Adaptations Lesson 81

Written Practice (continued) (page 566) 10. If x = 9, what does x 2 + x equal? 11. 3 to not 3 12. to 13. $12 14. 50% = is of 0.4? 15. 16 2_ 3 100 16. 17. 100 20 round total = 18. m CBD = because angles ABC and CBD are s and total. m DBE = because angles CBD and DBE are c and total. c. m EBA = because angles DBE and EBA are s and total. d. 19. Cancel matching zeros first. 3000 6300 = = ) ) ) 30 ) ) ) 63 = 20. A = 1 2 (b 1 + b 2 )h Draw the line of symmetry. Saxon Math Course 2 L81-327 Adaptations Lesson 81

Written Practice (continued) (page 567) 21. Double the number then s 1 to find the out n. Rule: y = The missing number is. 22. 56 10 7 = 56 10 7 = 23. Solve: Check: 5x = 16.5 5x = 16.5 5x = 16.5 = 16.5 x = 16.5 = 16.5 24. Solve: Check: 3 1 2 + a = 5 3 8 3 1 2 + a = 5 3 8 a = 5 3 8 3 1 2 + a = 5 3 8 = 5 3 8 = 5 3 8 25. 3 2 + 5[6 (10 2 3 )] = 26. 2 2 3 4 5 2 = Take half of the exponent of each prime factor. Multiply. 27. fraction answer 2 2 3 4.5 6 28. decimal answer ( 3 1 2 ) 2 (5 3.4) 5.. 29. ( 1.2)( 9) = ( 3)(2.5) = 30. ( 3) + 4 ( 5) = ( 18) (+20) + ( 7) = c. ( 1 2 ) ( 1 2 ) = c. 1 2 ( 1 2 ) = d. ( 1 2 ) ( 1 2 ) = c. Saxon Math Course 2 L81-328 Adaptations Lesson 81

LESSON 82 Area of a Circle (page 569) Name To find the areas of some polygons, multiply the two perpendicular dimensions. Teacher Note: Review Geometric Formulas on page 29 in the Student Reference Guide. A = lw A = lw A = bh Rectangle Parallelogram Triangle A = bh 2 A = 1 2 bh To find the area of a circle, begin by multiplying two perpendicular dimensions. 1. Multiply the radius by the radius. This equals the area of a square built on a radius. Area of a square = r 2 The area of the circle is less than the area of four of these squares, but it is more than the area of three squares. The exact number is π. π is between 3 and 4. π 3.14 2. Multiply π times the area of the square built on the radius to find the area of the circle. A = π r 2 Example: Find the area of a circle with a radius of 10 cm. Use 3.14 for π. The area of a square built on the radius is 10 cm 10 cm = 100 c m 2. Multiply this by π. A = π r 2 A (3.14)(100 c m 2 ) A 314 c m 2 Practice Set (page 571) Find the area of each of these circles. Round to the nearest foot. Use 3.14 for π. Use 3.14 for π. c. d. Leave π as π. Use 22 7 for π. e. Make a rough estimate of the area of a circle that has a diameter of 2 meters. Explain. The d of the circle is 2 m, so the radius is m. A = π and π is about 3, so the area is about m 2. Saxon Math Course 2 L82-329 Adaptations Lesson 82

Written Practice (page 571) 1. 2. Change to inches. Then find the average in feet and inches. 6' 3" 75 in. 6' 5" 5' 11" 6' 2" 6' 1" 5000 5000 3. 4. 2.54 cm 000cm 000cm = 5. x < 2 6. x 0 7. 8. If x = 5 and y = 3, compare: x 2 y 2? (x + y)(x y) 9. 100 10. Saxon Math Course 2 L82-330 Adaptations Lesson 82

Written Practice (continued) (page 572) 11. circumference 12. area 13. 14. is of? 100 15. 12 10 5 = 12 10 5 = 16. 100 64 17. 100 40 19. X (4, 3), Y (4, 1), Z (1, 1) Slide each vertex 5 units left and 3 units down. I used the percent box to set up a p and then solved for pages. 18. X (, ), Y (, ), Z (, ) Saxon Math Course 2 L82-331 Adaptations Lesson 82

Written Practice (continued) (page 573) 20. 240 816 = ) ) ) ) ) ) 240 ) ) ) ) ) ) 816 = 21. c. d. 22. 100 million 23. Solve: Check: 3 4 x = 36 3 4 x = 36 ( 3 4 ) x = 36 = 36 x = = 36 24. Solve: Check: 3.2 + a = 3.46 3.2 + a = 3.46 25. 3 2 + 4 2 5 = 3.2 + a = 3.46 = 3.46 a = = 3.46 26. (8 3) 2 (3 8) 2 = 27. decimal answer 28. mixed-number answer 29. ( 3)( 4) = ( 2) ( 2 3 ) ( 3 4 ) = 3 1 (7 0.2) 2 4.5 + 2 2 3 3 2 2 3 = 00 00 + 2 2 3 = 00 00 3 30. ( 0.3) + ( 0.4) ( 0.2) = ( 20) + (+30) 40 = Saxon Math Course 2 L82-332 Adaptations Lesson 82

LESSON Name 83 Multiplying Numbers in Scientific Notation (page 575) To multiply powers of 10, add the exponents. 10 3 10 4 = 10 3 + 4 = 10 7 To multiply numbers in scientific notation: 1. Multiply the decimal or whole numbers to find the decimal or whole number part of the product. 2. Multiply powers of 10. (Add the exponents.) 3. Write the expression in the proper form of scientific notation. Example: Multiply (1.2 10 5 )(3 10 7 ) 1. Multiply decimal (or whole) numbers. 1.2 3 = 3.6 2. Multiply powers of 10. 10 5 10 7 = 10 5 + 7 = 10 12 3. The product is 3.6 10 12. Teacher Note: Review Scientific Notation for Numbers Powers of 10 on page 21 in the Student Reference Guide. Example: Multiply (4 10 6 )(3 10 5 ) 1. Multiply whole (or decimal) numbers. 4 3 = 12 2. Multiply the powers of 10. 10 6 10 5 = 10 6 + 5 = 10 11 3. The product is 12 10 11. 12 is a two digit whole number so we rewrite the expression in the proper form of scientific notation. (1.2 10 1 ) 10 11 = 1.2 10 12 Practice Set (page 577) Multiply and write each product in scientific notation. (4.2 10 6 )(1.4 10 3 ) =. 10 (5 10 5 )(3 10 7 ) =. 10 c. (4 10 3 )(2.1 10 7 ) =. 10 d. (6 10 2 )(7 10 5 ) =. 10 e. Show the commutative and associative steps: 3 10 3 2 10 4 Given 3 2 Commutative Property (3 2) ( ) Associative Property 6 Simplified Saxon Math Course 2 L83-333 Adaptations Lesson 83

Written Practice (page 577) 1. oz $ oz $ 16? 24? 2. per 3. average in 20 days 4. $ hr? 42 15 50 5 5. shillings 12 pence = 6. x 1 1 shilling 7. 8. a = 1.5 4a + 5 = 9. is of? 10. sample space: { H1,, H2,,,, } Saxon Math Course 2 L83-334 Adaptations Lesson 83

Written Practice (continued) (page 578) 11. circumference 12. area Leave π as π. Use 22 7 for π. 13. 14. 15. $8.50 $8.50 16. 17. 18. Cancel the matching zeros first. 420 630 = = ) ) ) 42 ) ) ) 63 = 19. A = 1 2 (b 1 + b 2 )h 20. m A = m B m ECD = m ECB = c. m ACB = d. m BAC = Saxon Math Course 2 L83-335 Adaptations Lesson 83

Written Practice (continued) (page 579) 21. Multiply the number by and then add to find the out number. Rule: y = The missing number is. 22. (3 10 4 )(6 10 5 ) = (1.2 10 3 )(4 10 6 ) = 23. Solve: Check: b 1 2 3 b 1 2 3 = 4 1 2 = 4 1 2 b = b 1 2 3 = 4 1 2 = 4 1 2 = 4 1 2 24. Solve: Check: 0.4y = 1.44 0.4y = 1.44 0.4y = 1.44 = 1.44 y = = 1.44 25. 2 3 + 2 2 + 2 1 + 2 0 + 2 1 = 26. 0.6 3 1 3 2 = 27. ( 4)( 6) ( 2)( 3) = ( 3)( 4)( 5) = 28. 5 24 = 00 00 7 60 = 00 00 30. P (0, 1), Q (0, 0), R ( 2, 0) 180 clockwise rotation around origin 29. ( 3) + ( 4) ( 5) = ( 1.5) (+1.4) + (+1.0) = P (, ), Q (, ), R (, ) Saxon Math Course 2 L83-336 Adaptations Lesson 83

LESSON 84 Algebraic Terms (page 580) Name Term in algebra refers to a part of an algebraic expression or equation. An algebraic expression may have 1, 2, 3, or more terms. Some Polynomials Teacher Note: Review Properties of Operations on page 20 in the Student Reference Guide. Type of Polynomials Number of Terms Example monomial 1 2x binomial 2 a 2 4b 2 trinomial 3 3x 2 x 4 Each term has a signed number and may have one or more variables (letters). When a term is written without a number, it is understood that the number is 1. When a term is written without a sign, it is understood that the sign is positive. A term with no variable is called a constant term. Its value does not change. Constant terms can be combined by algebraic addition. Variable terms can also be combined by algebraic addition. They must be like terms (identical letter parts). 3xy and xy are like terms. 3xy + 1xy = 2xy Example: Collect like terms 3x + 2x 2 + 4 + x 2 x 1 There are three kinds of terms in this expression: two x terms, two x 2 terms, and two constant terms. 2x 2 + x 2 + 3x x + 4 1 Commutative Property 3x 2 + 3x x + 4 1 combined x 2 terms 3x 2 + 2x + 4 1 combined x terms 3x 2 + 2x + 3 combined constant terms Notice that x and x 2 are not like terms and cannot be combined. Always arrange terms in descending order of exponents. The term with the largest exponent is on the left and the constant term is on the right. Practice Set (page 582) Describe each of these expressions as a monomial, a binomial, or a trinomial. x 2 y 2 3x 2 2x 1 c. 2x 3 yz 2 d. 2x 2 y 4xy 2 e. State the number of terms in the expressions in problems a d. c. d. Saxon Math Course 2 L84-337 Adaptations Lesson 84

Practice Set (continued) (page 583) Collect the terms. f. 3a + 2a 2 a + a 2 = 3a 2 + g. 5xy x + xy 2x = h. 3 + x 2 + x 5 + 2x 2 = i. 3π + 1.4 π + 2.8 = Written Practice (page 583) 1. An increase of 100 C is an increase of 180 F. 2. 2xy + xy 3x + x = C F 100 180? 3. 4. 80, 85, 90, 90, 95, 95, 100, 100, 100, 100 c. c. d. 5. 6. A ( 4, 1), B ( 1, 3), C ( 1, 1) Reflect across the x-axis. 7. items $? 8. A (, ), B (, ), C (, ) 9. Evaluate each expression for x = 5. x 2 2x + 1 = (x 1) 2 = Saxon Math Course 2 L84-338 Adaptations Lesson 84

Written Practice (continued) (page 584) 10. Compare: f? g 11. 12. 4.8 m cm cm = if f g = 1 Use 3.14 for π. f g 13. 14. How many faces? 15. $18.00 $18.00 16. 12 1_ 2 100 17. 100 40 18. 100 60 19. 20. Think in fractions of 360. A 60 B 90 C 45 D 30 E 75 F 40 G 20 A 360 = C 360 = c. E 360 = c. Saxon Math Course 2 L84-339 Adaptations Lesson 84

Written Practice (continued) (page 585) 21. To find a term in the sequence, d the preceding term and add. 1, 3, 7, 15, 31,,, 22. (1.5 10 3 )(3 10 6 ) = (3 10 4 )(5 10 5 ) = 23. 10 2 10 2 10 2 = 10 102 10 = 10 6 24. Solve: Check: b 4.75 = 5.2 b 4.75 = 5.2 b 4.75 = 5.2 = 5.2 b = 5.2 = 5.2 25. Solve: Check: 2 3 y = 36 2 3 y = 36 ( 2 3 ) y = 36 = 36 y = 36 = 36 26. 5 2 4 2 + 2 3 = 27. 1 m = mm 1 m 45 mm 28. decimal answer 9 10 2 1 4 24 29. ( 8)(+6) ( 3)(+4) = ( 1 2 ) ( 1 3 ) ( 1 4 ) = 30. (+30) ( 50) (+20) = ( 0.3) ( 0.4) ( 0.5) = Saxon Math Course 2 L84-340 Adaptations Lesson 84

LESSON Name 85 Order of Operations with Positive and Negative Numbers (page 586) To simplify expressions that have several operations, perform the operations in a special order. 1. Simplify within parentheses, brackets, or braces. 2. Multiply and divide, in order, left to right. 3. Add and subtract, in order, left to right. Example: Simplify ( 2) [( 3) ( 4)( 5)] There are only two terms ( 2 and the quantity in brackets). The slash separates the two terms. ( 2) / [( 3) ( 4)( 5)] ( 2) / [( 3) (+20)] ( 2) / ( 23) ( 2) / +23 +21 Teacher Note: Review Order of Operations on page 22 and charts about operations with signed numbers on page 26 in the Student Reference Guide. Practice Set (page 589) Simplify: ( 3) + ( 3)( 3) ( 3) = ( 3) [( 4) ( 5)( 6)] = (+3) c. ( 2)[( 3) ( 4)( 5)] = d. ( 5) ( 5)( 5) + 5 = e. 3 + 4 5 2 = f. 2 + 3( 4) 5( 2) = g. 3( 2) 5(2) + 3( 4) = h. 4( 3)( 2) 6( 4) = Saxon Math Course 2 L85-341 Adaptations Lesson 85

Written Practice (page 589) 1. 70, 70, 75, 80, 80, 90, 90, 90, 95, 100 2. c. d. 3. 4. 5. 0.98 L ml ml = 6. x > 0 7. 8. 9. 2 5 = 1 4 = 10. Multiply the fraction shaded by itself. = Saxon Math Course 2 L85-342 Adaptations Lesson 85

Written Practice (continued) (page 590) 11. V = lwh 12. surface area 13. 14. 6% fee $180,000 $180,000 15. 17,640 = ) 17,640 ) 17,640 ) 17,640 ) 17,640 ) 17,640 ) 17,640 ) 17,640 ) 17,640 The exponents of the p factors of 17,640 are not all e numbers. 16. 8 1_ 3 100 17. 20. Complete the table. Graph the points and draw the line. Name another point on the line. (, ) y = 2x 1 x y 5 3 1 18. 19. p c. d. Locate point of symmetry. 100 035 Saxon Math Course 2 L85-343 Adaptations Lesson 85

Written Practice (continued) (page 591) 21. 22. (5 10 3 )(6 10 8 ) (5 10 8 )(6 10 3 ) c. d. 23. Solve: Check: 13.2 = 1.2w 13.2 = 1.2w 13.2 = 1.2w 13.2 = = w 13.2 = 24. Solve: Check: c + 5 6 c + 5 6 = 1 1 4 = 1 1 4 c = c + 5 6 = 1 1 4 = 1 1 4 = 1 1 4 25. 3{20 [6 2 3(10 4)]} = 26. 3 hr 15 min 25 s 2 hr 45 min 30 s 27. decimal answer 30. A (1, 2), B (4, 2), C (4, 1) 2 0 + 0.2 + 2 2 Reflect across the x-axis. D (, ) 28. 3 ( 2) (+2) ( 2) ( 2) = A ( 1, 2), B (, ), C (, ), D (, ) ( 3) [( 2) (+4)( 5)] = 29. x 2 + 6x 2x 12 = Saxon Math Course 2 L85-344 Adaptations Lesson 85

LESSON 86 Number Families (page 592) Name Teacher Note: Review Number Families on page 10 in the Student Reference Guide. Example: Graph the integers that are less than 4. On a number line draw a dot at every integer that is less than 4. Since the set of integers includes whole numbers, draw dots at 3, 2, 1, and 0. The set of integers also includes the negatives of the positive whole numbers, so draw dots at 1, 2, 3, and so on. The arrowhead indicates that the graph of integers which are less than 4 continues without end. Practice Set (page 594) Graph the integers that are greater than 4. Graph the whole numbers that are less than 4. Answer true or false. c. Every integer is a whole number. T F The integer family includes o of the whole numbers. Example: d. Every integer is a rational number. T F Saxon Math Course 2 L86-345 Adaptations Lesson 86

Written Practice (page 595) 1. $ oz 2? $ oz 4? 2. per 3. 197 lb 205 lb 207 lb 213 lb 213 lb 238 lb 246 lb c. 4. 12 bushels pecks bushel = d. 5. 7 m. to 4 p.m. = hours mi hr? 6. 7. 8. 9 10 of 1800 attended 10 did not attend 9. Evaluate: b 2 4ac if a = 1, b = 5, and c = 4 10. made total = 11. Saxon Math Course 2 L86-346 Adaptations Lesson 86

Written Practice (continued) (page 596) 12. 10 8 10 3 = 10 10 5 10 8 = 10 13. c. 14. 15. Since is a circle, it does not matter if Obi turns right or left. 16. 17. 100 175 18. is of =? 100 19. c. 20. c. Saxon Math Course 2 L86-347 Adaptations Lesson 86

Written Practice (continued) (page 597) 21. Complete the table. Graph the points and draw the line. Name another point on the line. 22. (1.2 10 5 )(1.2 10 8 ) = (6 10 3 )(7 10 4 ) = (, ) y = x + 1 x y 3 5 1 23. Solve: Check: 56 = 7 8 w 56 = 7 8 w (56) = ( 7 8 w ) 56 = 7 8 w 56 = w 56 = 7 8 w 24. Solve: Check: 4.8 + c = 7.34 4.8 + c = 7.34 25. 10 2 6 2 10 2 8 2 = 4.8 + c = 7.34 = 7.34 c = 7.34 = 7.34 26. 5 lb 9 oz + 4 lb 7 oz 27. decimal answer 1.4 3 1 2 103 = 28. ( 4)( 5) ( 4)(+3) = ( 2)[( 3) ( 4)(+5)] = 29. x 2 + 3xy + 2x 2 xy = 30. Write the factorization of 9xy 2. Saxon Math Course 2 L86-348 Adaptations Lesson 86

LESSON 87 Multiplying Algebraic Name When adding algebraic terms: Like terms can be added. Terms (page 598) Adding the terms does not change the variable. 3x + 2x = 5x When multiplying algebraic terms: 1. Multiply the numbers. 2. Gather variable factors with exponents. All of the factors in the terms that are multiplied appear in the product. (3x)(2x) = 3 2 x x = 6x 2 Terms may be multiplied even if they are not like terms. ( 2x)( 3y) = 6xy Example: Simplify ( 3x 2 y)(2x)( 4xy) ( 3) x x y (+2) x ( 4) x y listed all factors ( 3)(+2)( 4) x x x x y y Commutative Property (+24) x x x x y y multiplied numbers 24x 4 y 2 gathered variable factors with exponents When raising an algebraic term to a power, apply the exponent to each factor. Example: Simplify: ( 3a 2 b 3 ) 2 Practice Set (page 600) ( 3a 2 b 3 ) 2 = ( 3a 2 b 3 )( 3a 2 b 3 ) or ( 3) 2 (a 2 ) 2 (b 3 ) 2 ( 3) 2 (a 2 ) 2 (b 3 ) 2 = 9a 4 b 6 Find the following products: Remember that a power of a power multiplies the exponent. Teacher Note: Refer students to Multiplying Three or More Signed Numbers Powers of Negative Numbers on page 26 in the Student Reference Guide. ( 3x)( 2xy) = 3x 2 (xy 3 ) = c. (2a 2 )( 3ab 3 ) = d. ( 4x)( 5x 2 y) = e. ( xy 2 )(xy)(2y) = f. ( 3m)( 2mn)(m 2 n) = g. (4wy)(3wx)( w 2 )(x 2 y) = h. 5d( 2df)( 3d 2 fg) = i. Simplify: (3xy 3 ) 2 = (3) 2 (x) 2 (y 3 ) 2 = Saxon Math Course 2 L87-349 Adaptations Lesson 87

Written Practice (page 600) 1. mi hr 1? 2. 12.5 cm cm cm = 3. 4. 18 ft 13 in. 17 ft 10 in. + 17 ft 11 in. 5. mil gal? 1 6. 7. 8. m a = m b = c. m c = d. m d = e. m e = 9. x = 4 y = 3x 1 10. y = Saxon Math Course 2 L87-350 Adaptations Lesson 87

Written Practice (continued) (page 601) 11. A(5, 5), B(10, 5), C(5, 0), D(0, 0) 12. 13. area = c. m A = m B = m C = m D = 14. 25% = is of? 15. 16. 17. 19. is of =? 100 18. 20. 66 2_ 3 100 c. d. Saxon Math Course 2 L87-351 Adaptations Lesson 87

Written Practice (continued) (page 602) 21. Complete the table. Graph the points and draw the line. Name another point on the line. 22. (4 10 5 )(2.1 10 7 ) = (4 10 5 )(6 10 7 ) = (, ) y = 2x 3 x y 1 2 3 23. Solve: Check: d 8.47 = 9.1 d 8.47 = 9.1 d 8.47 = 9.1 = 9.1 d = 9.1 = 9.1 24. Solve: Check: 0.25m = 3.6 0.25m = 3.6 25. 3 + 5.2 1 4 3 + 2 = 0.25m = 3.6 = 3.6 m = 3.6 = 3.6 26. 1 kg = g 27. decimal answer 28. ( 5) ( 2)[( 3) (+4)] = 1 kg 75 g = 3.7 + 2 5 8 + 15 ( 3) + ( 3)(+4) (+3) + ( 4) = 29. (3x)(4y) = (6m)( 4m 2 n)( mnp) = 30. 3ab + a ab 2ab + a = c. (3x 3 ) 2 = c. Saxon Math Course 2 L87-352 Adaptations Lesson 87

LESSON 88 Multiple Unit Multipliers Name (page 604) Remember that a unit multiplier is a ratio equal to 1 composed of two equivalent measures. 3 ft 1 yd and 1 yd 3 ft More than one unit multiplier may be used without changing the measure since unit multipliers are equal to 1. To multiply by multiple (two or more) unit multipliers: 1. Set up the problem with units changing to in the numerator. 2. Cancel matching units of measurement. 3. Multiply. Example: Use two unit multipliers to convert 5 hours to seconds. hours minutes seconds 5 hr 60 min 1 hr 60 s 1 min = 18,000 s To convert units of area and volume: Remember that units 2 = unit unit and units 3 = unit unit unit. 1. Set up the problem with units changing to in the numerator. 2. Cancel matching units of measurement. 3. Multiply. Example: Convert 1.2 m 2 to square centimeters. (m 2 = m m) Practice Set (page 606) 1.2 m 2 100 cm 1 m 100 cm 1 m = 12,000 cm2 Teacher Note: Review Multiple Unit Multipliers on page 23 in the Student Reference Guide. Use two or more unit multipliers to perform each conversion. 5 yards to inches. 1 1 hours to seconds 2 ft 5 yd in. = 1 1 yd.ft 2 hr min s hr min = c. 15 yd 2 to square feet d. 270 ft 3 to cubic yards 15 yd 2 ft yd ft yd = 270 ft 3 yd ft yd ft yd ft = e. Robert ran 800 meters in two minutes. His average speed was how many kilometers per hour? 800 m 2 min km km min mhr = km hr f. One cubic inch is about how many cubic centimeters? (1 in. 2.54 cm) Use a calculator to multiply and then round the answer to the nearest cubic centimeter. 1 in. 3 cm in. cm in. cm in. = rounded: Saxon Math Course 2 L88-353 Adaptations Lesson 88

Written Practice (page 607) 1. 15 min = 1 4 hr $ hr? 2. 580 010 61 04 60 0 6 3. 4 yd 2 4 yd 3 ft yd ft yd ft yd = ft yd ft yd = 4. 5. 6. 7. 8. Evaluate: a [b (a b)] if a = 5 and b = 3 9. Write the answer as a decimal. A total 10. c. Saxon Math Course 2 L88-354 Adaptations Lesson 88

Written Practice (continued) (page 608) 11. 1 3 = + 5 12 = 12. 13. 2x + 3y 5 + x y 1 = 14. x 2 + 2x x 2 = 15. 16. 60 1 1_ 4 17. 18. 19. 25% = is of? 20. 22. (9 10 6 )(4 10 8 ) = (9 10 6 )(4 10 8 ) = c. 21. Complete the table. Graph the points and draw the line. Name another point on the line. (, ) y = x 5 x 3 7 5 y Saxon Math Course 2 L88-355 Adaptations Lesson 88

Written Practice (continued) (page 609) 23. Solve: Check: 8 5 6 8 5 6 = d 5 1 2 = d 5 1 2 = d 5 1 2 8 5 6 = d 5 1 2 8 5 6 = d 5 1 2 8 5 6 = d 5 1 2 24. Solve: Check: 5 6 m = 90 5 6 m = 90 ( 5 6 ) m = 90 = 90 m = 90 = 90 25. J( 4, 2), K(0, 2), L(0, 0) 26. Which of the following does not equal 4 3? Translate 4 right, 2 down. M(, ) J (, ), K (, ) L (, ), M (, ) A 2 6 B 4 4 2 C 44 4 D 4 2 + 4 27. Find 50% of 2_ of 0.12 and write the 3 answer as a decimal. 1. Change to fractions first. 2. Of means multiply. 3. Change to decimal answer. Is 2_ of 50% of 0.12 the same as 50% 3 of 2_ 3 of 0.12?, because of the c 28. 6{5 4 3[6 (3 1)]} = property of m 29. ( 3)( 4) ( 3) ( 3) (+4)(+3) = 30. ( 2x)( 3x) = (ab)(2a 2 b)( 3a) = (+5) + ( 2)[(+3) ( 4)] = c. ( 3x) 2 = c. Saxon Math Course 2 L88-356 Adaptations Lesson 88

LESSON Name 89 Diagonals Interior Angles Exterior Angles (page 610) Diagonals of a polygon are segments that pass through the polygon and connect two vertices. Three diagonals can be drawn from one vertex of a regular hexagon. The 3 diagonals divide the hexagon into 4 triangles. The sum of the angles of one triangle measures 180. The sum of the angles of four triangles measures 720. 4 180 = 720 The hexagon has six angles. Teacher Notes: Refer students to Finding the Degree of Exterior and Interior Angles of a Regular Polygon on page 33 in the Student Reference Guide. The activity in the Student Edition is optional. The sum of all the angles is 720. If all the angles have the same measure, then each angle of the hexagon is 720 6 = 120. These are all interior angles. Exterior angles of a polygon are measured by following along the perimeter and measuring the amount of turn at each corner. If all of the turns are in the same direction, the sum of the exterior angles of any polygon is 360. Going all the way around the hexagon completes one full turn of 360. Six corners are turned when going around the hexagon. So each exterior angle is 60. 360 6 = 60 Notice that the interior and exterior angles are supplementary (total 180 ). Practice Set (page 614) Read Examples 1 4 in the Student Edition. Then solve a f. How many diagonals can be drawn from The diagonals drawn in problem a divide one vertex? diagonals the pentagon into how many triangles? Draw the diagonals. triangles Saxon Math Course 2 L89-357 Adaptations Lesson 89

Practice Set (continued) (page 614) c. What is the sum of the measures of the five interior angles of a pentagon? I made triangles. Each triangle is, d. What is the measure of each interior angle of a regular pentagon? 5 = so the sum is. e. What is the measure of each exterior angle f. What is the sum of the measures of an of a regular pentagon? interior and exterior angle of a regular 5 = pentagon? They are supplementary. Written Practice (page 615) 1. 1 mi = ft 2. Use a ratio box to find how many b there are. Then use another ratio box to find how many f there are. 3. 4. Round to the nearest thousandth. 24 61 ) 5. 3000 m 10 min km m 7. min hr = 6. 8. m a = m b = m c = m d = Saxon Math Course 2 L89-358 Adaptations Lesson 89

Written Practice (continued) (page 615) 9. 10. 91 2_ 3 100 11. Evaluate: ab + a a + b if a = 10 and b = 5 12. Compare: a 2? a if a = 0.5 13. 14. 1_ of an hour = 15 min 4 1_ 3 of 60 min = min and 15. 16. 24 17. is of =? 100 18. Draw a line of symmetry on figure above. 19. How many angles? Saxon Math Course 2 L89-359 Adaptations Lesson 89

Written Practice (continued) (page 616) 20. Complete the table. Graph the points and draw the line. Name the point where the line crosses the y-axis. (, ) y = 1 2 x 21. (1.25 10 3 )(8 10 5 ) 22. Label the figure. perimeter = There can be only answer because a triangle that is cm, cm, cm cannot exist. 23. 4 p = 72 24. 12.3 = 4.56 + f 9 p = f = 25. 2x + 3y 4 + x 3y 1 26. 9 8 7 6 6 5 = 27. 3.2 4 2 10 2 = 28. mixed-number answer 29. (+3) + ( 4)( 6) ( 3) + ( 4) ( 6) = ( 5) (+6)( 2) + ( 2)( 3)( 1) = 13 1 3 ( 4.75 + 3 4 ) 30. (3x 2 )(2x) = ( 2ab)( 3b 2 )( a) = c. ( 4ab 3 ) 2 = c. Saxon Math Course 2 L89-360 Adaptations Lesson 89

LESSON Name 90 Mixed-Number Coefficients Negative Coefficients (page 618) To solve equations with mixed-number coefficients: 1. First change the mixed number to an improper fraction. 2. Multiply both sides of the equation by the reciprocal of the coefficient of x. Example: 3 1 3 x = 5 equation 1 1 10 x = 5 changed coefficient to improper fraction 3 3 10 10 3 x = 3 10 1 1 2 x = 3 simplified 2 To solve equations with negative coefficients: 5 multiplied both sides by reciprocal of coefficient Either divide both sides of the equation by the negative coefficient of x, or multiply both sides of the equation by the reciprocal of the negative coefficient of x. Example: 3x = 126 1 Divide both sides by 3. Multiply both sides by 1 3. 3x = 126 or 3x = 126 3x 3 = 126 3 ( 1 3 ) ( ( 3x) = 1 3 ) (126) x = 42 x = 42 Practice Set (page 620) 1 1 8 x = 36 3 1 2 a = 490 c. 2 3 4 w = 6 3 5 x = a = w = d. 2 2 3 y = 1 4 5 e. 3x = 0.45 f. 3 4 m = 2 3 y = x = m = g. 10 y = 1.6 h. 2 1 2 w = 3 1 3 y = w = i. How can you show that your answer is correct? I can check by substituting my a for the value of the v in the original equation. Saxon Math Course 2 L90-361 Adaptations Lesson 90

Written Practice (page 620) 1. ( ) ( ) = 2. 6, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10 mean words: median c. mode d. range 3. oz $ 24 1? oz $ 58 1? 4. 10 sides Draw in diagonals. each triangle = 180 sum of triangles interior angles = b The ounce jar costs more. per 5. x 2 + 2xy + y 2 + x 2 y 2 6. 7. 8. is of =? 100 is of =? 100 9. 2 ft 2 1 m 3 in. ft in. ft = cm m cm m cm m = 10. is of 300? 2 chose warm 3 3 did not choose warm Saxon Math Course 2 L90-362 Adaptations Lesson 90

Written Practice (continued) (page 621) 11. If x = 4.5 and y = 2x + 1, then y equals what number? 12. sample space { HHH,,,,,,, } y = heads at least twice all outcomes = 13. perimeter in. each side area 14. 15. $325 $325 16. (6 10 4 )(8 10 7 ) = 17. 18. 19. See the Student Reference Guide. 20. W(0, 3), X(5, 3), Y(5, 0) Z(, ) Rotate 90 clockwise about origin. W (, ) X (, ) Y (, ) Z ( 0, 0 ) Saxon Math Course 2 L90-363 Adaptations Lesson 90

Written Practice (continued) (page 622) 21. is of? 22. x 4 23. x + 3.5 = 4.28 x + 3.5 = 4.28 x = 24. 2 2 3 w = 24 ( w) = 24 w = 25. 4y = 1.4 4y = 1.4 26. decimal answer 10 1 + 10 0 + 10 1 y = 27. ( 2x 2 )( 3xy)( y) = (3x 2 y 3 ) 2 = 28. 8 75 = 00 00 9 100 = 00 00 29. ( 3) + ( 4)( 5) ( 6) = ( 2)( 4) ( 4) ( 2) = 30. Compare for x = 10 and y = 5: x 2 y 2? (x + y)(x y) Saxon Math Course 2 L90-364 Adaptations Lesson 90