Free Pre-Algebra Lesson 59! page 1

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1 Free Pre-Algebra Lesson 59! page 1 Lesson 59: Review for Final Exam Section VII. Proportions and Percents Comprehensive Practice Lessons Lesson 37: Scale and Proportion Skill: Write ratios of sides for similar figures. Check that ratios are equal using cross-products. Worksheet 37 #1. Fill in the table with the information from the rectangles. Skill: Find a missing side of a triangle or rectangle similar to a given triangle or rectangle. HW37A #9. The rectangles are similar. Find the width of the smaller rectangle. LENGTH WIDTH LARGE SMALL L W LARGE SMALL L W LARGE SMALL 2. Use the cross-products to check whether or not the rectangles are similar. SCALE CONV. MODEL 1 x feet REAL feet Skill: Read a scale as a ratio and compare the original to a scale model. Find missing values using the scale. HW37A #11. Pictured below is the Revell 1:180 USS Lionfish Submarine model. SCALE CONV. Skill: Read MODEL a map scale 1 and use in the context of a map. REAL 180 HW37A #12. A map legend shows that a length of 1 1 / 4 inches on the map corresponds to a distance of 500 miles. SCALE CONVERSION The distance between Oakland, California and Chicago, Illinois is MAP about 4 5 5/4 / 16 inches inches on the map. 4 5 /16 About inches how many miles apart REAL are the 500 cities? miles x miles a. The actual length of the submarine is feet. What is the length of the model, in feet? SCALE MODEL 1 CONV. MAP REAL SCALE 5/4 inches 500 miles CONVERSION REAL 180 b. What is the length of the model in inches?

2 Free Pre-Algebra Lesson 59! page 2 Lesson 38: Ratios and Rates with Weight Skill: Find and compare unit prices. Worksheet 37 #1. Unit prices: A bag of premium dog food comes in a 6 lb size for $18.99 and a 15 lb size for $ Find the price per pound for each bag. (Round to the nearest cent.) Skill: Use the given formulas for computing blood alcohol concentration. Worksheet 37 #5. Blood alcohol: Use the formula provided to approximate the blood alcohol concentration of a 155 pound man who has had four drinks, each 0.6 oz alcohol. Round to the nearest hundredth. 7A W Which bag has the lower price per pound? Skill: Use the recommended dosage ratio to find a medicine dosage given the patient s weight. HW37A #8. a. Convert 33 lbs to kilograms. (1 kg = 2.2 lb) b. If a medicine has a recommended dose of 125 mg / kg, and your child weighs 33 pounds, what amount of medicine should you give? Skill: Use the given formula for computing body mass index (BMI). HW39A #8. A man 6 feet 1 inch tall is aiming for a BMI of 24. What is his desired weight? W (lb) BMI = 703 H 2 (inches) c. If the medicine comes in 300 mg tablets, how many whole tablets should you give? Skill: Solve a density equation for any variable. HW38A #9. a. You have a piece of cedar that is a rectangular block measuring 4.1 cm by 6.7 cm by 1.2 cm. What is the volume. to the nearest whole cm 3? c. Another piece of cedar is an unusual shape and it is difficult to measure its volume. However you know that it weighs 58 g. Use the density to find the volume to the nearest whole cm 3. b. The piece of wood weighs 12.5 g. What is the density in g/cm 3 rounded to the nearest hundredth?

3 Free Pre-Algebra Lesson 59! page 3 Lesson 39: Units in Ratios and Rates Skill: Recognize and use a rate. Solve problems with rates using the units to set up an equation. HW39A #6. Find the population density (rate of people per square mile) in San Francisco, California. Write the units with the rate. Population 776,733; Area square miles Skill: Recognize and use a ratio. Solve problems with ratios using tables or words to set up a proportion. HW39A #5. The shadow of a bell tower is 80 feet long at the same time a person 5.5 feet tall has a shadow of 4.8 feet. How tall is the bell tower? Lesson 40: Percents Skill: Underline the words that represent the base of a percent in a sentence. Worksheet 40 #2. Underline or supply the words that tell the base of the percent. c. 28% of the test-takers studied more than 8 hours for the test. e. This jacket was 40% off. Convert any of fraction, decimal, or percent to any other. HW41A #11. Fill in the blanks: FRACTION DECIMAL PERCENT 1/8 7/ % 3%

4 Free Pre-Algebra Lesson 59! page 4 Lesson 41: Solving SImple Percent Problems Skill: Identify the amount, base, and percent in a percent sentence. Translate to a ratio or percent equation. Lesson 41 page 2: Identify the percent, base, and amount, and write the percent sentence as a ratio. That piece is 75% of the pizza. Skill: Solve problems to find the percent HW41A #12. Carlos earned 62 of the 70 points possible on the assignment. What percent of the points did Carlos get? Round to the nearest whole percent. amount base = % Skill: Solve problems to find the amount. HW41A #13. 80% of the crowd of 5000 wore the team colors. How many people wore the team colors? Skill: Solve problems to find the base. HW41A #14. Stuart had 480 car-themed songs on his ipod, which was only 16% of all his songs. How many songs did he have on his ipod? Lesson 42: A Few Consumer Percents Skill: Compute the sales tax given the rate and price. Worksheet 42 #2. In Pleasant Hill, California, the total state and local sales tax is 9.25%. Find the sales tax you pay on a pair of shoes for $110 in Sun Valley mall in Pleasant Hill, California. Skill: Compute the tip for a restaurant bill. Worksheet 42 #3. The dinner bill was $ Figure a tip of 15% and one of 20% on the bill. Skill: Compute simple interest on a loan or savings account when t = 1. Worksheet 42 #4. Juaquin borrowed $3000 at 8% interest. At the end of the year he must pay back the $3000 plus the interest. How much will he pay in all? Skill: Compute the sale price of an item on sale given the discount rate. Worksheet 42 #6. The jeans originally cost $85, but the sale was for 40% off. What was the sale price of the jeans?!

5 Free Pre-Algebra Lesson 59! page 1a Lesson 59: Review for Final Exam Section VII. Proportions and Percents Comprehensive Practice Lessons Answers Lesson 37: Scale and Proportion Skill: Write ratios of sides for similar figures. Check that ratios are equal using cross-products. Worksheet 37 #1. Fill in the table with the information from the rectangles. Skill: Find a missing side of a triangle or rectangle similar to a given triangle or rectangle. HW37A #9. The rectangles are similar. Find the width of the smaller rectangle. 2. Use the cross-products to check whether or not the rectangles are similar = = 9.36 The cross-products are equal. The rectangles are similar. Skill: Read a scale as a ratio and compare the original to a scale model. Find missing values using the scale. HW37A #11. Pictured below is the Revell 1:180 USS Lionfish Submarine model. a. The actual length of the submarine is feet. What is the length of the model, in feet? 180x = x / 180 = / 180 x! 1.73 feet SMALL LARGE LENGTH WIDTH SCALE CONV. MODEL 1 x feet REAL feet b. What is the length of the model in inches? 1.73 feet 12 inches = inches 1 1 foot 3.75W = (1.5)(1.25) 3.75W = W / 3.75 = / 3.75 W = 0.5 The width is 0.5 feet. Skill: Read a map scale and use in the context of a map. HW37A #12. A map legend shows that a length of 1 1 / 4 inches on the map corresponds to a distance of 500 miles. The distance between Oakland, California and Chicago, Illinois is about 4 5 / 16 inches on the map. About how many miles apart are the cities? SCALE 5 4 x =! 69 $ " # 16% & 500 ( ) = x = x = REAL 500 miles 5 x = LARGE Oakland and Chicago are about 1,725 miles apart. SMALL L W 1.25 W CONVERSION MAP 5/4 inches 4 5 /16 inches REAL 500 miles x miles

6 Free Pre-Algebra Lesson 38: Ratios and Rates with Weight Skill: Find and compare unit prices. Worksheet 37 #1. Unit prices: A bag of premium dog food comes in a 6 lb size for $18.99 and a 15 lb size for $ Find the price per pound for each bag. (Round to the nearest cent.) $18.99! $3.17 per lb 6 lb $29.99! $2.00 per lb 15 lb Which bag has the lower price per pound? The larger bag costs less per pound. Skill: Use the recommended dosage ratio to find a medicine dosage given the patient s weight. HW37A #8. a. Convert 33 lbs to kilograms. (1 kg = 2.2 lb) 33 lb 1 kg = 15 kg lb b. If a medicine has a recommended dose of 125 mg / kg, and your child weighs 33 pounds, what amount of medicine should you give? Since 33 lb = 15 kg, multiply the dose by 15 kg. 125 mg 1 kg 15 kg 1 = 1875 mg c. If the medicine comes in 300 mg tablets, how many whole tablets should you give? 1875 mg / 300 mg = 6.25 Lesson 59! page 2a Skill: Use the given formulas for computing blood alcohol concentration. Worksheet 37 #5. Blood alcohol: Use the formula provided to approximate the blood alcohol concentration of a 155 pound man who has had four drinks, each 0.6 oz alcohol. Round to the nearest hundredth. 7A W = 7(4 0.6) 155! 0.11 Skill: Use the given formula for computing body mass index (BMI). HW39A #8. A man 6 feet 1 inch tall is aiming for a BMI of 24. What is his desired weight? W (lb) BMI = 703 H 2 (inches) 6 feet 1 inch = 72 inches + 1 inch = 73 inches 24 = 703 W W 5329 = W 5329 = W = His desired weight is about 182 pounds. You should give 6 tablets. Skill: Solve a density equation for any variable. HW38A #9. a. You have a piece of cedar that is a rectangular block measuring 4.1 cm by 6.7 cm by 1.2 cm. What is the volume. to the nearest whole cm 3? (4.1)(6.7)(1.2) = 33 cm 3 b. The piece of wood weighs 12.5 g. What is the density in g/cm 3 rounded to the nearest hundredth? 12.5 g / 33 cm 3 = 0.38 g/cm 3 c. Another piece of cedar is an unusual shape and it is difficult to measure its volume. However you know that it weighs 58 g. Use the density to find the volume to the nearest whole cm g x cm = 0.38 g 3 1 cm x = x / 0.38 = 58 / 0.38 x! 153 cm 3

7 Free Pre-Algebra Lesson 59! page 3a Lesson 39: Units in Ratios and Rates Skill: Recognize and use a rate. Solve problems with rates using the units to set up an equation. HW39A #6. Find the population density (rate of people per square mile) in San Francisco, California. Write the units with the rate. Population 776,733; Area square miles 776,733 people = x people mi 2 1 mi x = 776, x / = 776,733 / x = 16, There are about 16,636 people per square mile in San Francisco. Skill: Recognize and use a ratio. Solve problems with ratios using tables or words to set up a proportion. HW39A #5. The shadow of a bell tower is 80 feet long at the same time a person 5.5 feet tall has a shadow of 4.8 feet. How tall is the bell tower? height (ft) shadow (ft) 4.8h = = h 80 ( )( 80) = h = h / 4.8 = 440 / 4.8 h = 91.6 The tower is about 91.7 feet tall. Lesson 40: Percents Skill: Underline the words that represent the base of a percent in a sentence. Worksheet 40 #2. Underline or supply the words that tell the base of the percent. c. 28% of the test-takers studied more than 8 hours for the test. 28% of the test-takers e. This jacket was 40% off. 40% of the original price Convert any of fraction, decimal, or percent to any other. HW41A #11. Fill in the blanks: FRACTION DECIMAL PERCENT 1/ % 1/ % 3/ % 3/ % 11/ % 7/ %

8 Free Pre-Algebra Lesson 59! page 4a Lesson 41: Solving SImple Percent Problems Skill: Identify the amount, base, and percent in a percent sentence. Translate to a ratio or percent equation. Lesson 41 page 2: Identify the percent, base, and amount, and write the percent sentence as a ratio. That piece is 75% of the pizza. amount = percent base amount base = % size of piece size of pizza = 75% Skill: Solve problems to find the amount. HW41A #13. 80% of the crowd of 5000 wore the team colors. How many people wore the team colors? percent base = amount = people wore the team colors. Skill: Solve problems to find the percent HW41A #12. Carlos earned 62 of the 70 points possible on the assignment. What percent of the points did Carlos get? Round to the nearest whole percent. amount base Carlo's points = points possible = Carlos got 89% of the possible points. Skill: Solve problems to find the base. HW41A #14. Stuart had 480 car-themed songs on his ipod, which was only 16% of all his songs. How many songs did he have on his ipod? percent base = amount 0.16b = b / 0.16 = 480 / 0.16 b = 3000 He had 3000 songs on his ipod. Lesson 42: A Few Consumer Percents Skill: Compute the sales tax given the rate and price. Worksheet 42 #2. In Pleasant Hill, California, the total state and local sales tax is 9.25%. Find the sales tax you pay on a pair of shoes for $110 in Sun Valley mall in Pleasant Hill, California $110 = $ rounded to the nearest cent, $ Skill: Compute simple interest on a loan or savings account when t = 1. Worksheet 42 #4. Juaquin borrowed $3000 at 8% interest. At the end of the year he must pay back the $3000 plus the interest. How much will he pay in all? 1.08 $3000 = $3240 He ll pay $3240. Skill: Compute the tip for a restaurant bill. Worksheet 42 #3. The dinner bill was $ Figure a tip of 15% and one of 20% on the bill $85.60 = $ $85.60 = $17.12 Skill: Compute the sale price of an item on sale given the discount rate. Worksheet 42 #6. The jeans originally cost $85, but the sale was for 40% off. What was the sale price of the jeans? 100%! 40$ = 60% 0.6 $85 = $51 The jeans were on sale for $51.!

9 Free Pre-Algebra Lesson 59! page 5 Lesson 59: Review for Final Exam Section VIII. Percents Continued Comprehensive Practice Lessons 43 46* *Optional Lessons 47 and 48 are not included. Lesson 43: Interest Skill: Compute simple interest using the memorized formula. Worksheet 43 #1. Find the simple interest earned if $3,500 is invested for six months at 1.6% per year. Skill: Use the given formula to compute compound interest. (See previous problem box for formula.) Worksheet 43 #4. $50,000 was invested at 3.5% compounded quarterly for 5 years. How much was in the account at the end of that time? Compound Interest! A = P 1+ r $ " # n % & Same as simple interest, except A = amount in account after t years n = number of compounding periods per year Skill: Find the combined simple interest for one year from an investment split into two accounts. nt Worksheet 43 #3. Liling has $60,000 to invest in two accounts. She puts $25,000 in one account earning 2.1% simple interest and the rest in another account earning 4.7% simple interest. How much interest will she receive from the two accounts at the end of the year? Lesson 44: Percents in Mixtures Skill: Find the amount of a substance in a measured mixture given the percent. Worksheet 44 #3. A 900 ml solution of alcohol and water is 78% alcohol. How many ml of alcohol are present? How many ml of water? Skill: Estimate the percent of a substance in a mixture of two different concentrations. Worksheet 44 #5. Mixture C is formed by combining Mixtures A and B. Mixture A: 2 cubic meters of soil mixture, 35% sand Mixture B: 6 cubic meters of soil mixture, 15% sand a. The percent of sand in Mixture C is between % and %.

10 Free Pre-Algebra Lesson 59! page 6 Lesson 44: Percents in Mixtures Continued Skill: Find the percent concentration of a mixture. Worksheet 44 #7. Solution A: 80 liters of 20% alcohol Solution B: 40 liters of 50% alcohol Solution C is formed by combining Solutions A and B. b. Solution C is liters in total. c. How many liters of alcohol are in Solution A? d. How many liters of alcohol are in Solution B? e. How many liters of alcohol are in Solution C? f. What percent of Solution C is alcohol? Lesson 45: Percent Decrease Skill: Solve a sales discount problem for any variable. Worksheet 45 #1. An item that originally cost $ is on sale for 25% off. What is the sale price? Skill: Solve a percent decrease problem for any variable. HW46A #9. If a man s weight changes from 218 lb to 186 lb, what is the percent decrease in weight? The sale price is $ The sale price of $38.36 is 30% off the original price. What was the original price of the item? 3. The original price was $44.80, and the sale price is $ What is the percent discount? PQ #20. The number of students fell to 20,056, a 4% drop in enrollment. What was the previous enrollment?

11 Free Pre-Algebra Lesson 59! page 7 Lesson 46: Percent Increase Skill: Solve a percent increase problem for any variable. Worksheet 46 #1. If your hourly pay increased from $14.50 to $15.66, what is the percent increase of your raise? 2. If your hourly pay of $16.80 increases by 5%, how much will you make? Skill: Fill in the blank in a news story with a percent increase. HW47A #13. Fill in the blank: Of the 2.9 million youth age 16 to 24 who graduated from high school in January through October 2009, 2.1 million ( percent) were enrolled in college in October U.S. Bureau of Labor Statistics 3. If your hourly pay increases 6% to $19.61, what was your original pay?!

12 Free Pre-Algebra Lesson 59! page 5a Lesson 59: Review for Final Exam Section VIII. Percents Continued Comprehensive Practice Lessons 43 46* Answers *Optional Lessons 47 and 48 are not included. Lesson 43: Interest Skill: Compute simple interest using the memorized formula. Worksheet 43 #1. Find the simple interest earned if $3,500 is invested for six months at 1.6% per year. I = Prt = ($3,500)(0.016)(6 / 12) = $28 Compound Interest! A = P 1+ r $ " # n % & Same as simple interest, except A = amount in account after t years n = number of compounding periods per year nt Skill: Use the given formula to compute compound interest. (See previous problem box for formula.) Worksheet 43 #4. $50,000 was invested at 3.5% compounded quarterly for 5 years. How much was in the account at the end of that time? P = $50,000 r = t = 5 n = 4! A = 50, $ " # 4 % & A = 50,000 ( ) A = 50, = ( ) After 5 years, there was $59, in the account. Skill: Find the combined simple interest for one year from an investment split into two accounts. Worksheet 43 #3. Liling has $60,000 to invest in two accounts. She puts $25,000 in one account earning 2.1% simple interest and the rest in another account earning 4.7% simple interest. How much interest will she receive from the two accounts at the end of the year? $60,000 $25,000 = $35, % of $25, % of $35,000 = $25, $35,000 = $525 + $1645 = $2170 The total interest was $2,170. Lesson 44: Percents in Mixtures Skill: Find the amount of a substance in a measured mixture given the percent. Worksheet 44 #3. A 900 ml solution of alcohol and water is 78% alcohol. How many ml of alcohol are present? How many ml of water? ml = 702 ml 900 ml 702 ml = 198 ml Skill: Estimate the percent of a substance in a mixture of two different concentrations. Worksheet 44 #5. Mixture C is formed by combining Mixtures A and B. Mixture A: 2 cubic meters of soil mixture, 35% sand Mixture B: 6 cubic meters of soil mixture, 15% sand a. The percent of sand in Mixture C is between 15 % and 35 %.

13 Free Pre-Algebra Lesson 44: Percents in Mixtures Continued Skill: Find the percent concentration of a mixture. Worksheet 44 #7. Solution A: 80 liters of 20% alcohol Solution B: 40 liters of 50% alcohol Solution C is formed by combining Solutions A and B. b. Solution C is 120 liters in total. c. How many liters of alcohol are in Solution A? 20% of 80 liters is = 16 liters d. How many liters of alcohol are in Solution B? 50% of 40 liters is = 20 liters e. How many liters of alcohol are in Solution C? 16 liters + 20 liters = 36 liters f. What percent of Solution C is alcohol? 36/120 = 0.3 = 30% Lesson 59! page 6a Lesson 45: Percent Decrease Skill: Solve a sales discount problem for any variable. Worksheet 45 #1. An item that originally cost $ is on sale for 25% off. What is the sale price? 25% off means 75% is paid 0.75 $ = $ The sale price is $ The sale price of $38.36 is 30% off the original price. What was the original price of the item? $38.36 is 70% of the original price. $38.36 = 0.7x x = $38.36 / 0.7 = $54.8 The original price was $ The original price was $44.80, and the sale price is $ What is the percent discount? Original Price Sale Price $44.80 $35.84 = $8.96 You save $8.96, which is some percent of the original price. $8.96 / $44.80 = 0.2 = 20% 20% discount Skill: Solve a percent decrease problem for any variable. HW46A #9. If a man s weight changes from 218 lb to 186 lb, what is the percent decrease in weight? decrease is = 32 decrease / original = 32 / 218 = about a 14.7% decrease PQ #20. The number of students fell to 20,056, a 4% drop in enrollment. What was the previous enrollment? 20,056 is 96% of previous enrollment 0.96x = 20,056 x = 20,056 / 0.96 = 20, About 20,892 students.

14 Free Pre-Algebra Lesson 59! page 7a Lesson 46: Percent Increase Skill: Solve a percent increase problem for any variable. Worksheet 46 #1. If your hourly pay increased from $14.50 to $15.66, what is the percent increase of your raise? The increase is = 1.16 The percent increase is 1.16 / = 0.08 = 8% 2. If your hourly pay of $16.80 increases by 5%, how much will you make? The new wage is 105% of the old wage = New wage is $17.64 per hour. 3. If your hourly pay increases 6% to $19.61, what was your original pay? New pay is 106% of original pay x x = / 1.06 = 18.5 Original wage was $18.50 Skill: Fill in the blank in a news story with a percent increase. HW47A #13. Fill in the blank: Of the 2.9 million youth age 16 to 24 who graduated from high school in January through October 2009, 2.1 million ( percent) were enrolled in college in October U.S. Bureau of Labor Statistics 2.1 million / 2.9 million = (_72_ percent)!

15 Free Pre-Algebra Lesson 59! page 8 Lesson 59: Review for Final Exam Section IX. The Number Line Comprehensive Practice Lessons 49 52* *Optional Lessons 53 and 54 not included. Lesson 49: Squares and Square Roots Skill: Write the related square and square root equations for a given number. Worksheet 49 #2. Write the related square and square root problems for 6 2. Skill: Estimate a square root using perfect squares. Worksheet 49 #3 Which two perfect squares is the number between? 30 Skill: Evaluate square roots with a calculator. HW 49A #14. Find the square roots using your calculator. Round to three decimal places if rounding is necessary. a. 95 c. 361 Skill: Evaluate squares and square roots with negatives appropriately. HW50A #1. Evaluate. Round to three decimal places if rounding is necessary. b.!121 c.! 121 d. (!11) 2 Skill: Use the square root symbol correctly in the order of operations when simplifying. HW50A #12. Evaluate. Round to three decimal places if rounding is necessary. a c d b Skill: Use the square root symbol correctly in the order of operations when simplifying. Worksheet 49 #6. Evaluate. a. 100! 36 b. 100! 36 c d

16 Free Pre-Algebra Lesson 59! page 9 Lesson 50: The Pythagorean Theorem Skill: Identify the right angle, hypotenuse, and legs of a right triangle. Worksheet 50 #2. Label the sides of the triangle a, b, and c. Label the legs and hypotenuse. Skill: Use the memorized Pythagorean Theorem to find any missing side of a right triangle. Worksheet 50 #3. Find the length of the hypotenuse. Skill: Use the memorized Pythagorean Theorem to find any missing side of a right triangle. Round appropriately. Worksheet 50 #6. Find the missing length.

17 Free Pre-Algebra Lesson 59! page 10 Lesson 51: Practical Uses of the Pythagorean Theorem Skill: Apply the converse of the Pythagorean Theorem to determine whether or not a given angle is right (90º). HW51A #13. If the diagonal measures 34 inches, is the frame square? Skill: Apply the Pythagorean Theorem in a variety of physical situations. Worksheet 51 #2. Gutters are to be installed along the roofline and extend another 6 inches past the end of the roof. How many feet of gutter are needed? Lesson 52: The Real Numbers Skill: Use the vocabulary for sets of real numbers, including natural numbers; whole numbers; integers; rational numbers; irrational numbers; real numbers. Identify to which set a particular number belongs. Worksheet 52 #3 a. Circle the irrational numbers. Skill: Determine whether statements about the real number system are true or false. Explain. Worksheet 53 #3. Answer true or false, and give a reason for your answer. a. True or False? A rational number must be positive. c. Circle the integers. b. True or False? An integer is always negative. c. True or False? The real numbers do not include!.

18 Free Pre-Algebra Lesson 59! page 11 Section X. Get Ready for Algebra I Comprehensive Review Lesson 55 Answers Lesson 55: Perimeter Problems with Related Variables Skill: Use a given relationship between length and width in a rectangle to write an expression for width in terms of length, and substitute in the perimeter formula. Worksheet 55 #1. The perimeter of each rectangle is 120 inches. Fill in the missing part of the equation. Do not solve. The width of the rectangle is 10 more than the length. P = 2L + 2W 120 = 2L + 2( ) The width of the rectangle is 10 less than the length. P = 2L + 2W 120 = 2L + 2( ) The width of the rectangles is 5 times the length. P = 2L + 2W 120 = 2L + 2( ) The width of the rectangle is 1/5 of the length. P = 2L + 2W 120 = 2L + 2( ) Skill: Solve the perimeter equation to find the length and width of the rectangle. Worksheet 55 #7. The perimeter is 82 inches, and the width is 3 inches less than the length. Find the width and length.!

19 Free Pre-Algebra Lesson 59! page 8a Lesson 59: Review for Final Exam Section IX. The Number Line Comprehensive Practice Lessons 49 52* Answers *Optional Lessons 53 and 54 not included. Lesson 49: Squares and Square Roots Skill: Write the related square and square root equations for a given number. Worksheet 49 #2. Write the related square and square root problems for 6 2. ( 6) 2 = = 6 Skill: Estimate a square root using perfect squares. Worksheet 49 #3 Which two perfect squares is the number between? < 30 < 36 5 < 30 < 6 30 is between 5 and 6. Skill: Evaluate square roots with a calculator. HW 49A #14. Find the square roots using your calculator. Round to three decimal places if rounding is necessary. a. 95! c. 361 = 19 Skill: Evaluate squares and square roots with negatives appropriately. HW50A #1. Evaluate. Round to three decimal places if rounding is necessary. b.!121 not a real number c.! 121 =!11 d. (!11) 2 = 121 = 11 Skill: Use the square root symbol correctly in the order of operations when simplifying. HW50A #12. Evaluate. Round to three decimal places if rounding is necessary. a = 10 5 = 2 b = 4 = 2 c = 324 = 18 d = 6 3 = 18 Skill: Use the square root symbol correctly in the order of operations when simplifying. Worksheet 49 #6. Evaluate. a. 100! 36 = 10! 6 = 4 b. 100! 36 = 64 = 8 c = = 17 d = 169 = 13

20 Free Pre-Algebra Lesson 59! page 9a Lesson 50: The Pythagorean Theorem Skill: Identify the right angle, hypotenuse, and legs of a right triangle. Worksheet 50 #2. Label the sides of the triangle a, b, and c. Label the legs and hypotenuse. Skill: Use the memorized Pythagorean Theorem to find any missing side of a right triangle. Worksheet 50 #3. Find the length of the hypotenuse = = 5329 c 2 = = c c = 73 cm Skill: Use the memorized Pythagorean Theorem to find any missing side of a right triangle. Round appropriately. Worksheet 50 #6. Find the missing length a 2 = a 2 = 2209 a 2 = 2209! 2025 = = a a " cm

21 Free Pre-Algebra Lesson 51: Practical Uses of the Pythagorean Theorem Skill: Apply the converse of the Pythagorean Theorem to determine whether or not a given angle is right (90º). HW51A #13. If the diagonal measures 34 inches, is the frame square? Lesson 59! page 10a Skill: Apply the Pythagorean Theorem in a variety of physical situations. Worksheet 51 #2. Gutters are to be installed along the roofline and extend another 6 inches past the end of the roof. How many feet of gutter are needed? a 2 + b 2 = c = c = c 2 c 2 = 1156 c = 1156! 34 Yes, since = 34 2, the corner must be square (a right angle). Each side of the roof is calculated using the Pythagorean theorem. a 2 + b 2 = c = c 2 c 2 = 360 c = 360! The six inches we need to add is 0.5 feet, so the total length of one side is feet. For the two sides, that is feet. About 39 feet of gutter. Lesson 52: The Real Numbers Skill: Use the vocabulary for sets of real numbers, including natural numbers; whole numbers; integers; rational numbers; irrational numbers; real numbers. Identify to which set a particular number belongs. Worksheet 52 #3 a. Circle the irrational numbers. c. Circle the integers. Skill: Determine whether statements about the real number system are true or false. Explain. Worksheet 53 #3. Answer true or false, and give a reason for your answer. a. True or False? A rational number must be positive. False. The rational numbers are the results of integer division and so include negative fractions. For example, 1/2 is a rational number. b. True or False? An integer is always negative. False. The integers include the natural numbers, which are positive. For example, 3 is an integer. c. True or False? The real numbers do not include!. False.! is an irrational number, and the real numbers include all the irrational and all the rational numbers.

22 Free Pre-Algebra Lesson 59! page 11a Section X. Get Ready for Algebra I Comprehensive Review Lesson 55 Answers Lesson 55: Perimeter Problems with Related Variables Skill: Use a given relationship between length and width in a rectangle to write an expression for width in terms of length, and substitute in the perimeter formula. Worksheet 55 #1. The perimeter of each rectangle is 120 inches. Fill in the missing part of the equation. Do not solve. The width of the rectangle is 10 more than the length. P = 2L + 2W 120 = 2L + 2(L + 10) The width of the rectangle is 10 less than the length. P = 2L + 2W 120 = 2L + 2(L 10) The width of the rectangles is 5 times the length. P = 2L + 2W 120 = 2L + 2( 5L ) The width of the rectangle is 1/5 of the length. P = 2L + 2W 120 = 2L + 2(L / 5) Skill: Solve the resulting equation to find the length and width of the rectangle. Worksheet 55 #7. The perimeter is 82 inches, and the width is 3 inches less than the length. Find the width and length. P = 2L + 2W 82 = 2L + 2( L 3 ) 82 = 2L + 2L 6 82 = 4L 6 4L 6 = 82 4L = L = 88 4L / 4 = 88 / 4 L = 22 The length is 22 inches. The width is 3 inches less than the length = 19, so the width is 19 inches.!