Comprehensive Review Lessons 1 30! page 1a

Transcription

1 Lessons 1 30 Comprehensive Review Comprehensive Review Lessons 1 30! page 1a Name Lesson 1 #1 Estimate the number of cars in the photo. Lesson 1 # Round as indicated. a. Round 55,119 to the hundred thousands place b. Round 357 km. to two sig figs c. Round using your judgment. In January of 009, Facebook had 4,089,00 U.S. users; by January 010 that had grown to 103,085,50 users and 471,447,000 users worldwide. (Reference) Lesson #1 Draw a line 4 cm long, then measure to the nearest inch. Lesson 3 #1 Find the area and perimeter of the figure. Units are centimeters and square centimeters. The perimeter of the figure is. The area of the figure is. Lesson 3 # A rectangle has length 14 inches and width 1 inches. a. Find the perimeter. Lesson 4 #1 Write out the exponential expression 7 4 as a multiplication, and evaluate. b. Find the area. Lesson 4 # Find the volume of a box with length 1 inches, width 1 inches, height 1 inches.

2 Comprehensive Review Lessons 1 30! page a Lesson 5 #1 Evaluate the expression using the correct order of operations. Lesson 5 # Write the four related addition/subtraction equations using the numbers 9, 6, and 15. (85 9) + (1 3) Write the four related multiplication/division equations using the numbers 9, 6, and 54. Lesson 6 #1 Audiobooks are spoken aloud at a recommended rate of 155 words per minute. If an audiobook recording is 39 minutes, how many words are in the book? Lesson 7 #1 What is the length of the line? Number of Words is Rate times Time 1 3 Lesson 8 #1 Find all the factor pairs for Lesson 9 #1 Is 13 prime, or not? # Find the prime factorization of 40. Lesson 10 #1 Use the rectangle to show that 3 4 = 9 1. Lesson 10 # Write 4 fractions equivalent to 3/ #3 Simplify 48/60 to lowest terms Lesson 11 #1 Change the improper fraction 3/4 to a mixed number. 3 4 Lesson 11 #3 Change the mixed number 6 3 / 5 to an improper fraction

3 Comprehensive Review Lessons 1 30! page 3a Lesson 1 #1 Multiply the fractions. Use cross-cancelling if possible. a. 5 8 of 8 Lesson 13 #1 Simplify. 4ab a. 10ab b b. 0! 7 1! 3 Lesson 14 #1 Solve a 1 = 36 Lesson 14 # The formula for the total cost of opening your booth at the crafts fair is (cost per item number of items) + cost of booth = total cost which we could write as CN + B = T If you have 400 items that cost $3 per item, and the total cost is $000, find the cost of the booth. Lesson 15 #1 Simplify. a. (8a)(a) Lesson 16 #1 Solve 3(x + 1) = 33 b. 8a + a c. (x + 1) Lesson 16 # The perimeter of a rectangle is 50 cm, and the length is 75 cm. What is the width? Lesson 18 #1 Use the distance-rate-time formula to write an equation and solve the problem. The factory workers assembled 03 products in 7 hours. What was their production rate?

4 Comprehensive Review Lessons 1 30! page 4a Lesson 17 #1 A triangle has the measurements shown. Because the triangle has a square corner, the side measuring 10 cm is also the height of the triangle. a. Find the perimeter. b. Find the area. 6 cm 4 cm 10 cm Lesson 18 #1 Use the structure sentence No. Boxes No. Items per Box = No. Items to write equations for the problems. Then solve. a. I got this great deal on toilet paper. Now we just need to find room in the garage. There are 40 cartons! That s 3840 rolls of toilet paper! We ll never be out of toilet paper again! How many rolls per carton? b. You know, my grandma did that, but she lived in New Orleans. She lost 5040 rolls in the flood! Each carton of 48 rolls was a soggy mess. How many cartons? Lesson 19 #1 Write a mathematical comparison. a. Owing $1 is better than owing $100. b. 7 Lesson 0 #1 Find the sums or differences c. 7 Lesson 1 #1 Change subtractions to additions and find the sums. 16! (!8)!16! (!8) Lesson 1 # Find the distance using the formula a b. The highest point in California is Mt. Whitney at 14,505 feet, and the lowest point is Badwater Basin in Death Valley, 8 feet below sea level. What is the difference in elevation? 1+ 3! 1+ 5! 3 Lesson #1 Simplify. 7(!3) (!4)(!6) Lesson # Simplify.!5(x! 1) (!)4!54 (!6) 35 (!7)

5 Comprehensive Review Lessons 1 30! page 5a Lesson 3 #1 Use the formula to convert ºF to Celsius. 5(F! 3) C = 9 Lesson 3 # From ground level a bullet is fired straight up into the air. The formula for the height of the bullet t seconds after firing is h =!16t + 100t. What is the height of the bullet 30 seconds after firing? Lesson 4 #1 Solve.!x! = 16 Lesson 5 #1 Find equivalent fractions with a common denominator for the pair of fractions Lesson 6 #1 Add or subtract as indicated Lesson 7 #1 How many 3/4 foot lengths can be cut from a 3 foot ribbon? a. Mark the cuts on the ribbon. 6 35! b. Write and solve the corresponding divison problem. Lesson 8 #1 Use the distributive property to simplify " 45 x 5! 8 % # $ 9& ' Lesson 8 # Simplify 9a! 3$ " # % &

6 Comprehensive Review Lessons 1 30! page 6a Lesson 9 #1 How many cups is 0 quarts? (1 quart = 4 cups) Lesson 9 # How many days is 3,000 minutes? (1 hour = 60 minutes, 1 day = 4 hours) Lesson 30 #1 Solve the equation 5 a = Lesson 30 # Solve the equation 5 8 x = 1 8.

7 Comprehensive Review Lessons 1 30! page 1a Lessons 1 30 Comprehensive Review Answers Lesson 1 #1 Estimate the number of cars in the photo. Lesson 1 # Round as indicated. a. Round 55,119 to the hundred thousands place 500,000 b. Round 357 km. to two sig figs 3600 km. c. Round using your judgment. In January of 009, Facebook had 4,089,00 U.S. users; by January 010 that had grown to 103,085,50 users and 471,447,000 users worldwide. (Reference) over 4 million; over 100 million; 470 million Lesson #1 Draw a line 4 cm long, then measure to the nearest inch. Lesson 3 #1 Find the area and perimeter of the figure. Units are centimeters and square centimeters. The line is about inches long. The perimeter of the figure is 0 cm. The area of the figure is 18 square cm. Lesson 3 # A rectangle has length 14 inches and width 1 inches. a. Find the perimeter. P = (L + W) = (14 in + 1 in) = (35 in) = 70 in. b. Find the area. A = LW = (14 in)(1 in) = 94 square in. Lesson 4 #1 Write out the exponential expression 7 4 as a multiplication, and evaluate. 7 4 = =,401 Lesson 4 # Find the volume of a box with length 1 inches, width 1 inches, height 1 inches. V = (1 in)(1 in)(1 in) = 178 in 3

8 Comprehensive Review Lessons 1 30! page a Lesson 5 #1 Evaluate the expression using the correct order of operations. (85 9) + (1 3) (85 9) + (1 3) = (76) + (1 3) = (76) + (9) = (9) = = 5857 Lesson 5 # Write the four related addition/subtraction equations using the numbers 9, 6, and = = = = 6 Write the four related multiplication/division equations using the numbers 9, 6, and = = = = 6 Lesson 6 #1 Audiobooks are spoken aloud at a recommended rate of 155 words per minute. If an audiobook recording is 39 minutes, how many words are in the book? Number of Words is Rate times Time Lesson 7 #1 What is the length of the line? 1 /16 inches N = (155)(39) = The book is 60,760 words. Lesson 8 #1 Find all the factor pairs for 40. Lesson 9 #1 Is 13 prime, or not? is not prime, because 3 divides it evenly = 71 # Find the prime factorization of = 5 Lesson 10 #1 Use the rectangle to show that 3 4 = 9 1. Lesson 10 # Write 4 fractions equivalent to 3/ = 6 16 = 9 4 = 1 3 = #3 Simplify 48/60 to lowest terms = i iii 3 i i 3 i5 = 4 5 Lesson 11 #1 Change the improper fraction 3/4 to a mixed number. Lesson 11 #3 Change the mixed number 6 3 / 5 to an improper fraction = 5r3 3 4 = = = 33 5

9 Comprehensive Review Lessons 1 30! page 3a Lesson 1 #1 Multiply the fractions. Use cross-cancelling if possible. a. 5 8 of 8 = = 5 1 = 5 b = = 50 7 Lesson 14 #1 Solve a 1 = 36 1 a 1 = 1 36 a = 43 check: 43 1 = 36 Lesson 13 #1 Simplify. 4ab a. 10ab = 4 a bb 10 a b = b 5 5 b. 0! 7 1! 3 = 0! 7 1! 8 = = 1 Lesson 14 # The formula for the total cost of opening your booth at the crafts fair is (cost per item number of items) + cost of booth = total cost which we could write as CN + B = T If you have 400 items that cost $3 per item, and the total cost is $000, find the cost of the booth. N = 400; C = 3; T = 000 CN + B = T B = 000 B = 000 B + 100! 100 = 000! 100 B = 800 The booth cost $800. Lesson 15 #1 Simplify. a. (8a)(a) = (8 ) (a a) = 16a b. 8a + a = 9a c. (x + 1) = x + Lesson 16 #1 Solve 3(x + 1) = 33 6x + 3 = 33 6x + 3! 3 = 33! 3 6x = 30 6x / 6 = 30 / 6 x = 5 Lesson 16 # The perimeter of a rectangle is 50 cm, and the length is 75 cm. What is the width? P = L + W 50 = (75) + W W + 150! 150 = 50! 150 W = 100 W = 100 W = 50 cm Lesson 18 #1 Use the distance-rate-time formula to write an equation and solve the problem. The factory workers assembled 03 products in 7 hours. What was their production rate? d = rt 03 = r 7 7r = 03 7r / 7 = 03 / 7 r = 9 9 products per hour

10 Comprehensive Review Lessons 1 30! page 4a Lesson 17 #1 A triangle has the measurements shown. Because the triangle has a square corner, the side measuring 10 cm is also the height of the triangle. a. Find the perimeter. P = 4 cm + 10 cm + 6 cm = 60 cm b. Find the area. A = bh/ = (4 cm)(10 cm)/ = 10 cm Lesson 19 #1 Write a mathematical comparison. a. Owing $1 is better than owing $ > 100 b. 7 < c. 7 > 6 cm 4 cm 10 cm Lesson 18 #1 Use the structure sentence No. Boxes No. Items per Box = No. Items to write equations for the problems. Then solve. a. I got this great deal on toilet paper. Now we just need to find room in the garage. There are 40 cartons! That s 3840 rolls of toilet paper! We ll never be out of toilet paper again! How many rolls per carton? 40N = N / 40 = 3840 / 40 N = rolls per carton b. You know, my grandma did that, but she lived in New Orleans. She lost 5040 rolls in the flood! Each carton of 48 rolls was a soggy mess. How many cartons? B 48 = B / 48 = 5040 / 48 B = 105 She had 105 cartons. Lesson 0 #1 Find the sums or differences = = = = 11 Lesson 1 #1 Change subtractions to additions and find the sums. 16! (!8) = = ! 1+ 5! 3 = !1+ 5 +!3!16! (!8) =! =!8 = (1+!1) + (3 +!3) + 5 = 5 Lesson #1 Simplify. 7(!3) =!1 (!4)(!6) = 4 Lesson 1 # Find the distance using the formula a b. The highest point in California is Mt. Whitney at 14,505 feet, and the lowest point is Badwater Basin in Death Valley, 8 feet below sea level. What is the difference in elevation? Lesson # Simplify. 14,505! (!8) = 14, = 14,787 = 14,787 14,787 feet difference.!5(x! 1) (!)4!54 (!6) = 9 35 (!7) =!5 =!10x + 5 = (!)(!)(!)(!) = 16

11 Comprehensive Review Lessons 1 30! page 5a Lesson 3 #1 Use the formula to convert ºF to Celsius. 5(F! 3) C = 9 6 5((!)! 3) C = = 5(! Lesson 4 #1 Solve.!x! = 16 ºF = 30ºC ) =!30!x! = 16!x! + = 16 +!x = 18!x = 18!x = 36 x =!36 Lesson 6 #1 Add or subtract as indicated = = Lesson 3 # From ground level a bullet is fired straight up into the air. The formula for the height of the bullet t seconds after firing is h =!16t + 100t. What is the height of the bullet 30 seconds after firing? h =!16(30) + 100(30) =!16(900) + 100(30) =! = 48,600 feet Lesson 5 #1 Find equivalent fractions with a common denominator for the pair of fractions = = = = Lesson 7 #1 How many 3/4 foot lengths can be cut from a 3 foot ribbon? a. Mark the cuts on the ribbon. 6 35! = ! = ! = b. Write and solve the corresponding divison problem = = 4 Lesson 8 #1 Use the distributive property to simplify " 45 x 5! 8 % # $ 9& ' 9 = 45 1! x $ # " 5 % & ' 45! 8 $ # & 1 " 9 % = 18x ' 40 5 Lesson 8 # Simplify 9a = 9a! 3$ 1 3 " # % & 3 = 9 a 1 3 = 6a

12 Comprehensive Review Lessons 1 30! page 6a Lesson 9 #1 How many cups is 0 quarts? (1 quart = 4 cups) Lesson 9 # How many days is 3,000 minutes? (1 hour = 60 minutes, 1 day = 4 hours) 0 qts 1 4 cups 1 qt = 80 cups 50 3,000 1 min 1 hour 60 min 1 day 4 hour = 50 4 days = 1 1 days Lesson 30 #1 Solve the equation 5 a = a = 19 8 a = a = Lesson 30 # Solve the equation 5 8 x = 1 8. Since all terms have denominator 8, the denominator can be dropped. 5x + 6 = 1 5x + 6! 6 = 1! 6 5x = 6 5x / 5 = 6 / 5 x = 6 5