Free Pre-Algebra Lesson 58! page 1. Lesson 58: Review for Final Exam Section IV. Signed Numbers Comprehensive Practice Lessons 19-24

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1 Free Pre-Algebra Lesson 8! page 1 Lesson 8: Review for Final Exam Section IV. Signed Numbers Comprehensive Practice Lessons Lesson 19: Negative Numbers Skill: Interpret negative numbers with an opposites model. Worksheet 19 #2. Should the number be represented as positive or negative? a. The company lost five million dollars. Skill: Find the absolute value of a number. Worksheet 19 #4. Find the absolute value. a. 40 b.!40 Skill: Interpret negative numbers with a directed distance model. Worksheet 19 #2. Should the number be represented as positive or negative? e. The wreckage of the airplane was found on the sea floor, 2000 feet below the surface. Skill: Compare negative and positive numbers with greater than and less than. Worksheet 19 #. Compare with >, <, or = Lesson 20: Adding with Negative Numbers Skill: Interpret addition of negatives in an opposites model. Worksheet 20 #1. Represent the addition problem using! for a positive and " for a negative, and find the total. + 6 Skill: Interpret addition of negatives in a directed distance model. Worksheet 20 #3. Translate the word problem into an addition with positives and/or negatives to answer the question. An elevator begins on the ground floor and travels up 6 floors. It then travels down 8 floors. What floor is it on? Skill: Add with positive and negative numbers. HW20A #8. Think through the additions and find the sums. Then check on your calculator Skill: Combine like terms with positive and negative coefficients. HW20A #12. Combine like terms. a. 7x + x b. 7x x

2 Free Pre-Algebra Lesson 8! page 2 Lesson 21: Negative Numbers and Subtraction Skill: Rewrite subtractions as adding the opposite. HW21A #6. Change any subtractions to additions, then find the sum. d.!4! 9 f. 4! (!9) Skill: Simplify expressions with negative numbers and subtractions. HW21A #7. Change any subtractions to additions, then simplify. a. 2! 8! + 8 Skill: Use correct algebraic notation for expressions 0x, 1x, and 1x. HW21A #8. Write efficient algebraic notation for the expressions. c. 0n + 3 d. 1a + 0b e. 1x + 1y Skill: Combine like terms with negative coefficients and subtractions. HW23A #4. Simplify the algebraic expressions. b. 6x! 4y! 7x + y Lesson 22: More Operations with Negative Numbers Skill: Multiply expressions with negative numbers. HW22A #7. Simplify. a.!4 9 b. (!4)(!9) Skill: Use the distributive property with negative numbers. HW22A #9. Simplify. b.!6(x! 3) Skill: Divide expressions with negative numbers. HW22A #7. Simplify. d.!36 (!9) e.!36 4 Skill: Use negative and positive fractions. Interpret negatives in numerator and denominator. Worksheet 22 # " 1 % " 1% # $!& ' # $!2& ' Skill: Use exponents with negative numbers. Lesson 22 page 2: Write each expression as a multiplication and find the product.! 2 (!) 2

3 Free Pre-Algebra Lesson 8! page 3 Lesson 23: Negatives in Formulas and Expressions Skill: Use the formula for the height of a falling object. HW23A #6. Solve the problems using the given formulas. a. A person standing on a balcony 80 feet above ground tosses a water balloon straight up at the rate of 10 feet per second. The height of the ballon t seconds after it is tossed is given by the formula h =!16t t + 80 What is the height of the water balloon after 2 seconds? Skill: Use the formulas for Fahrenheit-Celsius conversions with negative temperatures. HW23A #6. Solve the problems using the given formulas. c. Convert 40ºF to Celsius using the formula (F! 32) C = 9 Skill: Use the formula for distance. HW23A #6. Solve the problems using the given formulas. b. One branch store is located 18 miles north of the main office, and the other is located 13 miles south of the main office. Find the distance between the stores using the formula d = a! b Skill: Substitute positive and negative numbers in arbitrary algebraic expressions. Worksheet 23 #6. Evaluate each expression when x =. d. x! 1 e. 1! x h. (!x) 3 Lesson 24: Equations with Negatives Skill: Solve equations with negative and positive numbers. HW2A #4. Solve (equations with integers). a. 7x! 8 =!1 Skill: Solve equations with x. Worksheet 24 #4. Solve 14! d = 4!

4 Free Pre-Algebra Lesson 8! page 1a Lesson 8: Review for Final Exam Section IV. Signed Numbers Comprehensive Practice Lessons Answers Lesson 19: Negative Numbers Skill: Interpret negative numbers with an opposites model. Worksheet 19 #2. Should the number be represented as positive or negative? a. The company lost five million dollars. negative Skill: Find the absolute value of a number. Worksheet 19 #4. Find the absolute value. a. 40 = 40 b.!40 = 40 Skill: Interpret negative numbers with a directed distance model. Worksheet 19 #2. Should the number be represented as positive or negative? e. The wreckage of the airplane was found on the sea floor, 2000 feet below the surface. negative Skill: Compare negative and positive numbers with greater than and less than. Worksheet 19 #. Compare with >, <, or =. 3 > < 100 Lesson 20: Adding with Negative Numbers Skill: Interpret addition of negatives in an opposites model. Worksheet 20 #1. Represent the addition problem using! for a positive and " for a negative, and find the total. + 6! "! "! "! "! "! " + 6 = 1 Skill: Interpret addition of negatives in a directed distance model. Worksheet 20 #3. Translate the word problem into an addition with positives and/or negatives to answer the question. An elevator begins on the ground floor and travels up 6 floors. It then travels down 8 floors. What floor is it on? = 2 It is 2 floors below ground. Skill: Add with positive and negative numbers. HW20A #8. Think through the additions and find the sums. Then check on your calculator = = = = 12 Skill: Combine like terms with positive and negative coefficients. HW20A #12. Combine like terms. a. 7x + x =!2x b. 7x x =!12x

5 Free Pre-Algebra Lesson 8! page 2a Lesson 21: Negative Numbers and Subtraction Skill: Rewrite subtractions as adding the opposite. HW21A #6. Change any subtractions to additions, then find the sum. d.!4! 9 =!4 +!9 =!13 f. 4! (!9) = = 13 Skill: Use correct algebraic notation for expressions 0x, 1x, and 1x. HW21A #8. Write efficient algebraic notation for the expressions. c. 0n + 3 = 3 d. 1a + 0b = a e. 1x + 1y = x + y Skill: Simplify expressions with negative numbers and subtractions. HW21A #7. Change any subtractions to additions, then simplify. a. 2! 8! + 8 = 2 +!8 +! + 8 = (2 +!) + (!8 + 8) =!3 Skill: Combine like terms with negative coefficients and subtractions. HW23A #4. Simplify the algebraic expressions. b. 6x! 4y! 7x + y = 6x +!7x +!4y + y =!1x + 1y =!x + y Lesson 22: More Operations with Negative Numbers Skill: Multiply expressions with negative numbers. HW22A #7. Simplify. a.!4 9 =!36 b. (!4)(!9) = 36 Skill: Divide expressions with negative numbers. HW22A #7. Simplify. d.!36 (!9) = 4 e.!36 4 =!9 Skill: Use the distributive property with negative numbers. HW22A #9. Simplify. b.!6(x! 3)!6x + 18 Skill: Use negative and positive fractions. Interpret negatives in numerator and denominator. Worksheet 22 # 3 " % " 1 % " 1% # $!& ' # $!2& ' = " 1 % $ 1 ' $ ' #! & $!2 ' = 3 # $ & ' 2 Skill: Use exponents with negative numbers. Lesson 22 page 2: Write each expression as a multiplication and find the product.! 2 =!()() =!2 (!) 2 = (!)(!) = 2

6 Free Pre-Algebra Lesson 8! page 3a Lesson 23: Negatives in Formulas and Expressions Skill: Use the formula for the height of a falling object. HW23A #6. Solve the problems using the given formulas. a. A person standing on a balcony 80 feet above ground tosses a water balloon straight up at the rate of 10 feet per second. The height of the ballon t seconds after it is tossed is given by the formula h =!16t t + 80 What is the height of the water balloon after 2 seconds? h =!16(2) (2) + 80 =!16(4) =! = 36 feet above ground Skill: Use the formulas for Fahrenheit-Celsius conversions with negative temperatures. HW23A #6. Solve the problems using the given formulas. c. Convert 40ºF to Celsius using the formula (F! 32) C = 9 8 ((!40)! 32) C = = (! !40ºF =!40ºC ) =!40 Skill: Use the formula for distance. HW23A #6. Solve the problems using the given formulas. b. One branch store is located 18 miles north of the main office, and the other is located 13 miles south of the main office. Find the distance between the stores using the formula d = a! b d = 18! (!13) = = 31 = 31 miles between stores Skill: Substitute positive and negative numbers in arbitrary algebraic expressions. Worksheet 23 #6. Evaluate each expression when x =. d. x! 1 (!)! 1=! +!1=!6 e. 1! x 1! (!) = 1+ = 6 h. (!x) 3 (!(!)) 3 = () 3 = ()()() = 12 Lesson 24: Equations with Negatives Skill: Solve equations with negative and positive numbers. HW2A #4. Solve (equations with integers). a. 7x! 8 =!1 7x! 8 =!1 7x! =!1+ 8 7x = 7 7x / 7 = 7 / 7 x = 1 Skill: Solve equations with x. Worksheet 24 #4. Solve 14! d = 4!d + 14 = 4! d + 14! 14 = 4! 14!d = 31 d =!31!

7 Free Pre-Algebra Lesson 8! page 4 Lesson 8: Review for Final Exam Section V. Fractions, Part 2 Comprehensive Practice Lessons 2-30 Lesson 2: The Common Denominator Skill: Find equivalent fractions with a common denominator. HW26A #8. Find equivalent fractions with a common denominator for each pair of fractions Lesson 26: Adding and Subtracting Fractions Skill: Add fractions after finding equivalent fractions with a common denominator. HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference Skill: Subtract fractions after finding equivalent fractions with a common denominator. HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference. 9! 7 1 Skill: Add mixed numbers after finding equivalent fractions with a common denominator. Adapted from HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference. Skill: Subtract mixed numbers after finding equivalent fractions with a common denominator. HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference ! 12 3 Lesson 27: Dividing Fractions Skill: Divide fractions. HW27A #7. Divide Skill: Interpret word problems with division of fractions. Interpret the answer in context of the problem. HW26A #6. A 3-inch ribbon is cut into /8-inch lengths. How many lengths can be cut?

8 Free Pre-Algebra Lesson 8! page Lesson 27: Dividing Fractions, continued Skill: Divide mixed numbers by first converting to improper fractions. Worksheet 27 #9. Find the quotient Lesson 28: Fractions and Variables Skill: Simplify algebraic fractions (also in Lesson 13). Worksheet 28 #1. Simplify 60xy 144x 2. Skill: Multiply algebraic fractions. Worksheet 28 #2. Multiply 4a 8b 6b 60 Skill: Divide algebraic fractions. HW28A #12. Divide 9y 2x 1x 27. Skill: Simplify algebraic fractions with exponents. Worksheet 28 #4. Change to a multiplication and simplify! 4a $ " # % & 2 Skill: Add algebraic fractions after finding a common denominator. Worksheet 28 #7. Find equivalent fractions with a common denominator. 7 4a 6 8. Add 7 4a + 6 Skill: Subtract algebraic fractions after finding a common denominator. HW28A #9. Find equivalent fractions with a common denominator. 1 x Subtract 1 x! 8 2.

9 Free Pre-Algebra Lesson 8! page 6 Lesson 28: Fractions and Variables Continued Skill: Simplify arithmetic expressions with fractions using the correct order of operations. Worksheet 28 #11. Simplify 4! " 1 % # $ 2& ' 2 Skill: Simplify algebraic expressions with fractions. " HW28A #14. Simplify x! 3 % # $ 4& '. Skill: Simplify complex fractions using division. Worksheet 28 #. Simplify 9a! 3$ " # 2% & Skill: Evaluate algebraic expression by substituting a given fraction. HW28A #16. Evaluate x! 3 4 when x = 3 4 Lesson 29: Converting Units Skill: Use a unit equivalency to write a unit fraction. Cancel units to convert. HW30A #7. How many yards is 800 feet? (3 feet = 1 yard) Skill: Convert units in several steps. HW30A #8. How many hours is 2 weeks? (1 week = 7 days, 1 day = 24 hours) Lesson 30: Equations with Fractions Skill: Solve an equation and write the solution as an improper fraction (also in Lesson 16). Worksheet 30 #2.!2y + 8 =!1 Skill: Solve equations with fractional coefficient. HW30A #9. Solve the equation 9 8 y = 12.

10 Free Pre-Algebra Lesson 8! page 7 Lesson 30: Equations with Fractions Continued Skill: Write an equation with fractions for a word problem, and solve. Interpret the solution in the context of the problem. Worksheet 30 #4. 3/4 of the flowers were roses there were 36 roses. How many flowers were there in all? Skill: Solve equations with fractions added or subtracted from a variable. HW30A #10. Solve the equation t! 3 4 = 7. Skill: Solve multi-step equations with fractions. Worksheet 30 # x = 4 3 Skill: Drop a denominator common to every term in an equation. HW30A #11. Solve the equation x! 1 30 = 1 30.!

11 Free Pre-Algebra Lesson 8! page 4a Lesson 8: Review for Final Exam Section V. Fractions, Part 2 Comprehensive Practice Lessons 2-30 Answers Lesson 2: The Common Denominator Skill: Find equivalent fractions with a common denominator. HW26A #8. Find equivalent fractions with a common denominator for each pair of fractions. 9 = 3 3 = = = = 3 3 = = = = = = = Lesson 26: Adding and Subtracting Fractions Skill: Add fractions after finding equivalent fractions with a common denominator. HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference. Skill: Subtract fractions after finding equivalent fractions with a common denominator. HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference = = 11 9 = ! 7 1 = 2 4! 21 4 = 4 4 Skill: Add mixed numbers after finding equivalent fractions with a common denominator. Adapted from HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference. Skill: Subtract mixed numbers after finding equivalent fractions with a common denominator. HW26A #9. Use the equivalent fractions you found in problem 8 to find the sum or difference = = = ! 12 3 = 7 9! 16 9 = ! 16 9 = 8 9 Lesson 27: Dividing Fractions Skill: Divide fractions. HW27A #7. Divide = = = Skill: Interpret word problems with division of fractions. Interpret the answer in context of the problem. HW26A #6. A 3-inch ribbon is cut into /8-inch lengths. How many lengths can be cut? 3 8 = 3 8 = 24 = lengths measuring /8 inch, and another 4/ of a /8 inch length.

12 Free Pre-Algebra Lesson 8! page a Lesson 27: Dividing Fractions, continued Skill: Divide mixed numbers by first converting to improper fractions. Worksheet 27 #9. Find the quotient = = = = Lesson 28: Fractions and Variables Skill: Simplify algebraic fractions (also in Lesson 13). Worksheet 28 #1. Simplify = 60xy 144x x y x x = y 12x Skill: Multiply algebraic fractions. Worksheet 28 #2. Multiply 4a 8b 6b 60 = 3 3 a b b = 21a 4 Skill: Divide algebraic fractions. HW28A #12. Divide 3 9y 2x 1x 27. = 9 y 2x 27 1 x = 81y 12x 2 Skill: Add algebraic fractions after finding a common denominator. Worksheet 28 #7. Find equivalent fractions with a common denominator. 7 4a = a 3 3 = 21 12a 6 = a 2 a = 10a 12a 7 8. Add 4a + 6 = 21 12a + 10a 10a + 21 = 12a 12a Skill: Simplify algebraic fractions with exponents. Worksheet 28 #4. Change to a multiplication and simplify! 4a $ " # % & 2 = 4a 4a = 16a2 2 Skill: Subtract algebraic fractions after finding a common denominator. HW28A #9. Find equivalent fractions with a common denominator. 1 x = 1 x = 2x 8 2 = 8 x x = 8x 2x 10. Subtract 1 x! 8 2. = 2x! 8x 2x =!8x + 2x

13 Free Pre-Algebra Lesson 28: Fractions and Variables Continued Skill: Simplify arithmetic expressions with fractions using the correct order of operations. Worksheet 28 #11. Simplify 4! " 1 % # $ 2& ' 2 = 4! 1 4 = 4 4 = 1 Skill: Simplify complex fractions using division. Worksheet 28 #. Simplify 3 9a = 9a! 3$ = 9 a = 6a " # 2% & Lesson 8! page 6a Skill: Simplify algebraic expressions with fractions. " HW28A #14. Simplify x! 3 % # $ 4& '. 4 = 60 1! 2 # " 1 x $ & % + 60! ' 3 $ # & = 8x ' 4 " 4 % Skill: Evaluate algebraic expression by substituting a given fraction. HW28A #16. Evaluate x! 3 4 when x = 3 4! 3$ " # 4% & ' 3 4 = 0 = 0 Lesson 29: Converting Units Skill: Use a unit equivalency to write a unit fraction. Cancel units to convert. HW30A #7. How many yards is 800 feet? (3 feet = 1 yard) Skill: Convert units in several steps. HW30A #8. How many hours is 2 weeks? (1 week = 7 days, 1 day = 24 hours) 800 feet 1 1 yard 3 feet = yards = feet = yards 2 weeks 1 = 336 hours 7 days 1 week 24 hours 1 day Lesson 30: Equations with Fractions Skill: Solve an equation and write the solution as an improper fraction (also in Lesson 16). Worksheet 30 #2.!2y + 8 =!1!2y + 8 =!1! 2y + 8! 8 =!1! 8!2y =!9! 2y /!2 =!9 /!2 y = 9 2 Skill: Solve equations with fractional coefficient. HW30A #9. Solve the equation 9 8 y = y = y = y = 32 3

14 Free Pre-Algebra Lesson 8! page 7a Lesson 30: Equations with Fractions Continued Skill: Write an equation with fractions for a word problem, and solve. Interpret the solution in the context of the problem. Worksheet 30 #4. 3/4 of the flowers were roses there were 36 roses. How many flowers were there in all? 3 4 f = f = 36 f = There were 48 flowers. Skill: Solve multi-step equations with fractions. Worksheet 30 # x = x = ! 1 6 = 8 6! 1 6 = x = 7 6 x = x + 1 6! 1 6 = 4 3! x = Skill: Solve equations with fractions added or subtracted from a variable. HW30A #10. Solve the equation t! 3 4 = 7. t! 3 4 = 7 t! = y = = 31 4 Skill: Drop a denominator common to every term in an equation. HW30A #11. Solve the equation x! 1 30 = Since all terms have denominator 30, the denominator can be dropped. 24x! 1 = 1 24x! = x = 16 24x / 24 = 16 / 24 x = = 2 3!

15 Free Pre-Algebra Lesson 8! page 8 Lesson 8: Review for Final Exam Section VI. Decimals Comprehensive Practice Lessons Lesson 31: Decimal Fractions Skill: Read a decimal number using place value. Write a decimal number from the name. Worksheet 31 #1 Write the formal name for the decimal number. Skill: Read a ruler marked in tenths of centimeters. Write the numbers using decimals. Worksheet 31 #3. Write the name of each point as a decimal..07 three hundred eighty-one ten-thousandths Skill: Write a fraction as a decimal. Use the bar notation for repeating digits. HW31A #20. Write the fractions as decimals. Use a bar for repeating decimals Skill: Write a (terminating) decimal as a fraction in lowest terms. HW31A #19. Write the decimals as fractions or mixed numbers. Simplify to lowest terms Lesson 32: Arithmetic with Decimals Skill: Add and subtract decimal numbers, aligning place value at the decimal point. Lesson 32 page 1: Add Skill: Multiply decimal numbers and place the decimal point correctly in the result. Lesson 32 page 1: Multiply 0.03! 2.9

16 Free Pre-Algebra Lesson 8! page 9 Lesson 32: Arithmetic with Decimals Continued Skill: Divide decimal numbers. Lesson 32 page 2: Divide Skill: Use a calculator to evaluate expressions with decimals. Lesson 32 page 3: Evaluate calculator. ( ) with a Skill: Use the correct order of operations to simplify an expression with decimal numbers. Lesson 32 page 3: Evaluate pencil and paper: ( ) with Skill: Raise decimal numbers to a natural number power. Lesson 32 page 2: Evaluate ( 0.04) 2 Skill: Evaluate formulas by substituting decimal numbers for the variable. HW32A #7b. Find the volume of a box with sides 0.2 cm, 0.3 cm, and 0.4 cm. Skill: Round decimal numbers to a given place value or number of decimal places. Lesson 32 page 4: Round to the nearest hundredth. Lesson 32 page : Round to three decimal places.

17 Free Pre-Algebra Lesson 8! page 10 Lesson 33: Formulas for Circles Skill: Use vocabulary for circles: center, radius, diameter, circumference, and pi (!). Convert radius to diameter and vice-versa. Worksheet 33 #1. Fill in the labels for the parts of the circle, using the words center, radius, diameter, circumference. Skill: Use the memorized formula for the circumference of a circle. Round answers as indicated. HW33A #9. Find the circumference of a circle with radius 2.2 meters. Round to the nearest tenth. Skill: Use the memorized formula for the area of a circle. Round answers as indicated. HW33A #9. Find the area of a circle with radius 2.2 meters. Round to the nearest tenth. How many diameters make up one circumference? Skill: Use the given formula for the volume of a sphere. Round answers as indicated. HW33A #10. Find the volume of a sphere with radius 2.2 meters. V = 4 3!r 3 Lesson 34: Algebra with Decimals Skill: Simplify algebraic expressions with decimals by combining like terms and/or using the distributive property. Worksheet 34 #3. Simplify. ( ) x ! x Skill: Solve equations with decimals. Worksheet 34 #. Solve. 0.4x! 1= 0.6

18 Free Pre-Algebra Lesson 8! page 11 Lesson 34: Algebra with Decimals Continued Skill: Drop the decimal point to make an equivalent equation and solve. Worksheet 34 #7. 0.4x! 1= 0.6 Skill: Solve application problems involving formulas using decimal numbers. Worksheet 34 #12. The label said that there were 18 servings per bag, and that each serving was 1.6 ounces. How many ounces did the bag hold? Lesson 3: Comparing Sizes Skill: Compare fractions with > and < by finding a common denominator. Worksheet 3 #4. Compare with >, < or = and 6 Skill: Compare decimal numbers with > and <. Worksheet 3 #. Compare with >, < or = and 1.6 Skill: Compare fractions and decimals by converting the fractions to decimals. Worksheet 3 #7. Compare with >, < or =.! and Skill: Compare numbers in a chart in a sentence. HW36B #6. Write a sentence to compare the data Major League Statistics Player At Bats Hits Suzuki (SEA) Tulowitzki (COL)

19 Free Pre-Algebra Lesson 8! page 12 Lesson 3: Comparing Sizes Continued Skill: Find the difference of two numbers and write a sentence in comparison using the difference Major League Statistics Player At Bats Hits Suzuki (SEA) Tulowitzki (COL) HW36B #7. Find the difference of Suzuki s At Bats to Tulowitski s. Skill: Find the quotient of two numbers and write a sentence in comparison using the quotient Giants Season Statistics Player At Bats Hits Huff Fontenot HW36A #7. What is the ratio of Huff s At Bats to Fontenot s? Write a sentence comparing the number of At Bats. Write a sentence comparing the number of At Bats. Lesson 36: Scientific Notation Skill: Write a number in standard notation in scientific notation. HW36A #9. Write the numbers in scientific notation. a. 888,800,000,000 Skill: Write a number in scientific notation in standard notation. HW36A #10. Write the numbers in standard notation. a. 9.0 x 10 8 b.,009,000,000,000,000,000 b x Skill: Write a number written with a place value name and decimal point in standard form, and vice-versa. HW36A #11. a. Re-write with a place value name. Human stone age cultures arose about 2,00,000 years ago. b. Translate the written name to standard notation. Evidence from radiometric dating indicates that the Earth is about 4.70 billion years old. Skill: Compare numbers written in scientific notation using orders of magnitude. HW36A #12. Write the numbers from #11 in scientific notation: a. Human stone age culture: b. Age of Earth: c. What is the difference in order of magnitude of the two numbers? d. How many times greater is the age of the earth than the time since stone age culture began?!

20 Free Pre-Algebra Lesson 8! page 8a Lesson 8: Review for Final Exam Section VI. Decimals Comprehensive Practice Lessons Answers Lesson 31: Decimal Fractions Skill: Read a decimal number using place value. Write a decimal number from the name. Worksheet 31 #1 Write the formal name for the decimal number..07 five and seven hundredths Skill: Read a ruler marked in tenths of centimeters. Write the numbers using decimals. Worksheet 31 #3. Write the name of each point as a decimal. three hundred eighty-one ten-thousandths Skill: Write a fraction as a decimal. Use the bar notation for repeating digits. HW31A #20. Write the fractions as decimals. Use a bar for repeating decimals. 1 6 = = cm 2.6 cm 4. cm Skill: Write a (terminating) decimal as a fraction in lowest terms. HW31A #19. Write the decimals as fractions or mixed numbers. Simplify to lowest terms = 1000 = = = Lesson 32: Arithmetic with Decimals Skill: Add and subtract decimal numbers, aligning place value at the decimal point. Lesson 32 page 1: Add Skill: Multiply decimal numbers and place the decimal point correctly in the result. Lesson 32 page 1: Multiply 0.03! ! (The first number has two digits after the decimal point, and the second number has one digit. The product will have three digits after the decimal point.)

21 Free Pre-Algebra Lesson 8! page 9a Lesson 32: Arithmetic with Decimals Continued Skill: Divide decimal numbers. Lesson 32 page 2: Divide becomes (the decimal points moved one place to the right so as to have a whole number divisor) Skill: Use a calculator to evaluate expressions with decimals. ( ) with a Lesson 32 page 3: Evaluate calculator: Skill: Use the correct order of operations to simplify an expression with decimal numbers. ( ) with Lesson 32 page 3: Evaluate pencil and paper: ( ) ( ) = =.796 Skill: Evaluate formulas by substituting decimal numbers for the variable. HW32A #7b. Find the volume of a box with sides 0.2 cm, 0.3 cm, and 0.4 cm. ( )( 0.3) ( 0.4) V = 0.2 = cm 3 Skill: Raise decimal numbers to a natural number power. Lesson 32 page 2: Evaluate ( 0.04) 2 = ( 0.04) ( 0.04) = Skill: Round decimal numbers to a given place value or number of decimal places. Lesson 32 page 4: Round to the nearest hundredth rounds to 6.73 Lesson 32 page : Round to three decimal places rounds to 2.187

22 Free Pre-Algebra Lesson 8! page 10a Lesson 33: Formulas for Circles Skill: Use vocabulary for circles: center, radius, diameter, circumference, and pi (!). Convert radius to diameter and vice-versa. Worksheet 33 #1. Fill in the labels for the parts of the circle, using the words center, radius, diameter, circumference. Skill: Use the memorized formula for the circumference of a circle. Round answers as indicated. HW33A #9. Find the circumference of a circle with radius 2.2 meters. Round to the nearest tenth. C = 2!r = 2! 2.2 m ( ) " 13.8 m Skill: Use the memorized formula for the area of a circle. Round answers as indicated. HW33A #9. Find the area of a circle with radius 2.2 meters. Round to the nearest tenth. A =!r 2 =! ( 2.2 m) 2 " 1.2 m 2 How many diameters make up one circumference? Since the circumference is! times the diameter, there are! diameters in one circumference. Skill: Use the given formula for the volume of a sphere. Round answers as indicated. HW33A #10. Find the volume of a sphere with radius 2.2 meters. V = 4 3!r 3 V = 4 3!r 3 = 4 3! ( 2.2 m ) 3 " 44.6 m 3 Lesson 34: Algebra with Decimals Skill: Simplify algebraic expressions with decimals by combining like terms and/or using the distributive property. Worksheet 34 #3. Simplify. ( ) x ! x 30! 0.03x x = x Skill: Solve equations with decimals. Worksheet 34 #. Solve. 0.4x! 1= x! 1= x! 1+ 1= x = x / 0.4 = 1.6 / 0.4 x = 4

23 Free Pre-Algebra Lesson 8! page 11a Lesson 34: Algebra with Decimals Continued Skill: Drop the decimal point to make an equivalent equation and solve. Worksheet 34 #7. 0.4x! 1= x! 1.0 = 0.6 4x! 10 = 6 4x! = x = 16 4x / 4 = 16 / 4 x = 4 Skill: Solve application problems involving formulas using decimal numbers. Worksheet 34 #12. The label said that there were 18 servings per bag, and that each serving was 1.6 ounces. How many ounces did the bag hold? Bag size No. servings = Serving size B 18 = 1.6 oz. B B = = B = 28.8 The bag held 28.8 ounces. Lesson 3: Comparing Sizes Skill: Compare fractions with > and < by finding a common denominator. Worksheet 3 # and = = = = /20 > /6 Skill: Compare fractions and decimals by converting the fractions to decimals. Worksheet 3 #7.! and 3 113! = /113 = /113 >! Skill: Compare decimal numbers with > and <. Worksheet 3 # and > 1.6 Skill: Compare numbers in a chart in a sentence. HW36B #6. Write a sentence to compare the data Major League Statistics Player At Bats Hits Suzuki (SEA) Tulowitzki (COL) Suzuki had more at bats and more hits than Tulowitzki.

24 Free Pre-Algebra Lesson 3: Comparing Sizes Continued Skill: Find the difference of two numbers and write a sentence in comparison using the difference Major League Statistics Player At Bats Hits Suzuki (SEA) Tulowitzki (COL) HW36B #7. Find the difference of Suzuki s At Bats to Tulowitski s = 210 Write a sentence comparing the number of At Bats. Suzuki had 210 more at bats than Tulowitzki. Lesson 8! page 12a Skill: Find the quotient of two numbers and write a sentence in comparison using the quotient Giants Season Statistics Player At Bats Hits Huff Fontenot HW36A #7. What is the ratio of Huff s At Bats to Fontenot s? 69 / 240 = 2.37 Write a sentence comparing the number of At Bats. Huff had more than twice as many at bats as Fontenot. Lesson 36: Scientific Notation Skill: Write a number in standard notation in scientific notation. HW36A #9. Write the numbers in scientific notation. a. 888,800,000, x Skill: Write a number in scientific notation in standard notation. HW36A #10. Write the numbers in standard notation. a. 9.0 x ,000,000 b.,009,000,000,000,000,000 b x ,992,000,000, x Skill: Write a number written with a place value name and decimal point in standard form, and vice-versa. HW36A #11. a. Re-write with a place value name. Human stone age cultures arose about 2,00,000 years ago. 2. million b. Translate the written name to standard notation. Evidence from radiometric dating indicates that the Earth is about 4.70 billion years old. 4,70,000,000 Skill: Compare numbers written in scientific notation using orders of magnitude. HW36A #12. Write the numbers from #11 in scientific notation: a. Human stone age culture: 2,00,000 = 2. x 10 6 b. Age of Earth: 4.70 x 10 9 c. What is the difference in order of magnitude of the two numbers? The exponents are 9 and 6, so the difference is 9 6 = 3. d. How many times greater is the age of the earth than the time since stone age culture began? 10 3 = 1000 times!