Practice Integers PDF

Name Period Date Practice Go Online You can complete your homework online. Write an integer to represent...

Name Period Date Practice Go Online You can complete your homework online. Write an integer to represent each situation. Explain the meaning of zero in each situation.(Example 1) 1. Since his last vet appointment, a cat lost 2. On first down, the football team gained 2 ounces. 7 yards. 3. Abigail withdrew $15 from her checking 4. By noon, the temperature had risen account. 5 degrees Fahrenheit. 5. For the month of January, the amount of 6. A dolphin is 20 feet below sea level. snowfall was 3 inches above average. Graph each set of integers on a number line. (Example 2) 7. {-2, 0, 4} 8. {5, −5, −6} 9. {−8, −4, 1} 10. {−7 , 3, 5} Copyright © McGraw-Hill Education 11. {7, −3, −1} 12. {−1, 0, 1} Test Practice 13. The low temperatures for three consecutive 14. Multiple Choice Salton City, California is days were -5°F, 3°F, and 4°F. Graph this set located 38 meters below sea level. What is of integers on a number line. a possible elevation for Salton City? A 380 m B 38 m C 0m D −38 m Lesson 4-1 Represent Integers 197  Name Period Date Practice Go Online You can complete your homework online. Find the opposite of each integer. (Example 1) 1. -3 2. 2 3. 6 4. Chad is planting a plant that is 4 inches tall. 5. A hill on a dirt bike course is 5 feet tall. The He wants the hole he is digging to be as valley below the hill is as deep as the hill is deep as the plant is tall. What integer tall. What integer represents the location of represents the location of the bottom of the the bottom of the valley? How does this hole? How does this compare to the height compare to the height of the hill? (Example 2) of the plant? (Example 2) Find each value. (Examples 2 and 3) 6. −(−15) = 7. −(−11) = 8. −[−(−7)] = 9. −[−(−1)] = 10. −[−(55)] = 11. −[−(100)] = 13. The temperature was −5°F when Tiffany Copyright © McGraw-Hill Education 12. A mountain climber started at sea level and descended down a cliff. Her location can woke up in the morning. By noon, the be represented by -75 feet. How many temperature was 0°F. How many degrees feet did the mountain climber travel? did the temperature change? (Example 4) (Example 4) Test Practice 14. Multiselect Which of the following represent opposites? −4 and 4 −1 and 1 −2 and −1 0 and 1 −7 and −8 10 and −10 Lesson 4-2 Opposites and Absolute Value 203  Name Period Date Practice Go Online You can complete your homework online. 1. After playing 18 holes of golf, John’s score 2. The record low temperature for Buffalo, was −4 and Terry’s score was −1. Write an New York is −20°F. The record low inequality to compare the scores. Then temperature for Chicago, Illinois is −27°F. explain the meaning of the inequality. Write an inequality to compare the record (Example 1) low temperatures. Then explain the meaning of the inequality. (Example 1) 3. The table shows the freezing points for 4. The table shows the scores for players in a gases. Order the gases from least to trivia game after the first round. Order the greatest according to their freezing points. players from least to greatest according to (Example 2) their scores. (Example 2) Gas Freezing Points (°C) Player Score Argon −189 Ace −11 Carbon Monoxide −205 Diana 3 Ethane −297 Jace −3 Helium −272 Oneida −7 Oxygen −219 Nolan 5 Sulfur Dioxide −72 Rachel 1 5. Explain why an elevation less than −5 feet 6. Explain why a balance of less than −$10 represents a distance from sea level greater represents a debt greater than $10. Copyright © McGraw-Hill Education than 5 feet. (Example 3) (Example 3) Test Practice 7. In a golf match, Jesse scored 5 over par, 8. Table Item Order the integers from Neil scored 3 under par, Felipe scored least to greatest. 2 over par, and Dawson scored an even par. Order the players from least to greatest 9, −8, −2, 4, −9 score. least greatest Lesson 4-3 Compare and Order Integers 213  Name Period Date Practice Go Online You can complete your homework online. Graph each set of rational numbers on a number line. (Example 1) 1 3 1 4 1. −0.9, −2 _ { 2 , 0.25, −_ 4 } 2. − _ { 4 , −1.4, −1 _ 5 , −0.15 } 1 3. Mammoth Cave in Kentucky has a minimum 4. A scuba diver was at a depth of −80 _ 2 feet. elevation of −124.1 meters. Suppose a hiker How many feet did the scuba diver travel if traveled to the bottom of the cave. How the diver traveled to the surface of the many meters did the hiker travel? (Example 2) ocean? (Example 2) Fill in the with , or = to make a true statement. (Example 3) 3 5 5. −0.24 −_ 16 6. − _ 8 −0.76 4 7 7. −4 _ 25 −4.16 8. −5.52 −5 _ 15 Order each set of rational numbers from least to greatest. (Example 4) 7 3 11 23 9. −4.25, −4 _ { 10 , −4 _ 20 } 10. −1.55, −1 _ { 100 , −1 _ 25 } Copyright © McGraw-Hill Education Test Practice 11. The change in runners’ goals and their 12. Table Item Order the numbers from actual times is shown in the table. Order the least to greatest. changes from least to greatest. -1.75, 2, 1.25, −2, 0 Runner Change (min) least greatest Sean −3.2 2 Lacy 1_ 5 Maura 1.43 1 Amos −2_ 5 Lesson 4-4 Rational Numbers 223  Name Period Date Practice Go Online You can complete your homework online. Identify the quadrant in which each point is located. (Example 1) 3 1. (−1_21 , −2_41 ) 2. 5_ (4 , −6_ 5 1 ) 4 3 1 4 3. (_, 3_ 54 ) 4. −3_ ( , 2_ 2 5 ) 5. Identify the axis on which the 6. Identify the axis on which the 2 3 point −_ ( 3 ) , 0 is located. (Example 2) point 0, 6_ 5 ( ) is located. (Example 2) Use the coordinate plane. Identify the ordered pair that names each point. (Example 3) 7. A 8. B 9. C Use the coordinate plane. Identify the point for each ordered pair. (Example 4) 1 _1 10. _( ) , 22 1 11. (−1, 1_ 2) 1 12. (−2, −1_ 2) Copyright © McGraw-Hill Education Test Practice 1 1 13. Graph A (_, 1). (Example 5) 2 14. Grid Graph X −1_ 2 ,2. ( ) Lesson 4-5 The Coordinate Plane 235  Name Period Date Practice Go Online You can complete your homework online. Write the ordered pair that is a reflection of each point across the x-axis. (Example 1) 3 1 1 1. A −2_ ( ,1 4 ) 2. B 1_ ( ,− _ 4 2 ) 1 3 3. C −4, −2_ ( 2 ) 4. D _ ( ) 4 ,3 5. Aika is building a square garden. She places 6. A farmer is installing a chicken pen in the a garden post at (3.5, 3.5). What is the shape of a square. He placed a corner location of the corner that reflects (3.5, 3.5) of the enclosure at (−5.25, −5.25). What across the y-axis? (Example 2) is the location of the corner that reflects (−5.25, −5.25) across the y-axis? (Example 2) 1 1 7. The point C'(−4, −2) is the result of 8. The point B' −5 _ 4(, −3 _ 2 ) is the result of reflecting C(4, −2) in the coordinate plane. 1 1 reflecting B −5 4 , 3 _ _( 2 in)the coordinate Identify the axis across which the point was plane. Identify the axis across which the reflected. (Example 3) point was reflected. (Example 3) Copyright © McGraw-Hill Education Test Practice 9. Graph point Z(−4, −2.5) on the coordinate 10. Multiple Choice Which ordered pair 3 plane. Then graph its reflection across the represents a reflection of point Y 1 _ 4 ( , −4 ) y-axis. across the x-axis? A (−4, 1 _34 ) B (1 _34 , −4) C (1 _34 , 4) D (−1 _34 , 4) Lesson 4-6 Graph Reflections of Points 243  Name Period Date Practice Go Online You can complete your homework online. Find the horizontal or vertical distance between the two points. (Examples 1–4) 1. 2. 3. 4. 1 3 3 5. X(−2, 3) and Y −2, 1 _ ( 4 ) 6. Y 1, −_ ( 4 and Z -1, −_ ) ( 4 ) Copyright © McGraw-Hill Education 7. A(−1, 1.5) and B(−1, −1.5) 8. C(3.5, −0.25) and D(0.5, −0.25) Test Practice 9. Multiple Choice What is the vertical distance between the points C(2, −0.8) and D(2, 1.2)? A 0 units C 1 unit B 0.4 unit D 2 units Lesson 4-7 Absolute Value and Distance 253  Name Period Date Practice Go Online Y ou can complete your homework online. Write each product using an exponent. (Examples 1 and 2) 1. 4 × 4 × 4 2. 3 × 3 × 3 × 3 × 3 3. 15 × 15 × 15 × 15 3 __ 3 __ 3 __ 3 _ 3_ _ 3_ 1 1 1 1_ _ 1_ _ 1_ _ 1_ 4. __ 4× 4 4 4×4 4× × × 5. _3_ _3×3 _3_×3 3_ _× 3 × × × 6. 1.625 × 1.625 Evaluate each power. (Examples 3–5) 5 7. 5 = 8. 6 3= 9. 10 4= 1 2 2 3 1 4 10. _2_ = () 11. _5_ () = 12. _4_ () = 13. (1.5)3= 14. (0.2)2= 15. (0.4)3= Copyright © McGraw-Hill Education Test Practice 16.The table shows the approximate area 17. Multiselect Select all expressions that are in square miles of the largest and smallest equivalent to 7 × 7 × 7 × 7. states in the United States. What is the difference between the areas in 47 square miles? 74 State Area (mi2) 77 Alaska 873 28 Rhode Island 392 2,401 16,384  Name Period Date Practice Go Online Y ou can complete your homework online. Evaluate each expression. (Examples 1 and 2) 1. 64 ÷ (15 − 7) × 2 − 9 2. 9 + 8 × 3 − (5 × 2) 3. 4 × (5 2− 12) − 6 4. 78 − 2 4 ÷ (14 − 6) × 2 5. 9 + 7 × (15 + 3) ÷ 3 2 6. 13 + (4 3÷ 2) × 5 − 17 1 2 7. 4 + 62÷ _4_ × 3 ( ) 8. 12 + 2 3÷ __ ( 3 −2 ) 3 2 9. 36 ÷ 32÷ __ ( 4 − 2.4 ) 10. 80 ÷ 4 2÷ _5_ + 3.75 ( ) 11. Mei is shopping for the items shown in the 12. Roy and 2 friends are at a game center. table. Write an expression to represent the Each person buys a hot dog for $3, total cost of 6 bubbles, 2 beach balls, and fries for $2.49, and a drink for $2.50. They 3 sand buckets. Then find the total cost. also have a coupon for $1 off each drink. (Example 3) Write an expression to represent the total cost. Then find the total cost. (Example 3) Item bubbles beach ball sand buckets Cost $1.49 $2.00 $3.50 Copyright © McGraw-Hill Education Test Practice 13. Multiselect Alice takes an art class after school once a week. At each class, she buys a bottle of juice for $1.25 and a bag of pretzels for $0.85. Select all expressions that represent the amount of money, in dollars, Alice spends after attending 8 art classes. 8(1.25)(0.85) 8(1.25 + 0.85) 8(1.25) + 8(0.85) 8 + 1.25 + 0.85 (8 + 1.25) + (8 + 0.85) Lesson 5-2 Numerical Expressions 275  Name Period Date Practice Go Online You can complete your homework online. Identify the terms, like terms, coefficients, and constants in each expression. (Example 1) 1. 4e + 7e + 5 + 2e 2. 5a + 2 + 7 + 6a 3. 4 + 4y + y + 3 For each verbal phrase, define a variable to represent the unknown quantity. Then write the phrase as an algebraic expression. (Examples 2–4) 4. three more pancakes than Hector ate 5. twelve fewer questions than were on the first test 6. two and one-half times the number of minutes 7. one-third the number of yards spent exercising 8. four less than seven times Lynn’s age 9. $2.50 more than one-fourth the cost of a pizza 10. A plumber charges $50 to visit a house 11. A gymnastics studio charges an annual fee plus $40 for every hour of work. Define a of $35 plus $20 per class. Define a variable variable to represent the unknown quantity. to represent the unknown quantity. Then Copyright © McGraw-Hill Education Then write an expression to represent the write an expression to represent the total total cost of hiring a plumber. (Example 4) cost of taking classes. (Example 4) 12. A rectangle has a length that is half its 13. In a triangle there are two sides that have width. Define a variable to represent the the same length and the third side is unknown quantity. Then write an expression 1.5 times longer than the length of the other to represent the perimeter of the rectangle. two. Define a variable to represent the (Example 5) unknown quantity. Then write an algebraic expression to represent the perimeter of the triangle. (Example 5) Lesson 5-3 Write Algebraic Expressions 285  Name Period Date Practice Go Online You can complete your homework online. 3 Evaluate each expression when x = __ 4 and y = 2.5. (Example 1) 10 1. 8x 2. y 2 3. _y_ 2 4 Evaluate each expression when a = __ __ 3 , b = 5 , and c = 6. Write in simplest form. (Example 2) 4. a + b 5. c − b 6. b − a 1 Evaluate each expression when a = 4, b = 3, and c = _3_. (Example 3) 7. (3a + 18c) ÷ b 2 8. (a 2+ 12c) ÷ (7b − 1) 9. (2b + 3a)(c 2) 1 1 10. The expression _2_ a(b + c) can be used to 11. The expression _2_ a(b + c) can be used find the area of the trapezoid. What is the to find the area of the trapezoid. What area of the trapezoid when a = 5.5, b = 5, is the area of the trapezoid when a = 4.4, and c = 7.2? (Example 4) b = 8, and c = 3? (Example 4) Copyright © McGraw-Hill Education Test Practice 12. The perimeter of a rectangle can be found 13. Equation Editor What is the value of the 1 using the expression 2＀ + 2w, where ＀ expression when x = 7, y = _2_ , and z = 8? represents the length and w represents (Example 3) the width. Find the perimeter when 1 (24y + 2x) ÷ _4_z ( ) ＀ = 6.2 units and w = 3.5 units. 123 456 789 0. – Lesson 5-4 Evaluate Algebraic Expressions 293  Name Period Date Practice Go Online You can complete your homework online. Use any method to find the greatest common factor of each pair of numbers. (Examples 1 and 2) 1. 12, 30 2. 4, 16 3. 9, 36 4. 35, 63 5. 42, 56 6. 54, 81 7. On every fourth visit to the hair salon, 8. The table shows the city bus schedule for Margot receives a discount of $5. On every certain bus lines. Both buses are at the bus tenth visit, she receives a free hair product. stop right now. In how many minutes will After how many visits will Margot receive the both buses be at the bus stop again? discount and a free product at the same (Example 3) time? (Example 3) Bus Line Arrives at the bus stop every... A 25 minutes B 15 minutes Use any method to find the least common multiple of each pair of numbers. (Example 4) 9. 4, 6 10. 3, 5 Test Practice 11. Monique has the flowers shown in the table. 12. Equation Editor What is the greatest Copyright © McGraw-Hill Education She wants to put all the flowers into common factor of 35 and 28? decorative vases. Each vase must have the same number of flowers in it. Without mixing flowers, what is the greatest number of flowers that Monique can put in each vase? Flower Type Number Daisies 20 123 Roses 25 456 789 0. – Lesson 5-5 Factors and Multiples 303  Name Period Date Practice Go Online You can complete your homework online. Use the Distributive Property to expand each algebraic expression. (Example 1) 1. 3(x + 8) 2. 5(6 + x) 3. 9(3 + x) Use the Distributive Property to simplify each expression. (Example 2) 3 2 1 4. 12 · 3 __ 4 5. 15 · 2 _3_ 6. 8 · 4 _2_ Use the GCF to factor each numerical expression. (Example 3) 7. 16 + 48 8. 35 + 63 9. 26 + 39 Use the GCF to factor each algebraic expression. (Example 4) 10. 8x + 16 11. 24 + 6x 12. 42 + 7x Copyright © McGraw-Hill Education Test Practice 13. Five friends each bought a shirt and a pair 14. Multiple Choice Which expression has the of shoes. The table shows the cost of the same value as 9 + 24? items. The expression 5(x + 24) shows the A 3(3 + 24) total amount of money they spent. Expand the expression using the Distributive B 3(3 + 8) Property. C 3(9 + 8) Item Cost ($) D 9(1 + 24) Shirt x Shoes 24.00 Lesson 5-6 Use the Distributive Property 313  Name Period Date Practice Go Online You can complete your homework online. Use properties of operations to determine whether or not the expressions are equivalent.(Example 1) 1. (x + 10) + x + 9 and 2(x + 7) + 5 2. 0.5x + 1 and 1(0.5x) Use substitution to determine whether or not the expressions are equivalent. (Examples 2 and 3) 2 1 and 4. x + 2x2+ _1_x2+ 1 + x __ 3. 3x + 2x + x and 7x 3 3 Simplify each expression. (Examples 4 and 5) 5. 3x + 4 + 5x – 1 6. 10 + 7x − 5 + 4x 1 1 1 7. 4x 2 + 6x + 8 + x + 2 8. _2_x2+ x + _2_ + 2x + _2_x2 Test Practice Copyright © McGraw-Hill Education 9. Simplify 3__ _2_ _1_ 4 + 3 (9x + 6) + 4x + 3 4. (Example 6) 10. Multiselect Which of the following are 3 _1_ ? equivalent to __ 2 2 4 (8x + 1) + 3x + 4 Select all that apply. 3 _1_ 6x2+ __ 2 4 + 3x + 4 6x2+ 1 + 3x + 2 _1_ 4 1 9x2+ 1 _4_ 3 _ 1_ 9x2+ __ 4+4 9x2+ 2 9x2 + 1 Lesson 5-7 Equivalent Algebraic Expressions 327  Name Period Date Practice Go Online You can complete your homework online. Identify the solution of each equation from the specified set. (Example 1) 1. x + 5.6 = 11.6; 5, 6, 7 2. 4.2 + z = 11.2; 6, 7 , 8 3. b − 9.7 = 13.3; 23, 24, 25 4. d − 8.4 = 8.6; 15, 16, 17 5. 4.5x = 18; 3, 4, 5 6. 2.25c = 27; 12, 13, 14 7. d ÷ 5.5 = 4; 22, 23, 24 8. 36.3 ÷ y = 12.1; 2, 3, 4 9. Brinley is making headbands for her friends. 10. Maddox has $12.25 to spend on sports 1 Each headband needs 16_2_ inches of elastic drinks. Each drink costs $1.75. Use the guess, check, and revise strategy to solve and she has 132 inches of elastic. Use the the equation 1.75d = $12.25 to find d, the guess, check, and revise strategy to solve 1 number of drinks Maddox can buy.(Example 2) the equation 16_2_h = 132 to find h, the number of headbands Brinley can make. Copyright © McGraw-Hill Education (Example 2) 11. Manuel has two different recipes for chocolate chip Recipe Chocolate Chips (cups) muffins. The table shows the amount of chocolate 1 _3_ chips needed per batch for each recipe. He has 4 3 1 8_ 4 cups of chocolate chips. Use the guess, check, 2 1_4_ 1 3 and revise strategy to solve the equation _ 14 b = 8 _ 4 to find b, the number of batches of muffins he can make if he uses Recipe 2. Lesson 6-1 Use Substitution to Solve One Step Equations 339  Name Period Date Practice Go Online You can complete your homework online. 1. On Saturday and Sunday, Jarrod went 2. Maggie and her sister bought a gift for their running and burned a total of 647.5 Calories. mother that cost $54.75. Maggie contributed He burned 320 of those Calories on $26 to the cost of the gift. Write an addition Saturday. Write an addition equation that equation that could be used to find how could be used to find the number of Calories much money Maggie’s sister contributed to Jarrod burned on Sunday. (Example 1) the gift. (Example 1) 3. A piece of material measures 38.25 inches. 4. On a two-day car trip, the Roberts family Courtney cuts the piece of material into drove a total of 854.25 miles. On Day 1, the two pieces. One piece measures family drove 497.75 of those miles. Write an 19.5 inches. Write an addition equation addition equation that could be used to find that could be used to find the length of how many miles the Roberts family drove on the other piece of material. (Example 1) Day 2 of their trip. (Example 1) Solve each equation. Check your solution. (Examples 2 and 3) 5. 9 = 3 + a 6. 5 + x = 10 1 3 1 1 7. 3_4_ + z = 6__ 4 8. 9 _2_ = b + 2_4_ Copyright © McGraw-Hill Education Test Practice 9. 18.35 = c + 5.1 10. Equation Editor Solve x + 5.15 = 23.85. 123 456 789 0. – Lesson 6-2 One-Step Addition Equations 349  Name Period Date Practice Go Online You can complete your homework online. 1. On Monday, Homeroom 104 turned in 2. Izan’s youngest relative is 5 years old. This 64 canned goods. This is 17 less than the is 79 years less than the age of his oldest number of canned goods turned in by relative. Write a subtraction equation that Homeroom 106. Write a subtraction could be used to find the age of his oldest equation that could be used to find the relative. (Example 1) number of canned goods turned in by Homeroom 106 on Monday. (Example 1) 1 3. T o make a cake, Rose needed 1_2_ cups of 4. On Sunday, Jax biked 10.25 miles. This is 1 3.5 fewer miles than the number of miles he sugar. This is 1_4_ cups less than the amount biked on Saturday. Write a subtraction of flour she needed for the cake. Write a equation that could be used to find the subtraction equation that could be used number of miles Jax biked on Saturday. to find the amount of flour she needed (Example 1) for the cake. (Example 1) Solve each equation. Check your solution. (Examples 2 and 3) 5. 24 = x − 5 6. z − 7 = 19 1 5 1 1 7. z − 9_3_ + = 1_9_ 8. 5 _2_ = b − 12_4_ Copyright © McGraw-Hill Education Test Practice 9. 67.9 = c − 4.45 10. Equation Editor Solve x - 7.49 = 87.3. 123 456 789 0. – Lesson 6-3 One-Step Subtraction Equations 357  Name Period Date Practice Go Online You can complete your homework online. 1 1. Maribel and some friends went to an 2. It takes Samuel _5_ hour to walk a mile. 1 adventure park. The total cost of their tickets Yesterday, Samuel walked for 1_2_ hours. was $374 and each person paid $46.75. Write a multiplication equation that can Write a multiplication equation that can be be used to find the number of miles used to find how many people bought Samuel walked. (Example 1) tickets to the adventure park. (Example 1) 3. The distance around a lake is 2.6 miles. On 4. An express delivery company charges Saturday, Doug biked a total of 18.2 miles $3.25 per pound to mail a package. around the lake. Write a multiplication Georgia paid $9.75 to mail a package. equation that can be used to find how many Write a multiplication equation that can times Doug biked around the lake. be used to find the weight of the package (Example 1) in pounds. (Example 1) Solve each equation. Check your solution. (Examples 2 and 3) 5. 12 = 6x 6. 3z = 15 _2_ 1 5 7. 3__ 4z = 3 8. _2_ = _8_w Copyright © McGraw-Hill Education Test Practice 9. 60.536 = 9.2j 10. Equation Editor Solve 3.9x = 16.068. 123 456 789 0. – Lesson 6-4 One Step Multiplication Equations 367