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All Textbook Solutions for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
Write an algebraic expression for each word phrase. 10 less than xWrite an algebraic expression for each word phrase. 5 more than dWrite an algebraic expression for each word phrase. 7 minus fWrite an algebraic expression for each word phrase. The sum of 11 and kWrite an algebraic expression for each word phrase. x multiplied by 6Write an algebraic expression for each word phrase. A number t divided by 3Write an algebraic expression for each word phrase. one fourth of a number nWrite an algebraic expression for each word phrase. The product of 2.5 and a number tWrite an algebraic expression for each word phrase. The quotient of 15 and yWrite an algebraic expression for each word phrase. A number q tripledWrite an algebraic expression for each word phrase. 3 plus the product of 2 and hWrite an algebraic expression for each word phrase. 3 less than the quotient of 20 and xWrite a word phrase for each algebraic expression. n+6:Write a word phrase for each algebraic expression. 5cWrite a word phrase for each algebraic expression. 11.5+yWrite a word phrase for each algebraic expression. x417Write a word phrase for each algebraic expression. 3x+10Write a word phrase for each algebraic expression. 10x+7zWrite a rule in words and as an algebraic expression to model the relationship in each table. The local video store charges a monthly membership fee of $5 and $2.25 per video.Write a rule in words and as an algebraic expression to model the relationship in each table. Dorothy gets paid to walk her neighbors dog. For every week that she walks the dog, she earns $10.Write an algebraic expression for each word phrase. 8 minus the quotient of 15 and yWrite an algebraic expression for each word phrase. A number q tripled plus z doubledWrite an algebraic expression for each word phrase. The product of 8 and z plus the product of 6.5 and yWrite an algebraic expression for each word phrase. The quotient of 5 plus d and 12 minus wError Analysis A student writes 5y3 to model the relationship the sum of 5y and 3. Explain the error.Error Analysis A student writes the difference between 15 and the product of 5 and y to describe the expression 5y15. Explain the error.Jake is trying to mail a package to his grandmother. He already has s stamps on the package. The postal worker tells him that hes going to have to double the number of stamps on the package and then add 3 more. Write an algebraic expression that represents the number of stamps that Jake will have to put on the package.For Exercises 17, choose the correct letter. The word minus corresponds to which symbol? A. + B. - C. D. xFor Exercises 17, choose the correct letter. 2. The phrase product corresponds to which symbol? F. x G. + H. - I.For Exercises 17, choose the correct letter. The word plus corresponds to which symbol? A.- B. + C. D.For Exercises 17, choose the correct letter. What is an algebraic expression for the word phrase 10 more than a number f? F. 10f G. 10f H. 10f I. f+10For Exercises 17, choose the correct letter. 5. What is an algebraic expression for the word phrase the product of II and a number s? A. 11s B. 11s c. 11+s D. 11sFor Exercises 17, choose the correct letter. Hannah and Tim collect stamps. Tim is bringing his stamps to Hannahs house so that they can compare. Hannah has 60 stamps. Which expression represents the total number of stamps that they will have if t represents the number of stamps Tim has? F. 60t G. 60t H. 60+t I. 60tFor Exercises 17, choose the correct letter. Hershels bakery sells donuts by the box. There are d donuts in each box. Beverly is going to buy 10 boxes for a class field trip. Which expression represents the total number of donuts that Beverly is going to get for her field trip? A. 10d B. 10d C. 10d D. 10+dFor Exercises 17, choose the correct letter. There are 200 people interested in playing in a basketball league. The leaders of the league are going to divide all of the people into n teams. What algebraic expression represents the number of players on each team?Simplify each expression. 42Simplify each expression. 53Simplify each expression. 116Simplify each expression. 562Simplify each expression. (1+3)2Simplify each expression. (0.1)3Simplify each expression. 5+3(2)Simplify each expression. 1624(5)Simplify each expression. 44(5)+3(11)Simplify each expression. 17(2)42Simplify each expression. 205310(3)2Simplify each expression. 2712833Simplify each expression. (4(5))3Simplify each expression. 254222Simplify each expression. 3(6)1754Simplify each expression. s+6Simplify each expression. 5tSimplify each expression. 11.5+s2Simplify each expression. s4417Simplify each expression. 3(t)3+10Simplify each expression. s3+t2Simplify each expression. 4(s)2+t35Simplify each expression. s+25t22Simplify each expression. 3s(3)115(t)2Every weekend, Morgan buys interesting clothes at her local thrift store and then resells them on an auction website. If she brings $150.00 and spends s, write an expression for how much change she has. Evaluate your expression for s=27.13 and s=55.14.A bike rider is traveling at a speed of 15 feet per second. Write an expression for the distance the rider has traveled after s seconds. Make a table that records the distance for 3.0, 5.8, 11.1, and 14.0 seconds.Simplify each expression. 4(12+5)44Simplify each expression. 3(46)2+72Simplify each expression. 2.5133662Simplify each expression. (488)373Simplify each expression. 4(4)(3)115(1)3Simplify each expression. 41155353a. If the tax that you pay when you purchase an item is 12 of the sale price, write an expression that gives the tax on the item with a price p. Write another expression that gives the total price of the item, including tax. b. What operations are involved in the expressions you wrote? c. Determine the total price, including tax, of an item that costs $75. d. Explain how the order of operations helped you solve this problem.The cost to rent a hall for school functions is $60 per hour. Write an expression for the cost of renting the hall for h hours. Make a table to find how much it will cost to rent the hall for 2, 6, 8, and 10 hours.Evaluate each expression for the given values of the variables. 4(c+5)f4;c=1,f=4Evaluate each expression for the given values of the variables. 3(w6)2+x2;w=5,x=6Evaluate each expression for the given values of the variables. 3.5h33j62;h=3,j=4Evaluate each expression for the given values of the variables. xy255y53;x=6,y=6Solve each exercise and enter your answer on the grid provided. Round your answers to the nearest hundredth if necessary. What is the simplified form of (3.2)4? WSolve each exercise and enter your answer on the grid provided. Round your answers to the nearest hundredth if necessary. What is the simplified form of 62+415?Solve each exercise and enter your answer on the grid provided. Round your answers to the nearest hundredth if necessary. What is the simplified form of 4623+7?Solve each exercise and enter your answer on the grid provided. Round your answers to the nearest hundredth if necessary. What is the value of 4d2+15d25 for d=1?Solve each exercise and enter your answer on the grid provided. Round your answers to the nearest hundredth if necessary. What is the value of 5x23+16y4y for x=2 and y=3?Simplify each expression. 4Simplify each expression. 36Simplify each expression. 25Simplify each expression. 81Simplify each expression. 121Simplify each expression. 169Simplify each expression. 625Simplify each expression. 225Simplify each expression. g. 649Simplify each expression. 2581Simplify each expression. 225169Simplify each expression. 1625Simplify each expression. 0.64Simplify each expression. 0.81Simplify each expression. 6.25Estimate the square root. Round to the nearest integer. 10Estimate the square root. Round to the nearest integer. 15Estimate the square root. Round to the nearest integer. 38Estimate the square root. Round to the nearest integer. 50Estimate the square root. Round to the nearest integer. 16.8Estimate the square root. Round to the nearest integer. 37.5Estimate the square root. Round to the nearest integer. 67.5Estimate the square root. Round to the nearest integer. 81.49Estimate the square root. Round to the nearest integer. 121.86Find the approximate side length of each square figure to the nearest whole unit. A rug with an area of 64ft2Find the approximate side length of each square figure to the nearest whole. unit. an exercise mat that is 6.25m2Find the approximate side length of each square figure to the nearest whole. unit. A plate that is 49cm2Name the subset(s) of the real numbers to which each number belongs. 1218Name the subset(s) of the real numbers to which each number belongs. 5Name the subset(s) of the real numbers to which each number belongs.Name the subset(s) of the real numbers to which each number belongs. 2Name the subset(s) of the real numbers to which each number belongs. 32.5564Name the subset(s) of the real numbers to which each number belongs. 13Name the subset(s) of the real numbers to which each number belongs. 43Name the subset(s) of the real numbers to which each number belongs. 61Compare the numbers in each exercise using an inequality symbol. 25,64Compare the numbers in each exercise using an inequality symbol. 45,1.3Compare the numbers in each exercise using an inequality symbol. ,196Compare the numbers in each exercise using an inequality symbol. 81,121Compare the numbers in each exercise using an inequality symbol. 2717,1.7781356Compare the numbers in each exercise using an inequality symbol. 1415,0.8711Order the numbers from least to greatest. 1.875,64,121Order the numbers from least to greatest. 0.8711,45,1.3Order the numbers from least to greatest. 8.775,67.4698,64.568.477Order the numbers from least to greatest. 1415,5.587,81Order the numbers from least to greatest. 10022,25,2717Order the numbers from least to greatest. ,10.5625,155.8Marsha, Josh, and Tyler are comparing how fast they can type. Marsha types 125 words in 7.5 minutes. Josh types 65 words in 3 minutes. Tyler types 400 words in 28 minutes. Order the students according to who can type the fastest.For Exercises 16, choose the correct letter. To which subset of the real numbers does -18 not belong? A. irrational B. Rational C. Integer D. negative integersFor Exercises 16, choose the correct letter. To which subset of the real numbers does 2 belong? F. irrational G. Rational H. Integer I. wholeFor Exercises 16, choose the correct letter. You can tell that is an irrational number because it has a what? A. non-repeating decimal C. repeating decimal B. non-terminating decimal D. non-repeating and a non-terminating decimalFor Exercises 16, choose the correct letter. What is 324? F. 15 G. 18 H. 19 I. 24For Exercises 16, choose the correct letter. What is 196? A. 14 B. 0 C. 4 D. 19For Exercises 16, choose the correct letter. What is 36x6y4? F. 6x6y4 G. 6x3y2 H. 18x3y2 I. 24x6y4Why is 8.8 classified as a rational number?Name the property that each statement illustrates. 12+917=917+12Name the property that each statement illustrates. 74.50=0Name the property that each statement illustrates. 35x=x35Name the property that each statement illustrates. 3(1p)=3(p)Name the property that each statement illustrates. m+0=mName the property that each statement illustrates. 53.71=53.7Use mental math to simplify each expression. 36+12+4Use mental math to simplify each expression. 19.2+0.6+12.4+0.8Use mental math to simplify each expression. 216105Use mental math to simplify each expression. 1218017Simplify each expression. Justify each step. 6+(8x+12)Simplify each expression. Justify each step. 5(16p)Simplify each expression. Justify each step. (2+7m)+5Simplify each expression. Justify each step. 12st4tTell whether the expressions in each pair are equivalent. 7x and 7x1Tell whether the expressions in each pair are equivalent. 4+6+x and 4x6Tell whether the expressions in each pair are equivalent. (127)+x and 5xTell whether the expressions in each pair are equivalent. p(44) and 0Tell whether the expressions in each pair are equivalent. 24xy2x and 12yTell whether the expressions in each pair are equivalent. 27m(3+912) and 27 m$You have prepared 42mL of distilled water, 18mL of vinegar and 47mL of salt water for an experiment. a. How many milliliters of solution will you have if you first pour the distilled water, then the salt water, and finally the vinegar into your beaker? b. How many milliliters of solution will you have if you first pour the salt water, then the vinegar, and finally the distilled water into your beaker? c. Explain why the amounts described in parts (a) and (b) are equal.Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample. For all real numbers a and b,ab=b+a.Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample. For all real numbers p, q and r,pqr=prq.Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample. For all real numbers x, y and z,(x+y)+z=z+(x+y).Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample. For all real numbers m and n,mmn=nnm.Writing Explain why the commutative and associative properties dont hold true for subtraction and division but the identity properties do.Reasoning A recipe for brownies calls for mixing one cup of sugar with two cups of flour and 4 ounces of chocolate. They are all to be mixed in a bowl before baking. Will the brownies taste different if you add the ingredients in different orders? Relate your answer to a property of real numbers.Simplify each expression. Justify each step. 6753+2(22)Simplify each expression. Justify each step. (m16)(77)Open-Ended Provide examples to show the following. a. The associative property of addition holds true for negative integers. b. The commutative property of multiplication holds true for non-integers. c. The multiplicative property of negative one holds true regardless of the sign of the number on which the operation is performed. d. The commutative property of multiplication holds true if one of the factors is zero.For Exercises 15, choose the correct letter. Which of the following statements is not always true? A. a+(b)=b+a C. (a+b)+(c)=a+[b+(c)] B. a(b)=(b)a D. (a)=aFor Exercises 15, choose the correct letter. Which pair of expressions are equivalent? F. 18m0 and 1 H. (125)+ and 7 G. 6+r+11 and 6r11 I. x(33) and 0For Exercises 15, choose the correct letter. What property is illustrated by the equation (8+2)+7=(2+8)+7? A. Commutative Property of Addition B. Associative Property of Addition C. Distributive Property D. Identity Property of AdditionFor Exercises 15, choose the correct letter. Which expression is equivalent to ab? F. a(b) G. ba H. (a)(b) I. a+bFor Exercises 15, choose the correct letter. Which is an example of an identity property? A. a0=0 B. x1=x C. (1)x=x D. a+b=b+aThe fact that changing the grouping of addends does not change the sum is the basis of what property of real numbers?Use a number line to find each sum. 4+8Use a number line to find each sum. 7+8Use a number line to find each sum. 9+(4)Use a number line to find each sum. 6+(2)Use a number line to find each sum. 6+3Use a number line to find each sum. 5+(10)Use a number line to find each sum. 7+(7)Use a number line to find each sum. + 9+(9)Use a number line to find each sum. 8+0Find each sum. 22+(14)Find each sum. 36+(13)Find each sum. 15+17Find each sum. 45+77Find each sum. 19+(30)Find each sum... 18+(18)Find each sum. 1.5+6.1Find each sum. 2.2+(16.7)Find each sum. 5.3+(7.4)Find each sum. 19+59Find each sum. 34+38Find each sum. 15+710Writing Explain how you would use a number line to find 6+(8).Open-Ended Write an addition equation with a positive addend and a negative addend and a resulting sum of -8.The Bears football team lost 7 yards and then gained 12 yards. What is the result of the two plays?Find each difference. 714Find each difference. 812Find each difference. 5(16)Find each difference. 33(14)Find each difference. 6271Find each difference. 25(25)Find each difference. 1.7(3.8)Find each difference. 4.55.8Find each difference. 3.7(4.2)Find each difference. 7818Find each difference. 2312Find each difference. 4923Evaluate each expression for m=4,n=5, and p=1.5. mpEvaluate each expression for m=4,n=5, and p=1.5. m+npEvaluate each expression for m=4,n=5, and p=1.5. n+mpAt 4: 00 A.M., the temperature was 9 F. At noon, the temperature was 18F. What was the change in temperature?A teacher had $57.72 in his checking account. He made a deposit of $209.54 Then he wrote a check for $72.00 and another check for $27.50. What is the new balance in his checking account?A scuba diver went down 20 feet below the surface of the water. Then she dove down 3 more feet. Later, she rose 7 feet. What integer describes her depth?Reasoning Without doing the calculations, determine whether 47(33) or 47+(33) is greater. Explain your reasoning.For Exercises 15, choose the correct letter. Which expression is equivalent to 17+(15)? A. 17+15 C. 1715 B. 1715 D. 17+15For Exercises 15, choose the correct letter Which number could be placed in the square to make the equation true? 5=14 F.19 G. -9 H. 9 I. 19For Exercises 15, choose the correct letter. Which expression has the greatest value? A. 14(5) C. 145 B. 5(14) D. 514For Exercises 15, choose the correct letter. The wheel was invented about 2500 BC. The gasoline automobile was invented in AD $1885 .$ How many years passed between the invention of the wheel and the invention of the automobile? F. 1615 years H. 1725 years G. 4385 years I. 5385 yearsFor Exercises 15, choose the correct letter. If r=18,s=27, and t=15, what is the value of rst? A. -60 B. -30 C. 6 D. 6In golf, there is a number of strokes assigned to each hole, called the par for that hole. If you get the ball in the hole in fewer strokes than par, you are under par for the hole. If it takes you more strokes than the par, you are over par for the hole. On the first 9 holes of golf, Avery had a par, 1 over par, 2 under par, another par, 1 under par, 1 over par, 3 over par, 2 under par, and I under par. a. What addition expression would represent all 9 holes? b. What is Averys score relative to par?Find each product. Simplify, if necessary. 5(7)Find each product. Simplify, if necessary. 8(-11)Find each product. Simplify, if necessary. 912Find each product. Simplify, if necessary. (9)2Find each product. Simplify, if necessary. 312Find each product. Simplify, if necessary. 5(9)Find each product. Simplify, if necessary. 3(2.3)Find each product. Simplify, if necessary. (0.6)2Find each product. Simplify, if necessary. 8(-2.4)Find each product. Simplify, if necessary. 3429Find each product. Simplify, if necessary. 2558Find each product. Simplify, if necessary. 232Find each product. Simplify, if necessary. After hiking to the top of a mountain, Raul starts to descend at the rate of 350 feet per hour. What real number represents his vertical change after 112 hours?Find each product. Simplify, if necessary. A dolphin starts at the surface of the water. It dives down at a rate of 3 feet per r second. If the water level is zero, what real number describes the dolphins location after 312 seconds?Simplify each expression. 1600Simplify each expression. 625Simplify each expression. 10,000Simplify each expression. 0.81Simplify each expression. 1.44Simplify each expression. 0.04Simplify each expression. 49Simplify each expression. 1649Simplify each expression. 100121Writing Explain the differences among 25,25, and 25.Reasoning Can you name a real number that is represented by 36? Explain.Find each quotient. Simplify, if necessary. 513Find each quotient. Simplify, if necessary. 250(25)Find each quotient. Simplify, if necessary. 982Find each quotient. Simplify, if necessary. 84(4)Find each quotient. Simplify, if necessary. 93(3)Find each quotient. Simplify, if necessary. 1055Find each quotient. Simplify, if necessary. 14.4(3)Find each quotient. Simplify, if necessary. 1.7(10)Find each quotient. Simplify, if necessary. 8.13Find each quotient. Simplify, if necessary. 1713Find each quotient. Simplify, if necessary. 38910Find each quotient. Simplify, if necessary. 5612Evaluate each expression for a=12,b=34, and c=6. abEvaluate each expression for a=12,b=34, and c=6. bcEvaluate each expression for a=12,b=34, and c=6. caWriting Explain how you know that -5 and 15 are multiplicative inverses.At 6: 00 P.M., the temperature was 55F. At 11: 00 P.M. That same evening, the temperature was 40F. What real number represents the average change in temperature per hour?For Exercises 15, choose the correct letter. Which expression has a negative value? A. (2)2 B. (-5)(-7) C. (3)3 D. 0(5)For Exercises 15, choose the correct letter. If x=34 and y=16, what is the value of 2xy? F14 G. 16 Đ½. 16 14For Exercises 15, choose the correct letter. Which expression has the same value as 1723? A. 1732 B. 1732 Ñ�. 7123 D. 7123For Exercises 15, choose the correct letter. ABC stock sold for $64.50. Four days later, the same stock sold for $47.10. What is the average change per day? F. 4.35 G. 3.48 H. $3.48 I. $4.35For Exercises 15, choose the correct letter. The formula C=59(F32) converts a temperature reading from the Fahrenheit scale F to the Celsius scale C. What is the temperature 5F measured in Celsius? A. 2059C B. 15C C. 15C D. 2059CA clock loses 2 minutes every 6 hours. At 3: 00 P.M., the clock is set to the correct time and allowed to run without interference. a. What integer would describe the time loss after exactly 3 days? b. What would the clock read at 3: 00 P.M. Three days later?Use the Distributive Property to simplify each expression. 3(h5)Use the Distributive Property to simplify each expression. 7(5+m)Use the Distributive Property to simplify each expression. (6+9v)6Use the Distributive Property to simplify each expression. (5n+3)12Use the Distributive Property to simplify each expression. 20(8a)Use the Distributive Property to simplify each expression. 15(3y5)Use the Distributive Property to simplify each expression. 21(2x+4)Use the Distributive Property to simplify each expression. (7+6w)6Use the Distributive Property to simplify each expression. (149p)1.1Use the Distributive Property to simplify each expression. (2b10)3.2Use the Distributive Property to simplify each expression. 13(3z+12)Use the Distributive Property to simplify each expression. 412t5Use the Distributive Property to simplify each expression. (5x14)(5.1)Use the Distributive Property to simplify each expression. 112r57Use the Distributive Property to simplify each expression. 10(6.85j+7.654)Use the Distributive Property to simplify each expression. 2323m23Write each fraction as a sum or difference. 3n+57Write each fraction as a sum or difference. 146x19Write each fraction as a sum or difference. 3d+56Write each fraction as a sum or difference. 9p63Write each fraction as a sum or difference. 18+8z6Write each fraction as a sum or difference. 15n4214Write each fraction as a sum or difference. 5628w8Write each fraction as a sum or difference. 81f+639Simplify each expression. (14+x)Simplify each expression. (86t)Simplify each expression. (6+d)Simplify each expression. (r+1)Simplify each expression. (4m6n)Simplify each expression. (5.8a+4.2b)Simplify each expression. (x+y1)Simplify each expression. (f+3g7)Use mental math to find each product. 3.23Use mental math to find each product. 58.2