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All Textbook Solutions for Elementary Algebra
For the number 27,493,615, find the place value of each digit: (a) 2 (b) 1 (c) 4 (d) 7 (e) 5For the number 519,711,641,328, find the place value of each digit: 9 4 2 6 7Name the number 9,258, 137, 904, 061 using words.Name the number 17,864, 325, 619, 004 using words.Write the number two billion, four hundred sixty-six million, seven hundred fourteen thousand, fifty-one as a whole number using digits.Write the number eleven billion, nine hundred twenty-one million, eight hundred thirty thousand, one hundred six as a whole number using digits.Round to the nearest hundred: 17,852.Round to the nearest hundred: 468,751.Round 206,981 to the nearest: (a) hundred (b) thousand (c) ten thousand.Round 784.951 to the nearest: (a) hundred (b) thousand (c) ten thousand.Determine whether 4,962 is divisible by 2, by 3, by 5, by 6, and by 10.Determine whether 3,765 is divisible by 2, by 3, by 5, by 6, and by 10.Find the prime factorization of 80.Find the prime factorization of 60.Find the prime factorization of 126.Find the prime factorization of 294.Find the least common multiple by listing multiples: 9 and 12.Find the least common multiple by listing multiples: 18 and 24.Find the LCM using the prime factors method: 9 and 12.Find the LCM using the prime factors method: 18 and 24.Find the LCM using the prime factors method: 21 and 28.Find the LCM using the prime factors method: 24 and 32.In the following exercises, find the place value of each digit in the given numbers. 1. 51493 (a) 1 (b) 4 (c) 9 (d) 5 (e) 3In the following exercises, find the place value of each digit in the given numbers. 2. 87,210 (a)2 (b)8 (c) 0 (d) 7 (e) 1In the following exercises, find the place value of each digit in the given numbers. 3. 164,285 (a)5 (b)6 (c)1 (d)8 (e) 2In the following exercises,, find the place value of each digit in the given numbers. 4. 395,076 (a) 5 (b) 3 (c) 7 (d) 0 (e) 9In the following exercises, find the place value of each digit in the given numbers. 5. 93,285,170 (a) 9 (b) 8 (c) 7 (d) 5 (e) 3In the following exercises, find the place value of each digit in the given numbers. 6. 36,084,215 (a) 8 (b) 6 (c) 5 (d) 4 (e) 3In the following exercises, find the place value of each digit in the given numbers. 7. 7,284,915,860,132 (a)7 (b) 4 (c)5 (d)3 (e)0In the following exercises, find the place value of each digit in the given numbers. 8. 2,850,361,159,433 (a) 9 (b) 8 (c) 6 (d) 4 (e) 2In the following exercises, name each number using words. 9. 1,078In the following exercises, name each number using words. 10. 5.902In the following exercises, name each number using words. 11. 364,510In the following exercises, name each number using words. 12. 146,023In the following exercises, name each number using words. 13. 5,846,103In the following exercises, name each number using words. 14. 1,458.398In the following exercises, name each number using words. 15. 37,889,005In the following exercises, name each number using words. 16. 62,008,465In the following exercises, write each number as a whole number using digits. 17. four hundred twelveIn the following exercises, write each number as a whole number using digits. 18. two hundred fifty-threeIn the following exercises, write each number as a whole number using digits. 19. thirty-five thousand, nine hundred seventy-fiveIn the following exercises, write each number as a whole number using digits. 20. sixty-one thousand, four hundred fifteenIn the following exercises, write each number as a whole number using digits. 21. eleven million, forty-four thousand, one hundred sixty-seven.In the following exercises, write each number as a whole number using digits. 22. eighteen million, one hundred two thousand, seven hundred eighty-threeIn the following exercises, write each number as a whole number using digits. 23. three billion, two hundred twenty-six million, five hundred twelve thousand, seventeenIn the following exercises, write each number as a whole number using digits. 24. eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six.In the following, round to the indicated place value. 25. Round to the nearest ten. (a) 386 (b) 2,931In the following, round to the indicated place value. 26. Round to the nearest ten. (a)792 (b)5,647In the following, round to the indicated place value. 27. Round to the nearest hundred. (a) 13,748 (b) 391,794In the following, round to the indicated place value. 28. Round to the nearest hundred. (a)28,166 (b)481,628In the following, round to the indicated place value. 29. Round to the nearest ten. (a) 1,492 (b) 1,497In the following, round to the indicated place value. 30. Round to the nearest ten. (a) 2,791 (b) 2,795In the following, round to the indicated place value. 31. Round to the nearest hundred. (a) 63,994 (b) 63,040In the following, round to the indicated place value. 32. Round to the nearest hundred. (a) 49,584 (b) 49,548In the following exercises, round each number to the nearest (a) hundred, (b) thousand, (c) ten thousand. 33. 392,546In the following exercises, round each number to the nearest (a) hundred, (b) thousand, (c) ten thousand. 34. 619,348In the following exercises, round each number to the nearest (a) hundred, (b) thousand, (c) ten thousand. 35. 2,586,991In the following exercises, round each number to the nearest (a) hundred, (b) thousand, (c) ten thousand. 36. 4,287,965In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 37. 84In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 38. 9,696In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 39.75In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 40. 78In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 41. 900In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 42. 800In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 43. 986In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 44. 942In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 45. 350In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 46.550In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 47. 22,335In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10. 48. 39.075In the following exercises, find the prime factorization. 49.86In the following exercises, find the prime factorization. 50. 78In the following exercises, find the prime factorization. 51. 132In the following exercises, find the prime factorization. 52. 455In the following exercises, find the prime factorization. 53. 693In the following exercises, find the prime factorization. 54.400In the following exercises, find the prime factorization. 55. 432In the following exercises, find the prime factorization. 56. 627In the following exercises, find the prime factorization. 57. 2,160In the following exercises, find the prime factorization. 58.2,520In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 59. 8, 12In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 60. 4, 3In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 61. 12, 16In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 62. 30, 40In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 63. 20, 30In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 64. 44, 55In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 65. 8, 12In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 66. 12, 16In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 67. 28, 40In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 68. 48, 90In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 69. 55, 88In the following exercises, find the least common multiple of the each pair of numbers using the multiples method. 70. 60, 72Writing a Check Jorge bought a car for $24,493. He paid for the car with a check. Write the purchase price in words.Writing a Check Marissa’s kitchen remodeling cost $18,549. She wrote a check to the contractor. Write the amount paid in words.Buying a Car Jorge bought a car for $24,493. Round the price to the nearest (a) ten (b) hundred (c) thousand; and (d) ten-thousand.Remodeling a Kitchen Marissa’s kitchen remodeling cost $18,549, Round the cost to the nearest (a) ten (b) hundred (c) thousand and (d) ten-thousand.Population The population of China was 1,339,724,852 on November 1, 2010. Round the population to the (a) nearest (b) billion (c) hundred-million; and (d) million.Astronomy The average distance between Earth and the sun is 149,597,888 kilometers. Round the distance to the nearest (a) hundred-million (b) ten million; (c) and million.Grocery Shopping Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?Grocery Shopping Paper plates are sold in packages of 12 and party cups come in packs of eight. What is the smallest number that makes the plates and cups come out even?Give an everyday example where it helps to round numbers.If a number is divisible by 2 and by 3 why is it also divisible by 6?What is the difference between prime numbers and composite numbers?Explain in your own words how to find the prime factorization of a composite number, using any you prefer.Translate from algebra into English: (a)1427 (b)1928 (c)1242 (d)x71Translate from algebra into English: (a)1915 (b)7=125 (c)1538 (d)y+36Determine if each is an expression or an equation: (a) 3(x7)=27 (b) 5(4y2)7Determine if each is an expression or an equation: (a)y214 (b)4x6=22 .Simplify: (a)53 (b)17 .Simplify: (a) 72 (b) 05 .Simplify: (a)1252 (b)(125)2Simplify: (a)8+39 (b)(8+3)9Simplify: 305+10(32) .Simplify: 7010+4(62) .Simplify: 9+53[4(9+3)].Simplify: 722[4(5+1)].Evaluate 8x3 , when (a) x=2 and (b) x=1 .Evaluate 4y4 , when (a) y=3 and (b) y=5 .Evaluate x=3 , when (a) x2 (b) 4x .Evaluate x=6 , when (a) x3 (b) 2xEvaluate 3x2+4x+1 when x=3 .Evaluate 6x24x7 when x=2 .Identify the coefficient of each term: (a) 17x (b) 41b2 (c) z.Identify the coefficient of each term: (a) 9p (b) 13a3 (c) y3 .Identify the like terms: 9, 2x3 , y2,8x3 , 15 9y , 11y2Identify the like terms: 4x3,8x2,19,3x2,24,6x3 .Identify the terms in the expression 4x2+5x+17 .Identify the terms in the expression 5x+2y .Simplify: 3x2+7x+9+7x2+9x+8 .Simplify: 4y2+5y+2+8y2+4y+5 .Translate the English phrase into an algebraic expression: (a) the difference of 14x2 and 13(b) the quotient of 12x and 2.Translate the English phrase into an algebraic expression: (a) the sum of 17y2 and 19 (b) the product of 7 and y.Translate the English phrase into an algebraic expression: (a) Eleven more than x (b) Fourteen less than 11a.Translate the English phrase into an algebraic expression: (a) 13 more than z (b) 18 less than 8x.Translate the English phrase into an algebraic expression: (a) four times the sum of p and q (b) the sum of four times p and q.Translate the English phrase into an algebraic expression: (a) the difference of two times x and 8, (b) two times t difference of x and 8.The length of a rectangle is 7 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.The width of a rectangle is 6 less than the length. Let I represent the length of the rectangle. Write an expression for the width of the rectangle.Geoffrey has dimes and quarters in his pocket. The number of dimes is eight less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.In the following exercises, translate from algebra to English. 83. 169In the following exercises, translate from algebra to English. 84. 39In the following exercises, translate from algebra to English. 85. 284In the following exercises, translate from algebra to English. 86. x+11In the following exercises, translate from algebra to English. 87. (2)(7)In the following exercises, translate from algebra to English. 88. (4)(8)In the following exercises, translate from algebra to English. 89. 1421In the following exercises, translate from algebra to English. 90. 1735In the following exercises, translate from algebra to English. 91. 3619In the following exercises, translate from algebra to English. 92. 6n=36In the following exercises, translate from algebra to English. 93. y16In the following exercises, translate from algebra to English. 94. y48In the following exercises, translate from algebra to English. 95. 2186In the following exercises, translate from algebra to English. 96. a112In the following exercises, determine if each is an expression or an equation. 97. 96=54In the following exercises, determine if each is an expression or an equation. 98. 79=63In the following exercises, determine if each is an expression or an equation. 99. 54+3In the following exercises, determine if each is an expression or an equation. 100. x+7In the following exercises, determine if each is an expression or an equation. 101. x+9In the following exercises, determine if each is an expression or an equation. 102. y5=25In the following exercises, simplify each expression. 103. 53In the following exercises, simplify each expression. 104. 83In the following exercises, simplify each expression. 105. 28In the following exercises, simplify each expression. 106. 105In the following exercises, simplify using the order of operations. (a)3+85 (b)(3+8)5In the following exercises, simplify using the order of operations. 108. (a) 2+63 (b) (2+6)3In the following exercises, simplify using the order of operations. 109. 2312(95)In the following exercises, simplify using the order of operations. 110. 3218(115)In the following exercises, simplify using the order of operations. 111. 38+52In the following exercises, simplify using the order of operations. 112. 47+35In the following exercises, simplify using the order of operations. 113. 2+8(6+1)In the following exercises, simplify using the order of operations. 114. 4+6(3+6)In the following exercises, simplify using the order of operations. 115. 412/8In the following exercises, simplify using the order of operations. 116. 236/6In the following exercises, simplify using the order of operations. 117. (6+10)(2+2)In the following exercises, simplify using the order of operations. 118. (9+12)(3+4)In the following exercises, simplify using the order of operations. 119. 204+65In the following exercises, simplify using the order of operations. 120. 333+82In the following exercises, simplify using the order of operations. 121. 32+72In the following exercises, simplify using the order of operations. 112. (3+7)2In the following exercises, simplify using the order of operations. 123. 3(1+96)42In the following exercises, simplify using the order of operations. 124. 5(2+84)72In the following exercises, simplify using the order of operations. 125. 2[1+3(102)]In the following exercises, simplify using the order of operations. 126. 5[2+4(32)]In the following exercises, evaluate the following expressions. 127. 7x+8 when x=2In the following exercises, evaluate the following expressions. 128. 8x6 when x=7In the following exercises, evaluate the following expressions. 129. x2 when x=12In the following exercises, evaluate the following expressions. 130. x3 when x=5In the following exercises, evaluate the following expressions. 131. x2 when x=2In the following exercises, evaluate the following expressions. 132. 4x when x=2In the following exercises, evaluate the following expressions. 133. x2+3x7 when x=4In the following exercises, evaluate the following expressions. 134. 6x+3y9 , when x=6,y=9In the following exercises, evaluate the following expressions. 135. (xy)2 when x=10,y=7In the following exercises, evaluate the following expressions. 136. (x+y)2 when x=6,y=9In the following exercises, evaluate the following expressions. 137. a2+b2 when a=3,b=8In the following exercises, evaluate the following expressions. 138. r2s2 when r=12 , s=5In the following exercises, evaluate the following expressions. 139. 2l+2w when l=15,w=12In the following exercises, evaluate the following expressions. 140. 2l+2w when l=18,w=14In the following exercises, identify the coefficient of each term. 141. 8aIn the following exercises, identify the coefficient of each term. 142. 13mIn the following exercises, identify the coefficient of each term. 143. 5r2In the following exercises, identify the coefficient of each term. 144. 6x3In the following exercises, identify the like terms. 145. x3,8x,14,8y,5,8x3In the following exercises, identify the like terms. 146. 6z,3w2,1,6z2,4z,w2In the following exercises, identify the like terms. 147. 9a,a2,16,16b2,4,9b2In the following exercises, identify the like terms. 148. 3,25r2,10s,10r,4r2,3sIn the following exercises, identify the terms in each expression. 149. 15x2+6x+2In the following exercises, identify the terms in each expression. 150. 11x2+8x+5In the following exercises, identify the terms in each expression. 151. 10y3+y+2In the following exercises, identify the terms in each expression. 152. 9y3+y+5In the following exercises, simplify the following expressions by combining like terms. 153. 10x+3xIn the following exercises, simplify the following expressions by combining like 154. 15x+4xIn the following exercises, simplify the following expressions by combining like terms. 155. 4c+2c+cIn the following exercises,, simplify the following expressions by combining like terms. 156. 6y+4y+yIn the following exercises, simplify the following expressions by combining like terms. 157. 7u+2+3u+1In the following exercises, simplify the following expressions by combining like terms. 158. 8d+6+2d+5In the following exercises, simplify the following expressions by combining like terms. 159. 10a+7+5a2+7a4In the following exercises,, simplify the following expressions by combining like terms. 160. 7c+4+6c3+9c1In the following exercises, simplify the following expressions by combining like terms. 161. 3x2+12x+11+14x2+8x+5In the following exercises, simplify the following expressions by combining like terms. 162. 5b2+9b+10+2b2+3b4In the following exercises, translate the phrases into algebraic expressions. 163. the difference of 14 and 9In the following exercises, translate the phrases into algebraic expressions. 164. the difference of 19 and 8In the following exercises, translate the phrases into algebraic expressions. 165. the product of 9 and 7In the following exercises, translate the phrases into algebraic expressions. 166. the product of 8 and 7In the following exercises, translate the phrases into algebraic expressions. 167. the quotient of 36 and 9In the following exercises, translate the phrases into algebraic expressions. 168. the quotient of 42 and 7In the following exercises, translate the phrases into algebraic expressions. 169. the sum of 8x and 3xIn the following exercises, translate the phrases into algebraic expressions. 170. the sum of 13x and 3x.In the following exercises, translate the phrases into algebraic expressions. 171. the quotient of y and 3In the following exercises, translate the phrases into algebraic expressions. 172. the quotient of y and 8In the following exercises, translate the phrases into algebraic expressions. 173. eight times the difference of y and nineIn the following exercises, translate the phrases into algebraic expressions. 174. seven times the difference of y and oneIn the following exercises, translate the phrases into algebraic expressions. 175. Eric has rock and classical CD5 in his car. The number of rock CDs is 3 more than the number of classical CDs. Let c represent the number of classical CDs. Write an expression for the number of rock CDs.In the following exercises, translate the phrases into algebraic expressions. 176. The number of girls in a second-grade class is 4 less than the number of boys. Let b represent the number of boys. Write an expression for the number of girls.In the following exercises, translate the phrases into algebraic expressions. 177. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.In the following exercises, translate the phrases into algebraic expressions. 178. Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.Car insurance Justin’s car insurance has a $750 deductible per incident. This means that he pays $750 and his insurance company will pay all costs beyond $750. If Justin files a claim for $2,100. how much will he pay? how much will his insurance company pay?Home insurance Armando’s home insurance has a $2,500 deductible per incident. This means that he pays $2,500 and the insurance company will pay all costs beyond $2,500. If Armando files a claim for $19,400. (a) how much will he pay? (b) how much will the insurance company pay?Explain the difference between an expression and equation.Why is it important to use the order of operations to simplify an expression?Explain how you identify the like terms in the expression 8a2+4a+9a21.Explain the difference between the phrases “4 times the sum of x and y” and “the sum of 4 times x and y.”Order each of the following pairs of numbers, using < or >: (a)157 (b)25 (c)-3_7 (d)5_17Order each of the following pairs of numbers, using < or >: 8_13 3_4 -5_-2 9_-21Find: (a) the opposite of 4 (b) the opposite of 3 (c) (1).Find: (a) the opposite of 8 (b) the opposite of 5(5)(5) .Evaluate n, when (a) n=4 (b) n=4 .Evaluate m. when (a) m=11 (b) m=11 .Simplify: (a) 4 (b) 28 (c) |0| .Simplify: (a) 13 (b) 47 (c) 0 .Fill in <, >, or = for each of the following pairs of numbers: (a) |9||9| (b) 2|2| (c) 8|8| (d) (9)|9| .Fill in <, >, or = for each of the following pairs of numbers: (a)77 (b)(10)10 (c)44 (d)11Simplify: 19114(31).Simplify : 984(75) .Evaluate: when (a) x=17 (b) y when y=39 (c) m when m=22 (d) p when p=11 .Evaluate: (a) y when y=23 (b) y when y=21 (c) n when n=37 (d) q when q=49 .Add : (a) 2+4 (b) 2+(4) .Add: (a) 2+5 (b) 2+(5)Add: (a) 2+4 (b) 2+(4) .Add: (a) 2+5 (b) 2+(5) .Simplify: (a) 31+(19) (b) 15+(32) .Simplify: (a) 42+(28) (b) 25+(61) .Simplify: 2+5(4+7) .Simplify: 4+2(3+5) .Subtract: (a) 64 (b) 6(4) .Subtract: (a) 74 (b) 7(4) .Subtract: (a) 64 (b) 6(4) .Subtract: (a) 74 (b) 7(4) .Simplify: (a) 2113 and 21+(13) (b) 117 and 11+(7).Simplify: (a) 157 and 15+(7) (b) 148 and 14+(8) .Simplify: (a) 6(13) and 6+13 (b) 5(1)and5+1 .Simplify: (a) 6(13) and 6+13 (b) 5(1) and -5+1.Simplify: 8(31)9 .Simplify: 12(96)14 .In the following exercises, order each of the following pairs of numbers, using . 185. (a) 9_____4 (b) 3_____6 (c)-8______2 (d) 1______10In the following exercises, order each of the following pairs of numbers, using < or >. 186. (a) 7____3 (b) 10___5 (c) 2___6 (d) 8__9In the following exercises, find the opposite of each number. 187. (a) 2 (b) 6In the following exercises, find the opposite of each number. 188. (a) 9 (b) 4In the following exercises, simplify. 189. (4) .In the following exercises, simplify. 190. (8)In the following exercises, simplify. 191. (15)In the following exercises, simplify. 192. (11)In the following exercises, evaluate. 193. c when M (a) c=12 (b) c=12In the following exercises, evaluate. 194. d when (a) d=21 (b) d=21In the following exercises, simplify. 195. (a) 32 (b) 0 (c) 16In the following exercises, simplify. 196. (a) 0 (b) 40 (c) 22In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 197. (a) 66 (b) 33In the following exercises, fill in <, >, or = for each of the following pairs of numbers. 198. (a) 55 (b) 99In the following exercises, simplify. 199. (5)and 5In the following exercises, simplify. 200. 9 and (9)In the following exercises, simplify. 201. 87In the following exercises, simplify. 202. 55In the following exercises, simplify. 203. 157146In the following exercises, simplify. 204. 178134In the following exercises, simplify. 205. 182(83)In the following exercises, simplify. 206. 183(85)In the following exercises, evaluate. 207. (a) p when p=19 (b) q when q=33In the following exercises, evaluate. 208. (a) a when a=60 (b) b when b=12In the following exercises, simplify each expression. 209. 2+(59)In the following exercises, simplify each expression. 210. 35+(47)