5.3 The Rational Numbers 247 Alternative methods for adding and subtracting two fractions are shown below. These methods may not result in a solution in its lowest terms. + = + − = − a b c d ad bc bd a b c d ad bc bd and In Exercises 77–80, use the appropriate formula above to evaluate the expression. 77. + 2 7 1 2 11 14 78. + 4 7 2 5 34 35 79. − 5 6 7 8 − 1 24 80. − 7 3 5 12 23 12 In Exercises 81–90, evaluate each expression using the order of operations. 81. + ⋅ 1 3 1 4 2 5 13 30 82. + ÷ 4 9 5 6 2 3 61 36 83. − ÷ 7 8 3 4 5 6 − 1 40 84. − ⋅ 13 15 9 10 5 6 7 60 85. ÷ ⋅ 7 8 3 4 3 16 7 32 86. − ÷ ⋅ 8 15 2 3 7 9 − 28 45 87. ⋅ + ⋅ 1 3 3 7 3 5 10 11 53 77 88. ⋅ + ⋅ 3 5 10 21 6 11 33 32 95 112 89. ⎛ + ⎝⎜ ⎞ ⎠⎟ ÷ ⎛ − ⎝⎜ ⎞ ⎠⎟ 3 4 1 6 2 7 6 11 10 90. ⎛ − ⎝⎜ ⎞ ⎠⎟ ÷ ⎛ + ⎝⎜ ⎞ ⎠⎟ 3 4 9 4 2 3 23 42 Problem Solving In Exercises 91–100, (a) write an expression that will solve the problem and (b) evaluate the expression. 91. Thistles Rachel has four different varieties of thistles invading her pasture. She estimates that of these thistles, 1 2 are Canada thistles, 1 4 are bull thistles, 1 6 are plumeless thistles, and the rest are musk thistles. What fraction of the thistles are musk thistles? a) − ⎛ + + ⎝⎜ ⎞ ⎠⎟ 1 1 2 1 4 1 6 b) 1 12 92. Running Duy started a running program in January. At that time, he could run a mile in 10 minutes. 1 5 By July, Duy could run a mile in 7 minutes. 3 5 Determine the difference in Duy’s times from January to July. a) − 10 1 5 7 3 5 b) 2 3 5 minutes 93. Stairway Height A stairway consists of 14 stairs, each 85 8 inches high. What is the vertical height of the stairway? a) × 14 8 5 8 b) 120 3 4 in. 94. Alphabet Soup Margaret’s recipe for alphabet soup calls for (among other items) 1 4 cup snipped parsley, 1 8 teaspoon pepper, and 1 2 cup sliced carrots. Margaret is expecting company and needs to multiply the amounts of the ingredients by 11 2 times. Determine the amount of (a) snipped parsley, (b) pepper, and (c) sliced carrots she needs for the soup. a) 1 1 2 1 4 , 1 1 2 1 8 , 1 1 2 1 2 × × × b) snipped parsley: 3 8 cup, pepper: 3 16 tsp, sliced carrots: 3 4 cup 95. Height Increase When David finished his first year of high school, his height was 69 inches. 7 8 When he returned to school after the summer, David’s height was 71 inches. 5 8 How much did David’s height increase over the summer? a) − 71 5 8 69 7 8 b) 1 3 4 in 96. Crop Storage Todd has a silo on his farm in which he stores silage made from various crops. His silo is currently 1 4 full of corn silage, 2 5 full of hay silage, and 1 3 full of oats silage. What fraction of Todd’s silo is currently in use? a) 1 4 2 5 1 3 + + b) 59 60 97. Department Budget Jaime is chair of the humanities department at Santa Fe College. Jaime has a budget in which 1 2 of the money is for photocopying, 2 5 of the money is for computer-related expenses, and the rest of the money is for student tutors in the languages lab. What fraction of Jaime’s budget is for student tutors? a) − ⎛ + ⎝⎜ ⎞ ⎠⎟ 1 1 2 2 5 b) 1 10 98. Art Supplies Denise teaches kindergarten and is buying supplies for her class to make papier-mâché piggy banks. Each piggy bank to be made requires 11 4 cups of flour. If Denise has 15 students who are going to make piggy banks, how much flour does Denise need to purchase? a) × 15 1 1 4 b) 18 3 4 cups 99. Height of a Computer Stand The instructions for assembling a computer stand include a diagram illustrating its dimensions. Determine the total height of the stand. a) + + 4 1 2 30 1 4 24 1 8 b) 58 7 8 in. 30 1 4 " 4 1 2 " 24 1 8 " Hurst Photo/Shutterstock
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