This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
5. Find the absolute value in each of the following expressions. a) (3)/(8) - (1)/(16) + (5)/(4) Step 1: Find a common denominator, which is 16. Convert the fractions. (3)/(8) = (3 × 2)/(8 × 2) = (6)/(16) (5)/(4) = (5 × 4)/(4 × 4) = (20)/(16) Step 2: Perform the operations. (6)/(16) - (1)/(16) + (20)/(16) = (6 - 1 + 20)/(16) = (25)/(16) Step 3: Find the absolute value. |(25)/(16)| = (25)/(16) (25)/(16) b) 1(1)/(3) + 2(3)/(4) + 3(1)/(5) Step 1: Convert mixed numbers to improper fractions. 1(1)/(3) = (4)/(3) 2(3)/(4) = (11)/(4) 3(1)/(5) = (16)/(5) Step 2: Find a common denominator for 3, 4, 5, which is 60. Convert the fractions. (4)/(3) = (4 × 20)/(3 × 20) = (80)/(60) (11)/(4) = (11 × 15)/(4 × 15) = (165)/(60) (16)/(5) = (16 × 12)/(5 × 12) = (192)/(60) Step 3: Perform the addition. (80)/(60) + (165)/(60) + (192)/(60) = (80 + 165 + 192)/(60) = (437)/(60) Step 4: Find the absolute value. |(437)/(60)| = (437)/(60) (437)/(60) c) -1(1)/(2) + (1)/(10) - 3(2)/(7) Step 1: Convert mixed numbers to improper fractions. -1(1)/(2) = -(3)/(2) -3(2)/(7) = -(23)/(7) Step 2: Find a common denominator for 2, 10, 7, which is 70. Convert the fractions. -(3)/(2) = -(3 × 35)/(2 × 35) = -(105)/(70) (1)/(10) = (1 × 7)/(10 × 7) = (7)/(70) -(23)/(7) = -(23 × 10)/(7 × 10) = -(230)/(70) Step 3: Perform the operations. -(105)/(70) + (7)/(70) - (230)/(70) = (-105 + 7 - 230)/(70) = (-98 - 230)/(70) = (-328)/(70) Step 4: Simplify the fraction. (-328)/(70) = (-328 ÷ 2)/(70 ÷ 2) = -(164)/(35) Step 5: Find the absolute value. |-(164)/(35)| = (164)/(35) (164)/(35) d) 62.15 - 28.705 + 45.67 Step 1: Perform the subtraction. 62.15 - 28.705 = 33.445 Step 2: Perform the addition. 33.445 + 45.67 = 79.115 Step 3: Find the absolute value. |79.115| = 79.115 79.115 e) 2(1)/(3) + 4(1)/(5) + (1)/(10) Step 1: Convert mixed numbers to improper fractions. 2(1)/(3) = (7)/(3) 4(1)/(5) = (21)/(5) Step 2: Find a common denominator for 3, 5, 10, which is 30. Convert the fractions. (7)/(3) = (7 × 10)/(3 × 10) = (70)/(30) (21)/(5) = (21 × 6)/(5 × 6) = (126)/(30) (1)/(10) = (1 × 3)/(10 × 3) = (3)/(30) Step 3: Perform the addition. (70)/(30) + (126)/(30) + (3)/(30) = (70 + 126 + 3)/(30) = (199)/(30) Step 4: Find the absolute value. |(199)/(30)| = (199)/(30) (199)/(30) f) (7(1)/(2) + 3(1)/(4)) - (2(3)/(8) + 4(1)/(4)) Step 1: Convert mixed numbers to improper fractions. 7(1)/(2) = (15)/(2) 3(1)/(4) = (13)/(4) 2(3)/(8) = (19)/(8) 4(1)/(4) = (17)/(4) Step 2: Calculate the sum in the first parenthesis. (15)/(2) + (13)/(4) = (15 × 2)/(2 × 2) + (13)/(4) = (30)/(4) + (13)/(4) = (43)/(4) Step 3: Calculate the sum in the second parenthesis. (19)/(8) + (17)/(4) = (19)/(8) + (17 × 2)/(4 × 2) = (19)/(8) + (34)/(8) = (53)/(8) Step 4: Perform the subtraction. (43)/(4) - (53)/(8) = (43 × 2)/(4 × 2) - (53)/(8) = (86)/(8) - (53)/(8) = (86 - 53)/(8) = (33)/(8) Step 5: Find the absolute value. |(33)/(8)| = (33)/(8) (33)/(8) Last free one today — make it count tomorrow, or type /upgrade for unlimited.