Evaluate: (a) 2.4 (0.123 - 0.095) 0.009 / (0.015 * (0.042 + 0.030)); (b) Simplify: 1 3/4 + [5 - 2 3/4 / 3/5] - [ (3-1)/5 of 4 1/2 ]

a) Evaluate: (2.4 × (0.123 - 0.095) × 0.009)/(0.015 × (0.042 + 0.030)) Step 1: Simplify the expressions inside the parentheses. 0.123 - 0.095 = 0.028 0.042 + 0.030 = 0.072 Step 2: Substitute these values back into the expression. (2.4 × 0.028 × 0.009)/(0.015 × 0.072) Step 3: Calculate the numerator. 2.4 × 0.028 = 0.0672 0.0672 × 0.009 = 0.0006048 Step 4: Calculate the denominator. 0.015 × 0.072 = 0.00108 Step 5: Divide the numerator by the denominator. (0.0006048)/(0.00108) = 0.56 The evaluated value is 0.56. b) Simplify: 1(3)/(4) + [5 - 2(3)/(4) ÷ (3)/(5)] - [(3-1)/(5) of 4(1)/(2)] Step 1: Convert all mixed numbers to improper fractions and simplify the first bracket in the third term. 1(3)/(4) = (1 × 4 + 3)/(4) = (7)/(4) 2(3)/(4) = (2 × 4 + 3)/(4) = (11)/(4) 4(1)/(2) = (4 × 2 + 1)/(2) = (9)/(2) (3-1)/(5) = (2)/(5) The expression becomes: (7)/(4) + [5 - (11)/(4) ÷ (3)/(5)] - [(2)/(5) of (9)/(2)] Step 2: Perform the division inside the first square bracket. (11)/(4) ÷ (3)/(5) = (11)/(4) × (5)/(3) = (55)/(12) The expression becomes: (7)/(4) + [5 - (55)/(12)] - [(2)/(5) of (9)/(2)] Step 3: Perform the subtraction inside the first square bracket. 5 - (55)/(12) = (5 × 12)/(12) - (55)/(12) = (60)/(12) - (55)/(12) = (5)/(12) The expression becomes: (7)/(4) + (5)/(12) - [(2)/(5) of (9)/(2)] Step 4: Perform the "of" (multiplication) operation inside the second square bracket. (2)/(5) of (9)/(2) = (2)/(5) × (9)/(2) = (18)/(10) = (9)/(5) The expression becomes: (7)/(4) + (5)/(12) - (9)/(5) Step 5: Find a common denominator for 4, 12, and 5, which is 60. Convert the fractions. (7)/(4) = (7 × 15)/(4 × 15) = (105)/(60) (5)/(12) = (5 × 5)/(12 × 5) = (25)/(60) (9)/(5) = (9 × 12)/(5 × 12) = (108)/(60) The expression becomes: (105)/(60) + (25)/(60) - (108)/(60) Step 6: Perform the addition and subtraction from left to right. (105 + 25 - 108)/(60) = (130 - 108)/(60) = (22)/(60) Step 7: Simplify the fraction. (22)/(60) = (11)/(30) The simplified value is (11)/(30). Send me the next one 📸