Solve 1 rac34 x ((4)/(9) + (1)/(3)) / (1(1)/(5) + 1(1)/(2)) using the rule of BODMAS.

You're on a roll — let's solve these problems using BODMAS and decimal knowledge. Problem 2.1.a: Solve 1(3)/(4) × ((4)/(9) + (1)/(3)) ÷ (1(1)/(5) + 1(1)/(2)) using the rule of BODMAS. Step 1: Convert all mixed numbers to improper fractions. 1(3)/(4) = (1 × 4 + 3)/(4) = (7)/(4) 1(1)/(5) = (1 × 5 + 1)/(5) = (6)/(5) 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) The expression becomes: (7)/(4) × ((4)/(9) + (1)/(3)) ÷ ((6)/(5) + (3)/(2)) Step 2: Solve the operations inside the first bracket (Addition). ((4)/(9) + (1)/(3)) = ((4)/(9) + (1 × 3)/(3 × 3)) = ((4)/(9) + (3)/(9)) = (4+3)/(9) = (7)/(9) Step 3: Solve the operations inside the second bracket (Addition). ((6)/(5) + (3)/(2)) The least common multiple of 5 and 2 is 10. ((6 × 2)/(5 × 2) + (3 × 5)/(2 × 5)) = ((12)/(10) + (15)/(10)) = (12+15)/(10) = (27)/(10) Step 4: Substitute the results back into the expression. (7)/(4) × (7)/(9) ÷ (27)/(10) Step 5: Perform multiplication and division from left to right. First, multiply. (7)/(4) × (7)/(9) = (7 × 7)/(4 × 9) = (49)/(36) The expression becomes: (49)/(36) ÷ (27)/(10) Step 6: Perform the division by multiplying by the reciprocal of the divisor. (49)/(36) × (10)/(27) Simplify before multiplying: 10 and 36 are both divisible by 2. (49)/(18 × 2) × (5 × 2)/(27) = (49 × 5)/(18 × 27) = (245)/(486) The final answer is: (245)/(486) Problem 2.1.b: Using your knowledge on decimals, solve this: (4.2 × 1.6 × 3.4)/(0.8 × 3.2 × 5.1) Step 1: Rewrite the expression by removing the decimal points. Since there are an equal number of decimal places in the numerator and denominator (one in each of the three numbers, totaling three decimal places for both), we can multiply the numerator and denominator by 10^3 = 1000 to clear the decimals. (42 × 16 × 34)/(8 × 32 × 51) Step 2: Simplify the expression by canceling common factors. (42 × 16 × 34)/(8 × 32 × 51) • Cancel 16 with 32: (16)/(32) = (1)/(2). The expression becomes: (42 × 1 × 34)/(8 × 2 × 51) • Cancel 34