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
Okay, let's continue with these problems. 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 by canceling common factors (10 and 36 are 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 without changing the value of the fraction. (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 with 51. Both are divisible by 17: 34 = 17 × 2 and 51 = 17 × 3. So, (34)/(51) = (2)/(3). The expression becomes: (42 × 1 × 2)/(8 × 2 × 3) • Cancel 2 from the numerator and denominator: (42 × 1)/(8 × 3) • Cancel 42 with 3: (42)/(3) = 14. The expression becomes: (14)/(8) • Simplify (14)/(8) by dividing both numerator and denominator by 2: (14 ÷ 2)/(8 ÷ 2) = (7)/(4) Step 3: Convert the fraction to a decimal (optional, but often expected with decimal problems). (7)/(4) = 1.75 The final answer is: (7)/(4) or 1.75 Problem 3.a: In a class of 70 pupils, (1)/(2) of them speak English, (2)/(5) speak... a. What is the percentage of pupils who speak both English... This question is incomplete. The information about what the (2)/(5) of pupils speak is cut off, and the full question for part 'a' is also cut off. Please provide the complete question for me to solve it. Last free one today — make it count tomorrow, or type /upgrade for unlimited.