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
Here are the solutions to the problems: 1a) i) Step 1: Convert mixed numbers to improper fractions. 2(1)/(2) = (5)/(2) 1(1)/(3) = (4)/(3) 1(2)/(3) = (5)/(3) The expression becomes: ((5)/(2) + (4)/(3)) ÷ ((5)/(3) - (1)/(2)) Step 2: Perform the addition inside the first parenthesis. (5)/(2) + (4)/(3) = (5 × 3)/(2 × 3) + (4 × 2)/(3 × 2) = (15)/(6) + (8)/(6) = (15+8)/(6) = (23)/(6) Step 3: Perform the subtraction inside the second parenthesis. (5)/(3) - (1)/(2) = (5 × 2)/(3 × 2) - (1 × 3)/(2 × 3) = (10)/(6) - (3)/(6) = (10-3)/(6) = (7)/(6) Step 4: Perform the division. (23)/(6) ÷ (7)/(6) = (23)/(6) × (6)/(7) = (23)/(7) The simplified value is (23)/(7). 1a) ii) Step 1: Rewrite the decimals as fractions or powers of 10. 0.25 = 25 × 10^-2 0.35 = 35 × 10^-2 0.14 = 14 × 10^-2 0.05 = 5 × 10^-2 Step 2: Substitute these into the expression. (0.25 × 0.35)/(0.14 × 0.05) = (25 × 10^-2) × (35 × 10^-2)(14 × 10^-2) × (5 × 10^-2) Step 3: Simplify by cancelling common factors. = 25 × 35 × 10^-414 × 5 × 10^-4 = (25 × 35)/(14 × 5) = ((5 × 5) × (5 × 7))/((2 × 7) × 5) = (5 × 5 × 5 × 7)/(2 × 7 × 5) Cancel one 5 and one 7 from numerator and denominator: = (5 × 5)/(2) = (25)/(2) The evaluated value is (25)/(2) or 12.5. 1b) Step 1: Define the shares using a variable. Let Akon's share be x. Step 2: Express Atango's share in terms of x. Atango takes two more than Akon, so Atango's share is x + 2. Step 3: Express Abomo's share in terms of x. Abomo takes twice as much as Atango, so Abomo's share is 2 × (x+2). Step 4: Express their shares as a ratio. Akon : Atango : Abomo = x : (x+2) : 2(x+2) The ratio of their shares is x : (x+2) : 2(x+2). 2a) Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. The prime numbers between 4 and 15 are 5, 7, 11, 13. The set is \5, 7, 11, 13\. 2b) Square numbers are the result of multiplying an integer by itself. 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 (which is not less than 20) The square numbers less than 20 are 1, 4, 9, 16. The set is \1, 4, 9, 16\. 2c) Multiples of 3 are numbers that can be divided by 3 without a remainder. The multiples of 3 between 11 and 22 are 12, 15, 18, 21. The set is \12, 15, 18, 21\. 2d) Even numbers are integers that are divisible by 2. The even numbers between 10 and 22 (exclusive of 10 and 22) are 12, 14, 16, 18, 20. The set is $\12,