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 given problems: i) Step 1: To divide fractions, multiply the first fraction by the reciprocal of the second fraction. (5)/(6) ÷ (7)/(12) = (5)/(6) × (12)/(7) Step 2: Multiply the numerators and the denominators. Simplify common factors before multiplying. (5)/(6)_1 × 12^27 = (5 × 2)/(1 × 7) Step 3: Calculate the product. (10)/(7) The final answer is (10)/(7). iv) Step 1: Write the integer as a fraction and then multiply by its reciprocal. (16)/(15) ÷ (-18) = (16)/(15) ÷ (-18)/(1) Step 2: Multiply the first fraction by the reciprocal of the second fraction. (16)/(15) × (1)/(-18) Step 3: Multiply the numerators and the denominators. Simplify common factors (16 and 18 are both divisible by 2). 16^815 × (1)/(-18)_9 = (8 × 1)/(15 × (-9)) Step 4: Calculate the product. (8)/(-135) = -(8)/(135) The final answer is -(8)/(135). vii) Step 1: Write the integer as a fraction and then multiply by its reciprocal. -12 ÷ ((-5)/(6)) = (-12)/(1) ÷ (-5)/(6) Step 2: Multiply the first fraction by the reciprocal of the second fraction. (-12)/(1) × (6)/(-5) Step 3: Multiply the numerators and the denominators. (-12 × 6)/(1 × (-5)) Step 4: Calculate the product. (-72)/(-5) = (72)/(5) The final answer is (72)/(5).