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 fraction problems: 1) ((1)/(2) ÷ (1)/(3)) × (1)/(3) Step 1: Perform the division inside the parentheses. To divide by a fraction, multiply by its reciprocal. (1)/(2) ÷ (1)/(3) = (1)/(2) × (3)/(1) = (3)/(2) Step 2: Multiply the result by (1)/(3). (3)/(2) × (1)/(3) = (3)/(6) Step 3: Simplify the fraction. (3)/(6) = (1)/(2) The final answer is (1)/(2). 2) (1)/(2) + (2)/(3) × (1)/(4) Step 1: Perform the multiplication first. (2)/(3) × (1)/(4) = (2 × 1)/(3 × 4) = (2)/(12) Simplify the fraction: (2)/(12) = (1)/(6) Step 2: Perform the addition. Find a common denominator for (1)/(2) and (1)/(6), which is 6. (1)/(2) + (1)/(6) = (1 × 3)/(2 × 3) + (1)/(6) = (3)/(6) + (1)/(6) = (3+1)/(6) = (4)/(6) Step 3: Simplify the fraction. (4)/(6) = (2)/(3) The final answer is (2)/(3). 3) (1)/(4) - (2)/(3) + (5)/(6) Step 1: Find a common denominator for 4, 3, and 6, which is 12. Convert each fraction. (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) (5)/(6) = (5 × 2)/(6 × 2) = (10)/(12) Step 2: Perform the operations from left to right. (3)/(12) - (8)/(12) + (10)/(12) = (3-8)/(12) + (10)/(12) = (-5)/(12) + (10)/(12) = (-5+10)/(12) = (5)/(12) The final answer is (5)/(12). 4) (3)/(4) ÷ (1)/(2) × (1)/(6) Step 1: Perform the division first (from left to right). To divide by a fraction, multiply by its reciprocal. (3)/(4) ÷ (1)/(2) = (3)/(4) × (2)/(1) = (6)/(4) Simplify the fraction: (6)/(4) = (3)/(2) Step 2: Multiply the result by (1)/(6). (3)/(2) × (1)/(6) = (3)/(12) Step 3: Simplify the fraction. (3)/(12) = (1)/(4) The final answer is (1)/(4). 5) (2)/(3) of 2(1)/(4) ÷ (1)/(4) Step 1: Convert the mixed number to an improper fraction. 2(1)/(4) = ((2 × 4) + 1)/(4) = (9)/(4) Step 2: Replace "of" with multiplication and perform the multiplication. (2)/(3) × (9)/(4) = (18)/(12) Simplify the fraction: (18)/(12) = (3)/(2) Step 3: Perform the division. To divide by a fraction, multiply by its reciprocal. (3)/(2) ÷ (1)/(4) = (3)/(2) × (4)/(1) = (12)/(2) Step 4: Simplify the result. (12)/(2) = 6 The final answer is 6. 6) (2)/(3) - (5)/(6) + (1)/(2) Step 1: Find a common denominator for 3, 6, and 2, which is 6. Convert each fraction. (2)/(3) = (2 × 2)/(3 × 2) = (4)/(6) (1)/(2) = (1 × 3)/(2 × 3) = (3)/(6) Step 2: Perform the operations from left to right. (4)/(6) - (5)/(6) + (3)/(6) = (4-5)/(6) + (3)/(6) = (-1)/(6) + (3)/(6) = (-1+3)/(6) = (2)/(6) Step 3: Simplify the fraction. (2)/(6) = (1)/(3) The final answer is (1)/(3). 7) (1)/(2) ÷ (4)/(3) Step 1: To divide by a fraction, multiply by its reciprocal. (1)/(2) ÷ (4)/(3) = (1)/(2)