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
Hey Shanti, good to see you again. Here are the solutions to the problems: 1. (2)/(3) + (1)/(6) Step 1: Find a common denominator for the fractions. The least common multiple of 3 and 6 is 6. Step 2: Convert (2)/(3) to an equivalent fraction with a denominator of 6. (2)/(3) = (2 × 2)/(3 × 2) = (4)/(6) Step 3: Add the fractions. (4)/(6) + (1)/(6) = (4+1)/(6) = (5)/(6) The sum is (5)/(6). 2. 2(1)/(3) + 1(2)/(3) Step 1: Add the whole number parts. 2 + 1 = 3 Step 2: Add the fractional parts. (1)/(3) + (2)/(3) = (1+2)/(3) = (3)/(3) = 1 Step 3: Combine the sum of the whole numbers and the sum of the fractions. 3 + 1 = 4 The sum is 4. 3. 3(1)/(2) + 2(1)/(4) Step 1: Add the whole number parts. 3 + 2 = 5 Step 2: Find a common denominator for the fractional parts. The least common multiple of 2 and 4 is 4. Step 3: Convert (1)/(2) to an equivalent fraction with a denominator of 4. (1)/(2) = (1 × 2)/(2 × 2) = (2)/(4) Step 4: Add the fractional parts. (2)/(4) + (1)/(4) = (2+1)/(4) = (3)/(4) Step 5: Combine the sum of the whole numbers and the sum of the fractions. 5 + (3)/(4) = 5(3)/(4) The sum is 5(3)/(4). 4. 6(2)/(5) = 1(3)/(5) Step 1: Convert both mixed numbers to improper fractions to compare them. 6(2)/(5) = ((6 × 5) + 2)/(5) = (30 + 2)/(5) = (32)/(5) 1(3)/(5) = ((1 × 5) + 3)/(5) = (5 + 3)/(5) = (8)/(5) Step 2: Compare the improper fractions. (32)/(5) and (8)/(5) Since 32 ≠ 8, then (32)/(5) ≠ (8)/(5). Step 3: Conclude whether the statement is true or false. The statement 6(2)/(5) = 1(3)/(5) is False. Send me the next one 📸