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 Sharmadee, good to see you again. Here are the solutions for adding the mixed numbers: a) 3(7)/(8) + 5(3)/(4) Step 1: Add the whole numbers. 3 + 5 = 8 Step 2: Find a common denominator for the fractions (7)/(8) and (3)/(4). The least common denominator is 8. (3)/(4) = (3 × 2)/(4 × 2) = (6)/(8) So, the expression becomes: 8(7)/(8) + 68 Step 3: Add the fractions. (7)/(8) + (6)/(8) = (7+6)/(8) = (13)/(8) Step 4: Convert the improper fraction to a mixed number. (13)/(8) = 1(5)/(8) Step 5: Add this to the whole number from Step 1. 8 + 1(5)/(8) = 9(5)/(8) The final answer is 9(5)/(8). b) 2(2)/(5) + 3(7)/(10) Step 1: Add the whole numbers. 2 + 3 = 5 Step 2: Find a common denominator for the fractions (2)/(5) and (7)/(10). The least common denominator is 10. (2)/(5) = (2 × 2)/(5 × 2) = (4)/(10) So, the expression becomes: 5410 + (7)/(10) Step 3: Add the fractions. (4)/(10) + (7)/(10) = (4+7)/(10) = (11)/(10) Step 4: Convert the improper fraction to a mixed number. (11)/(10) = 1(1)/(10) Step 5: Add this to the whole number from Step 1. 5 + 1(1)/(10) = 6(1)/(10) The final answer is 6(1)/(10). c) 7(3)/(10) + 8(1)/(6) Step 1: Add the whole numbers. 7 + 8 = 15 Step 2: Find a common denominator for the fractions (3)/(10) and (1)/(6). The least common multiple of 10 and 6 is 30. (3)/(10) = (3 × 3)/(10 × 3) = (9)/(30) (1)/(6) = (1 × 5)/(6 × 5) = (5)/(30) Step 3: Add the fractions. (9)/(30) + (5)/(30) = (9+5)/(30) = (14)/(30) Step 4: Simplify the fraction. (14)/(30) = (14 ÷ 2)/(30 ÷ 2) = (7)/(15) Step 5: Combine the whole number and the simplified fraction. 15 + (7)/(15) = 15(7)/(15) The final answer is 15(7)/(15). d) 6(4)/(5) + (5)/(6) Step 1: The whole number is 6. Step 2: Find a common denominator for the fractions (4)/(5) and (5)/(6). The least common multiple of 5 and 6 is 30. (4)/(5) = (4 × 6)/(5 × 6) = (24)/(30) (5)/(6) = (5 × 5)/(6 × 5) = (25)/(30) Step 3: Add the fractions. (24)/(30) + (25)/(30) = (24+25)/(30) = (49)/(30) Step 4: Convert the improper fraction to a mixed number. (49)/(30) = 1(19)/(30) Step 5: Add this to the whole number from Step 1. 6 + 1(19)/(30) = 7(19)/(30) The final answer is 7(19)/(30). e) (3)/(4) + 4(1)/(6) Step 1: The whole number is 4. Step 2: Find a common denominator for the fractions (3)/(4) and (1)/(6). The least common multiple of 4 and 6 is 12. (3)/(4) = 3 × 3