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 word problems: 1. Michael took 1(1)/(4) hours to do his homework. Henry took (1)/(2) hour more than Michael to do his homework. How long did Henry take to do his homework? Step 1: Identify the given times. Michael's time: 1(1)/(4) hours Henry's additional time: (1)/(2) hour Step 2: Add Michael's time and Henry's additional time to find Henry's total time. 1(1)/(4) + (1)/(2) Step 3: Find a common denominator for the fractions. The least common denominator for 4 and 2 is 4. (1)/(2) = (1 × 2)/(2 × 2) = (2)/(4) Step 4: Add the fractions and the whole number. 1(1)/(4) + (2)/(4) = 1(1+2)/(4) = 1(3)/(4) Henry took 1(3)/(4) hours to do his homework. 2. Alan wanted to complete his project in 2 hours. He completed his project in 3(1)/(10) hours instead. How much more time did he take to complete his project? Step 1: Identify the planned and actual times. Planned time: 2 hours Actual time: 3(1)/(10) hours Step 2: Subtract the planned time from the actual time to find the difference. 3(1)/(10) - 2 Step 3: Subtract the whole numbers. 3 - 2 = 1 Step 4: Combine the result with the fraction. 1 + (1)/(10) = 1(1)/(10) Alan took 1(1)/(10) hours more time to complete his project. 3. Mrs Davies bought 6(2)/(5) kilograms of flour and 2(5)/(8) kilograms of sugar. What was the total mass of the flour and sugar she bought? Step 1: Identify the masses of flour and sugar. Flour: 6(2)/(5) kg Sugar: 2(5)/(8) kg Step 2: Add the masses to find the total mass. 6(2)/(5) + 2(5)/(8) Step 3: Add the whole numbers. 6 + 2 = 8 Step 4: Find a common denominator for the fractions (2)/(5) and (5)/(8). The least common multiple of 5 and 8 is 40. (2)/(5) = (2 × 8)/(5 × 8) = (16)/(40) (5)/(8) = (5 × 5)/(8 × 5) = (25)/(40) Step 5: Add the fractions. (16)/(40) + (25)/(40) = (16+25)/(40) = (41)/(40) Step 6: Convert the improper fraction to a mixed number. (41)/(40) = 1(1)/(40) Step 7: Add this mixed number to the sum of the whole numbers from Step 3. 8 + 1(1)/(40) = 9(1)/(40) The total mass of the flour and sugar she bought was 9(1)/(40) kg. 3 done, 2 left today. You're making progress.