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 to the word problems: Problem 1: Alan jogged (5)/(8) kilometre. He jogged (1)/(4) kilometre more than Aiden. How far did Aiden jog? Step 1: Identify the operation needed. Since Alan jogged (1)/(4) km more than Aiden, Aiden jogged (1)/(4) km less than Alan. We need to subtract the difference from Alan's distance. Aiden's distance = (5)/(8) - (1)/(4) Step 2: Find a common denominator for the fractions. The least common multiple of 8 and 4 is 8. Convert (1)/(4) to an equivalent fraction with a denominator of 8. (1)/(4) = (1 × 2)/(4 × 2) = (2)/(8) Step 3: Perform the subtraction. (5)/(8) - (2)/(8) = (5-2)/(8) = (3)/(8) Aiden jogged (3)/(8) kilometre. The distance Aiden jogged is (3)/(8) km. Problem 2: Mrs Davies prepared (4)/(5) litre of apple juice. The next day, there were (3)/(10) litre of apple juice left. How many litres of apple juice were drunk? Step 1: Identify the operation needed. To find out how much juice was drunk, we subtract the amount left from the initial amount. Amount drunk = (4)/(5) - (3)/(10) Step 2: Find a common denominator for the fractions. The least common multiple of 5 and 10 is 10. Convert (4)/(5) to an equivalent fraction with a denominator of 10. (4)/(5) = (4 × 2)/(5 × 2) = (8)/(10) Step 3: Perform the subtraction. (8)/(10) - (3)/(10) = (8-3)/(10) = (5)/(10) Step 4: Simplify the fraction. (5)/(10) = (1)/(2) Mrs Davies' family drank (1)/(2) litre of apple juice. The amount of apple juice drunk is (1)/(2) litre. Problem 3: Jessica took (5)/(6) hour to complete her homework. She took another (3)/(4) hour to revise for her test. How many hours did Jessica put in to complete her homework and revise for her test? Step 1: Identify the operation needed. To find the total time Jessica spent, we need to add the time for homework and the time for revision. Total time = (5)/(6) + (3)/(4) Step 2: Find a common denominator for the fractions. The least common multiple of 6 and 4 is 12. Convert both fractions to equivalent fractions with a denominator of 12. (5)/(6) = (5 × 2)/(6 × 2) = (10)/(12) (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) Step 3: Perform the addition. (10)/(12) + (9)/(12) = (10+9)/(12) = (19)/(12) Jessica put in (19)/(12) hours. The total hours Jessica put in is (19)/(12) hours. What's next? Send 'em! 📸