Which is greater: a) 2/7 of 3/4 or 3/5 of 5/8? b) 1/2 of 6/7 or 2/3 of 3/7?

Here are the solutions to the problems. 4. Which is greater: a) (2)/(7) of (3)/(4) or (3)/(5) of (5)/(8) Step 1: Calculate the first product. (2)/(7) of (3)/(4) = (2)/(7) × (3)/(4) = (2 × 3)/(7 × 4) = (6)/(28) = (3)/(14) Step 2: Calculate the second product. (3)/(5) of (5)/(8) = (3)/(5) × (5)/(8) = (3 × 5)/(5 × 8) = (15)/(40) = (3)/(8) Step 3: Compare the two fractions (3)/(14) and (3)/(8). To compare, find a common denominator, which is 56. (3)/(14) = (3 × 4)/(14 × 4) = (12)/(56) (3)/(8) = (3 × 7)/(8 × 7) = (21)/(56) Since (21)/(56) > (12)/(56), then (3)/(8) is greater. Therefore, (3)/(5) of (5)/(8) is greater. (3)/(5) of (5)/(8) b) (1)/(2) of (6)/(7) or (2)/(3) of (3)/(7) Step 1: Calculate the first product. (1)/(2) of (6)/(7) = (1)/(2) × (6)/(7) = (1 × 6)/(2 × 7) = (6)/(14) = (3)/(7) Step 2: Calculate the second product. (2)/(3) of (3)/(7) = (2)/(3) × (3)/(7) = (2 × 3)/(3 × 7) = (6)/(21) = (2)/(7) Step 3: Compare the two fractions (3)/(7) and (2)/(7). Since the denominators are the same, compare the numerators. 3 > 2. Therefore, (3)/(7) is greater. (1)/(2) of (6)/(7) 5. Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is (3)/(4) m. Find the distance between the first and the last sapling. Step 1: Determine the number of gaps between the saplings. For 4 saplings planted in a row, there are 4 - 1 = 3 gaps. Step 2: Calculate the total distance. The distance between the first and the last sapling is the number of gaps multiplied by the distance between adjacent saplings. Total distance = 3 × (3)/(4) m Step 3: Perform the multiplication. 3 × (3)/(4) = (3 × 3)/(4) = (9)/(4) m Step 4: Convert the improper fraction to a mixed number. (9)/(4) = 2(1)/(4) m The distance between the first and the last sapling is 2(1)/(4) m. 6. Lipika reads a book for 1(3)/(4) hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book? Step 1: Convert the daily reading time from a mixed number to an improper fraction. 1(3)/(4) hours = ((1 × 4) + 3)/(4) hours = (4 + 3)/(4) hours = (7)/(4) hours Step 2: Calculate the total hours required to read the book. Total hours = (Hours read per day) × (Number of days) Total hours = (7)/(4) × 6 Step 3: Perform the multiplication. Total hours = (7 × 6)/(4) = (42)/(4) hours Step 4: Simplify the fraction and convert to a mixed number. (42)/(4) = (21)/(2) hours = 10(1)/(2) hours Lipika required 10(1)/(2) hours to read the book. 7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2(3)/(4) litres of petrol. Step 1: Convert the amount of petrol from a mixed number to an improper fraction. 2(3)/(4) litres = ((2 × 4) + 3)/(4) litres = (8 + 3)/(4) litres = (11)/(4) litres Step 2: Calculate the total distance covered. Distance covered = (Distance per litre) × (Total litres of petrol) Distance covered = 16 km/litre × (11)/(4) litres Step 3: Perform the multiplication. Distance covered = (16 × 11)/(4) km Step 4: Simplify the expression. Distance covered = 4 × 11 km = 44 km The car will cover 44 km. What's next?