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.
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7. Step 1: Determine the total number of slices. The pizza was divided into 8 equal slices. Total slices = 8. Step 2: Determine the number of slices the 3 friends had. Each of the 3 friends had 2 slices. Slices had by 3 friends = 3 × 2 = 6. Step 3: Form the ratio. The ratio of the number of slices the 3 friends had to the total number of slices is: Ratio = Slices had by 3 friendsTotal slices = (6)/(8) Step 4: Simplify the ratio. Divide both the numerator and the denominator by their greatest common divisor, which is 2. (6 ÷ 2)/(8 ÷ 2) = (3)/(4) The ratio is 3:4. The correct option is C. C. 3:4 8. Step 1: Understand the map scale. The scale is 1 cm on the map represents 500 m in actual distance. 1 cm (map) = 500 m (actual) Step 2: Calculate the actual distance for 6 cm on the map. Map distance = 6 cm. Actual distance = 6 cm × 500 m1 cm = 3000 m. Step 3: Convert the actual distance to kilometers. Since 1 km = 1000 m, divide the distance in meters by 1000. Actual distance in km = 3000 m1000 m/km = 3 km The correct option is C. C. 3km 9. Step 1: Identify the departure and arrival times. Departure time = 2:30 PM. Arrival time = 5:45 PM. Step 2: Calculate the duration in hours and minutes. From 2:30 PM to 5:45 PM: • From 2:30 PM to 3:00 PM is 30 minutes. • From 3:00 PM to 5:00 PM is 2 hours. • From 5:00 PM to 5:45 PM is 45 minutes. Total duration = 2 hours + 30 minutes + 45 minutes = 2 hours and 75 minutes. Since 75 minutes is 1 hour and 15 minutes, the total duration is 2 hours + 1 hour and 15 minutes = 3 hours and 15 minutes. Step 3: Convert the total duration to minutes. 3 hours × 60 minutes/hour + 15 minutes = 180 minutes + 15 minutes = 195 minutes The correct option is D. D. 195 10. Step 1: Identify the departure and arrival times. Departure time = 10:00 AM. Arrival time = 6:45 PM. Step 2: Calculate the duration in hours and minutes. • From 10:00 AM to 12:00 PM (noon) is 2 hours. • From 12:00 PM to 6:00 PM is 6 hours. • From 6:00 PM to 6:45 PM is 45 minutes. Total duration = 2 hours + 6 hours + 45 minutes = 8 hours and 45 minutes. The correct option is A. A. 8 hours and 45 minutes