Final answer:
To divide amounts in a given ratio, first sum the parts of the ratio, then divide the total amount by the sum to find the value of one part, and lastly multiply by each part of the ratio to find the respective amounts. 2 parts = 2 × 32 km = 64 km; 3 parts = 3 × 32 km = 96 km; 6 parts = 6 × 32 km = 192 km.
Step-by-step explanation:
Dividing Quantities in a Given Ratio
To divide 105 kg in the ratio of 3:4:
Add up the parts of the ratio: 3+4=7 parts in total. Then, divide the total weight by the number of parts: 105 kg ÷ 7 = 15 kg per part. Finally, multiply by the parts of the ratio: 3 parts = 3 × 15 kg = 45 kg; 4 parts = 4 × 15 kg = 60 kg.
To divide 360 minutes in the ratio of 4:5:
Similarly, add the parts of the ratio: 4+5=9. Divide the total minutes by the number of parts: 360 min ÷ 9 = 40 min per part. Multiply by the parts of the ratio: 4 parts = 4 × 40 min = 160 minutes; 5 parts = 5 × 40 min = 200 minutes.
To divide 352 km in the ratio of 2:3:6:
Add the parts of the ratio: 2+3+6=11. Divide the total distance by the number of parts: 352 km ÷ 11 = 32 km per part. Multiply by the parts of the ratio: 2 parts = 2 × 32 km = 64 km; 3 parts = 3 × 32 km = 96 km; 6 parts = 6 × 32 km = 192 km.