I see the image contains several math problems under Exercise 4.6. Let's work through them one by one.

1. If a car travels 283 ½ km in 4 ⅔ hours, how far does it go in 1 hour?

• The total distance is $283 \frac{1}{2}$ km and the time is $4 \frac{2}{3}$ hours.
• First, convert the mixed numbers to improper fractions:
  • $283 \frac{1}{2} = \frac{567}{2}$
  • $4 \frac{2}{3} = \frac{14}{3}$
• To find the distance per hour, divide the total distance by the time: $\text{Distance per hour} = \frac{\frac{567}{2}}{\frac{14}{3}} = \frac{567}{2} \times \frac{3}{14} = \frac{1701}{28} = 60.75 \text{ km}.$ So, the car travels 60.75 km per hour.

2. A boy exercises for a total of 5 ⅓ hours over 4 days. Find the number of hours he exercises each day.

• Convert the mixed number: $5 \frac{1}{3} = \frac{16}{3} \text{ hours}.$
• To find the time per day, divide by 4: $\text{Time per day} = \frac{\frac{16}{3}}{4} = \frac{16}{3} \times \frac{1}{4} = \frac{16}{12} = \frac{4}{3} = 1 \frac{1}{3} \text{ hours}.$ So, the boy exercises 1 ⅓ hours per day.

3. A set of 8 ribbons costs Rs 360 1/5. What is the cost of 1 ribbon?

• Convert the mixed number: $360 \frac{1}{5} = \frac{1801}{5}.$
• To find the cost of one ribbon, divide by 8: $\text{Cost per ribbon} = \frac{\frac{1801}{5}}{8} = \frac{1801}{40} = 45.025 \text{ Rs}.$ So, the cost of one ribbon is approximately Rs 45.03.

4. Two girls eat 10/11 of a pizza. What part of the pizza did each girl eat?

• If two girls eat $\frac{10}{11}$ of a pizza, the amount each girl eats is: $\text{Amount per girl} = \frac{\frac{10}{11}}{2} = \frac{10}{22} = \frac{5}{11}.$ Each girl ate 5/11 of the pizza.

5. A man walks 6 ⅓ km in 1 hour. How far will he walk in 3 ½ hours?

• Convert the mixed numbers:
  • $6 \frac{1}{3} = \frac{19}{3}$
  • $3 \frac{1}{2} = \frac{7}{2}$
• Multiply the distance per hour by the time: $\text{Total distance} = \frac{19}{3} \times \frac{7}{2} = \frac{133}{6} = 22 \frac{1}{6} \text{ km}.$ So, the man will walk 22 ⅙ km.

Would you like further clarification on any of these solutions?

Here are some related questions:

1. How do you simplify division involving mixed fractions?
2. What are some other real-world examples of dividing distances by time?
3. Can we express division of fractions in terms of multiplication of reciprocals?
4. How would changes in speed affect the answer to the first problem?
5. How would you convert the answers to decimal form?

Tip: When dividing fractions, it's often easier to multiply by the reciprocal (flip the second fraction).