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Exercise 4.4

1. I can walk $5 \frac{1}{8}$ km in an hour. What distance will I cover in $3 \frac{1}{8}$ hours?

• Convert the mixed fractions into improper fractions: $5 \frac{1}{8} = \frac{41}{8}, \quad 3 \frac{1}{8} = \frac{25}{8}$
• Multiply the two fractions: $\text{Distance} = \frac{41}{8} \times \frac{25}{8} = \frac{41 \times 25}{8 \times 8} = \frac{1025}{64} = 16 \frac{1}{64} \text{ km}$

2. The cost of one chocolate bar is Rs $9 \frac{2}{7}$. What is the cost of 9 such chocolate bars?

• Convert the mixed fraction into an improper fraction: $9 \frac{2}{7} = \frac{65}{7}$
• Multiply the cost by 9: $\text{Cost of 9 bars} = 9 \times \frac{65}{7} = \frac{585}{7} = 83 \frac{4}{7} \text{ Rs}$

3. One kg of apples costs Rs $68 \frac{1}{3}$. What is the cost of $2 \frac{1}{4}$ kg of apples?

• Convert the mixed fractions into improper fractions: $68 \frac{1}{3} = \frac{205}{3}, \quad 2 \frac{1}{4} = \frac{9}{4}$
• Multiply the two fractions: $\text{Cost} = \frac{205}{3} \times \frac{9}{4} = \frac{205 \times 9}{12} = \frac{1845}{12} = 153 \frac{9}{12} = 153 \frac{3}{4} \text{ Rs}$

4. One litre of petrol costs Rs $76 \frac{8}{9}$. What is the cost of 33 litres of petrol?

• Convert the mixed fraction into an improper fraction: $76 \frac{8}{9} = \frac{692}{9}$
• Multiply by 33: $\text{Cost of petrol} = 33 \times \frac{692}{9} = \frac{22836}{9} = 2537 \frac{3}{9} = 2537 \frac{1}{3} \text{ Rs}$

5. A bag contains $52 \frac{4}{5}$ kg of sugar. How much sugar do 8 such bags contain?

• Convert the mixed fraction into an improper fraction: $52 \frac{4}{5} = \frac{264}{5}$
• Multiply by 8: $\text{Sugar in 8 bags} = 8 \times \frac{264}{5} = \frac{2112}{5} = 422 \frac{2}{5} \text{ kg}$

Would you like more details or further clarification on any of these steps?

Here are 5 related questions to further your understanding:

1. How can you simplify the multiplication of improper fractions?
2. What is the method to convert mixed fractions into improper fractions?
3. How would you solve if the fractions involved had larger numerators or denominators?
4. What is the practical use of multiplication of fractions in real-life scenarios like shopping?
5. How can you estimate answers quickly before multiplying fractions?

Tip: Always convert mixed fractions to improper fractions first when performing operations like multiplication or division.