Here are the solutions to the problems: 1. Bari bought $2\frac{1}{2}$ kg of tomatoes and he also bought onions that were 3 times the weight of tomatoes. Find the weight of onions. Step 1: Convert the weight of tomatoes from a mixed fraction to an improper fraction. $$2\frac{1}{2} \text{ kg} = \frac{(2 \times 2) + 1}{2} \text{ kg} = \frac{5}{2} \text{ kg}$$ Step 2: Calculate the weight of onions, which is 3 times the weight of tomatoes. $$\text{Weight of onions} = 3 \times \frac{5}{2} \text{ kg} = \frac{15}{2} \text{ kg}$$ $$\text{Weight of onions} = 7.5 \text{ kg}$$ The weight of onions is $\boxed{\text{7.5 kg}}$. 2. Harish had 30 pieces of sweets. If he ate $\frac{7}{10}$ of them in one week, how many pieces of sweets did he eat? Step 1: Calculate the number of sweets Harish ate. $$\text{Sweets eaten} = \frac{7}{10} \times 30$$ $$\text{Sweets eaten} = 7 \times \frac{30}{10}$$ $$\text{Sweets eaten} = 7 \times 3$$ $$\text{Sweets eaten} = 21$$ Harish ate $\boxed{\text{21 pieces}}$ of sweets. 3. In a school, there are 480 children. If $\frac{1}{3}$ of them are boys, find the number of boys. Step 1: Calculate the number of boys. $$\text{Number of boys} = \frac{1}{3} \times 480$$ $$\text{Number of boys} = \frac{480}{3}$$ $$\text{Number of boys} = 160$$ The number of boys is $\boxed{\text{160}}$. 4. A student lives 5 km from the school. He travels $\frac{3}{5}$ km of the total distance by bus and walks the remaining distance. How far does he travel by bus? Step 1: Calculate the distance traveled by bus. $$\text{Distance by bus} = \frac{3}{5} \times 5 \text{ km}$$ $$\text{Distance by bus} = 3 \text{ km}$$ The student travels $\boxed{\text{3 km}}$ by bus. 5. A cylindrical rod of length $15\frac{1}{5}$ m is cut into 12 pieces. Find the length of each piece. Step 1: Convert the total length of the rod from a mixed fraction to an improper fraction. $$15\frac{1}{5} \text{ m} = \frac{(15 \times 5) + 1}{5} \text{ m} = \frac{75 + 1}{5} \text{ m} = \frac{76}{5} \text{ m}$$ Step 2: Divide the total length by the number of pieces to find the length of each piece. $$\text{Length of each piece} = \frac{76}{5} \text{ m} \div 12$$ $$\text{Length of each piece} = \frac{76}{5} \times \frac{1}{12} \text{ m}$$ $$\text{Length of each piece} = \frac{76}{60} \text{ m}$$ Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. $$\text{Length of each piece} = \frac{76 \div 4}{60 \div 4} \text{ m} = \frac{19}{15} \text{ m}$$ $$\text{Length of each piece} = 1\frac{4}{15} \text{ m}$$ The length of each piece is $\boxed{\frac{19}{15} \text{ m}}$ or $\boxed{1\frac{4}{15} \text{ m}}$. Send me the next one 📸