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Operations on Whole Numbers

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6. Operations on Whole Numbers

  • a) A sick person takes 10 ml of medicine three times a day.
    • (i) Mathematical expression: 10×310 \times 3
    • (ii) Medicine taken in 15 days:
  1. Calculate medicine per day.

        $$
        10 \text{ ml/dose} \times 3 \text{ doses/day} = 30 \text{ ml/day}
        $$
    
  2. Calculate medicine in 15 days.

        $$
        30 \text{ ml/day} \times 15 \text{ days} = \boxed{450 \text{ ml}}
        $$
    
    • b) The distance between Dakshe's house and his school is 7 km.
      • (i) Mathematical expression for total distance traveled in 1 day (to school and back): 7×27 \times 2
      • (ii) Kilometres traveled in 6 days:
  3. Calculate distance traveled in 1 day.

        $$
        7 \text{ km/way} \times 2 \text{ ways/day} = 14 \text{ km/day}
        $$
    
  4. Calculate distance traveled in 6 days.

        $$
        14 \text{ km/day} \times 6 \text{ days} = \boxed{84 \text{ km}}
        $$
    
    • c) Mrs. Chamling earns Rs 6,000 in a week. She spends Rs 250 for food and Rs 75 for transportation everyday.
      • (i) Mathematical expression to show her weekly savings: 6000−(250+75)×76000 - (250 + 75) \times 7
      • (ii) Money she saves in a week:
  5. Calculate daily expenses.

        $$
        250 \text{ Rs (food)} + 75 \text{ Rs (transport)} = 325 \text{ Rs/day}
        $$
    
  6. Calculate weekly expenses.

        $$
        325 \text{ Rs/day} \times 7 \text{ days/week} = 2275 \text{ Rs/week}
        $$
    
  7. Calculate weekly savings.

        $$
        6000 \text{ Rs (earnings)} - 2275 \text{ Rs (expenses)} = \boxed{3725 \text{ Rs}}
        $$
    
    • d) Sunayana had 20 marbles. She lost 6 marbles and she divided the rest of them among her 7 friends.
      • (i) Mathematical expression: 20−67\frac{20 - 6}{7}
      • (ii) Marbles each friend would get:
  8. Calculate remaining marbles.

        $$
        20 \text{ marbles} - 6 \text{ marbles lost} = 14 \text{ marbles}
        $$
    
  9. Divide remaining marbles among 7 friends.

        $$
        \frac{14 \text{ marbles}}{7 \text{ friends}} = \boxed{2 \text{ marbles/friend}}
        $$
    
    • e) Pratik has 300 rupees. He buys 2 boxes at Rs 60 each and 3 pens at Rs 30 each. Write a mathematical expression to show this information. Simplify it and find how much money is left with him?
      • Mathematical expression: 300−(2×60+3×30)300 - (2 \times 60 + 3 \times 30)
      • Money left with him:
  10. Calculate cost of boxes.

        $$
        2 \times 60 \text{ Rs} = 120 \text{ Rs}
        $$
    
  11. Calculate cost of pens.

        $$
        3 \times 30 \text{ Rs} = 90 \text{ Rs}
        $$
    
  12. Calculate total money spent.

        $$
        120 \text{ Rs} + 90 \text{ Rs} = 210 \text{ Rs}
        $$
    
  13. Calculate money left.

        $$
        300 \text{ Rs} - 210 \text{ Rs} = \boxed{90 \text{ Rs}}
        $$
    
    • f) There are two baskets each of them containing 18 apples. 10 apples are rotten and not fit for eating. You add 4 more apples and then divide among 6 friends. Show this information in a mathematical expression. Simplify it and find how many apples would each friend get?
      • Mathematical expression: ((2×18)−10)+46\frac{((2 \times 18) - 10) + 4}{6}
      • Apples each friend would get:
  14. Calculate initial total apples.

        $$
        2 \text{ baskets} \times 18 \text{ apples/basket} = 36 \text{ apples}
        $$
    
  15. Subtract rotten apples.

        $$
        36 \text{ apples} - 10 \text{ rotten apples} = 26 \text{ apples}
        $$
    
  16. Add new apples.

        $$
        26 \text{ apples} + 4 \text{ new apples} = 30 \text{ apples}
        $$
    
  17. Divide among friends.

        $$
        \frac{30 \text{ apples}}{6 \text{ friends}} = \boxed{5 \text{ apples/friend}}
        $$
    

    7. It's your time - Project work and Activity Section

    • a) Let's make a mathematical expression using the symbols ÷\div and ++ between the numbers 4, 12 and 8 to get the result 11.

      • Mathematical expression: 12÷4+8=1112 \div 4 + 8 = \boxed{11}
    • b) Let's use the symbol ÷\div and ×\times between the numbers 5, 20 and 2 at appropriate place to get the result 2. You can use brackets if necessary.

      • Mathematical expression: 20÷(5×2)=220 \div (5 \times 2) = \boxed{2}
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