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Complete the table: Items, Price of each, Total expenses. 5kg of meat 3000frw/kg, 5kg of rice 6600frw, litre of honey 4050frw. If he had 45000frw and save the rest, how much did he save?

Mathematics

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Question 30:

a)

  1. Convert the division to an equivalent form without decimals.

    0.4÷0.005=0.40.0050.4 \div 0.005 = \frac{0.4}{0.005}

    Multiply the numerator and denominator by 1000 to remove decimals:

    0.4×10000.005×1000=4005\frac{0.4 \times 1000}{0.005 \times 1000} = \frac{400}{5}
  2. Perform the division.

    4005=80\frac{400}{5} = 80

    The result is 80\boxed{80}.

    b)

  3. Perform the multiplication.

    215,327×216215,327 \times 216 215,327×216=46,500,632215,327 \times 216 = 46,500,632

    The product is 46,500,632\boxed{46,500,632}.

    Question 31:

    a) Complete the table:

  4. Calculate the total expenses for 5kg of meat.

    Price of meat =3000 Frw/kg= 3000 \text{ Frw/kg}.
    Total expenses for meat =5 kg×3000 Frw/kg=15000 Frw= 5 \text{ kg} \times 3000 \text{ Frw/kg} = 15000 \text{ Frw}.
    So, (i) is 15000 Frw\boxed{15000 \text{ Frw}}.

  5. Calculate the price per kg for 5kg of rice.

    Total expenses for rice =6600 Frw= 6600 \text{ Frw}.
    Price of rice per kg =6600 Frw5 kg=1320 Frw/kg= \frac{6600 \text{ Frw}}{5 \text{ kg}} = 1320 \text{ Frw/kg}.
    So, (ii) is 1320 Frw/kg\boxed{1320 \text{ Frw/kg}}.

  6. Calculate the quantity of honey.

    Price of honey =4050 Frw/litre= 4050 \text{ Frw/litre}.
    Total expenses for honey =18225 Frw= 18225 \text{ Frw}.
    Quantity of honey =18225 Frw4050 Frw/litre=4.5 litres= \frac{18225 \text{ Frw}}{4050 \text{ Frw/litre}} = 4.5 \text{ litres}.
    So, (iii) is 4.5 litres\boxed{4.5 \text{ litres}}.

  7. Calculate the total expenses.

    Total expenses =(Meat expenses)+(Rice expenses)+(Honey expenses)= (\text{Meat expenses}) + (\text{Rice expenses}) + (\text{Honey expenses})
    Total expenses =15000 Frw+6600 Frw+18225 Frw=39825 Frw= 15000 \text{ Frw} + 6600 \text{ Frw} + 18225 \text{ Frw} = 39825 \text{ Frw}.
    So, (iv) is 39825 Frw\boxed{39825 \text{ Frw}}.

    b) If he had 45000 Frw and saved the rest, how much did he save?

  8. Calculate the amount saved.

    Amount saved =Money had−Total expenses= \text{Money had} - \text{Total expenses}
    Amount saved =45000 Frw−39825 Frw=5175 Frw= 45000 \text{ Frw} - 39825 \text{ Frw} = 5175 \text{ Frw}.
    He saved 5175 Frw\boxed{5175 \text{ Frw}}.

    Question 32:

    a) Find the sum of all prime numbers between 0 and 10.

  9. Identify the prime numbers between 0 and 10.

    Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
    The prime numbers between 0 and 10 are $2, 3, 5, 7$.

  10. Calculate their sum.

    2+3+5+7=172 + 3 + 5 + 7 = 17

    The sum is 17\boxed{17}.

    b) Use quick calculation: 235×99235 \times 99

  11. Rewrite 99 as (100−1)(100 - 1).

    235×99=235×(100−1)235 \times 99 = 235 \times (100 - 1)
  12. Apply the distributive property.

    235×100−235×1235 \times 100 - 235 \times 1 23500−23523500 - 235
  13. Perform the subtraction.

    23500−235=2326523500 - 235 = 23265

    The result is 23265\boxed{23265}.

    Question 33:

    a) If 7 kg of rice is equivalent to 6,300 Frw. How much are 12 kg of the same rice?

  14. Find the price of 1 kg of rice.

    Price per kg =6300 Frw7 kg=900 Frw/kg= \frac{6300 \text{ Frw}}{7 \text{ kg}} = 900 \text{ Frw/kg}.

  15. Calculate the cost of 12 kg of rice.

    Cost of 12 kg =12 kg×900 Frw/kg=10800 Frw= 12 \text{ kg} \times 900 \text{ Frw/kg} = 10800 \text{ Frw}.
    12 kg of rice costs 10800 Frw\boxed{10800 \text{ Frw}}.

    b) Find the sum of LCM and GCF of 12, 15 and 36.

  16. Find the prime factorization of each number.

    12=22×3112 = 2^2 \times 3^1 15=31×5115 = 3^1 \times 5^1 36=22×3236 = 2^2 \times 3^2
  17. Calculate the GCF (Greatest Common Factor).

    The GCF is the product of the lowest powers of all common prime factors. The only common prime factor is 3, and its lowest power is 313^1.

    GCF(12,15,36)=31=3\text{GCF}(12, 15, 36) = 3^1 = 3
  18. Calculate the LCM (Least Common Multiple).

    The LCM is the product of the highest powers of all prime factors present in any of the numbers.
    Highest power of 2 is 222^2.
    Highest power of 3 is 323^2.
    Highest power of 5 is 515^1.

    LCM(12,15,36)=22×32×51=4×9×5=180\text{LCM}(12, 15, 36) = 2^2 \times 3^2 \times 5^1 = 4 \times 9 \times 5 = 180
  19. Find the sum of the LCM and GCF.

    Sum=LCM+GCF=180+3=183\text{Sum} = \text{LCM} + \text{GCF} = 180 + 3 = 183

    The sum of the LCM and GCF is 183\boxed{183}.

    Question 34:
    Calculate the area of a right-angled triangle whose base is 3 cm and height of 7 cm.

  20. Write the formula for the area of a triangle.

    Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
  21. Substitute the given values.

    Area=12×3 cm×7 cm\text{Area} = \frac{1}{2} \times 3 \text{ cm} \times 7 \text{ cm}
  22. Calculate the area.

    Area=12×21 cm2=10.5 cm2\text{Area} = \frac{1}{2} \times 21 \text{ cm}^2 = 10.5 \text{ cm}^2

    The area of the triangle is 10.5 cm2\boxed{10.5 \text{ cm}^2}.

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