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A) Change 1(1)/(5) as a percentage.

Mathematics

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3.

a) Change 1151\frac{1}{5} as a percentage.

  1. Convert the mixed number to an improper fraction.

    115=(1×5)+15=651\frac{1}{5} = \frac{(1 \times 5) + 1}{5} = \frac{6}{5}
  2. Convert the fraction to a decimal.

    65=1.2\frac{6}{5} = 1.2
  3. Convert the decimal to a percentage.

    1.2×100%=120%1.2 \times 100\% = 120\%

    The percentage is 120%\boxed{120\%}.

    b) Find the smallest number that can be divided by 48,3248, 32 and 40.

    This requires finding the Least Common Multiple (LCM) of 48,32,48, 32, and 40.

  4. Find the prime factorization of each number.

    48=24×348 = 2^4 \times 3 32=2532 = 2^5 40=23×540 = 2^3 \times 5
  5. Take the highest power of each prime factor present in any of the numbers.

    Highest power of 2: 252^5
    Highest power of 3: 313^1
    Highest power of 5: 515^1

  6. Multiply these highest powers together.

    LCM(48,32,40)=25×31×51=32×3×5=480\text{LCM}(48, 32, 40) = 2^5 \times 3^1 \times 5^1 = 32 \times 3 \times 5 = 480

    The smallest number is 480\boxed{480}.

    c) Find the next number in the series below: 2,3,5,7,9,_2, 3, 5, 7, 9, \_

  7. Analyze the differences between consecutive terms.

    3−2=13 - 2 = 1
    5−3=25 - 3 = 2
    7−5=27 - 5 = 2
    9−7=29 - 7 = 2

  8. Identify the pattern in the differences.

    The differences are $1, 2, 2, 2$. After the first term, each subsequent term is found by adding 2 to the previous term.

  9. Apply the pattern to find the next number.

    The next number is 9+2=119 + 2 = 11.
    The next number is 11\boxed{11}.

    4.

    a) Find the square of 323^2.

  10. Calculate 323^2.

    32=3×3=93^2 = 3 \times 3 = 9
  11. Find the square of the result.

    Square of 9=92=9×9=81\text{Square of } 9 = 9^2 = 9 \times 9 = 81

    The square of 323^2 is 81\boxed{81}.

    b) Calculate 441−256\sqrt{441} - \sqrt{256}.

  12. Calculate 441\sqrt{441}.

    441=21\sqrt{441} = 21
  13. Calculate 256\sqrt{256}.

    256=16\sqrt{256} = 16
  14. Subtract the values.

    21−16=521 - 16 = 5

    The result is 5\boxed{5}.

    c) Write 0.75 as a simple fraction.

  15. Write the decimal as a fraction.

    0.75=751000.75 = \frac{75}{100}
  16. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25.

    75÷25100÷25=34\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

    The simple fraction is 34\boxed{\frac{3}{4}}.

    5.

    a) The bus started the journey from Sumbawanga at 12201220hours and arrived in Tabora at 18551855hours. How long did the bus take to travel from Sumbawanga to Tabora?

  17. Identify the start and end times.

    Start time: 12 hours 20 minutes
    End time: 18 hours 55 minutes

  18. Subtract the start time from the end time.

    Subtract minutes: 55 minutes−20 minutes=35 minutes55 \text{ minutes} - 20 \text{ minutes} = 35 \text{ minutes}.
    Subtract hours: 18 hours−12 hours=6 hours18 \text{ hours} - 12 \text{ hours} = 6 \text{ hours}.
    The bus took 6 hours and 35 minutes\boxed{6 \text{ hours and } 35 \text{ minutes}}.

    b) A chicken hatches a chick after incubating eggs for 21 days. What is this duration in hours?

  19. Convert days to hours.

    There are 24 hours in 1 day.

  20. Multiply the number of days by 24.

    21 days×24hoursday=504 hours21 \text{ days} \times 24 \frac{\text{hours}}{\text{day}} = 504 \text{ hours}

    The duration in hours is 504 hours\boxed{504 \text{ hours}}.

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