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What percentage of the figure below is unshaded? Also, how many symbols would be needed to represent 65 huts if each symbol represents 13 huts? Simplify 9 - 11 + 6 ÷ 2.

Mathematics

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9. Pictograph

  1. Determine the number of symbols needed.

    Given that there are 65 huts in total and each symbol represents 13 huts, divide the total number of huts by the value each symbol represents.

    Number of symbols=Total hutsHuts per symbol=6513=5\text{Number of symbols} = \frac{\text{Total huts}}{\text{Huts per symbol}} = \frac{65}{13} = 5

  2. Describe the pictograph.

    To represent the information, you would draw 5 house symbols.

    Draw 5 house symbols\boxed{\text{Draw 5 house symbols}}

    10. Simplify: 9−11+6÷29 - 11 + 6 \div 2

  3. Perform the division first according to the order of operations (BODMAS/PEMDAS).

    6÷2=36 \div 2 = 3

  4. Substitute the result back into the expression.

    9−11+39 - 11 + 3

  5. Perform the subtraction and addition from left to right.

    (9−11)+3=−2+3=1(9 - 11) + 3 = -2 + 3 = 1 1\boxed{1}

    11. What percentage of the figure below is unshaded?

  6. Identify the total number of equal parts and the number of shaded parts.

    The figure is a square divided into 4 equal triangles by its diagonals. One of these triangles is shaded.
    Total parts = 4
    Shaded parts = 1

  7. Calculate the fraction of the figure that is unshaded.

    Fraction unshaded=Total parts−Shaded partsTotal parts=4−14=34\text{Fraction unshaded} = \frac{\text{Total parts} - \text{Shaded parts}}{\text{Total parts}} = \frac{4 - 1}{4} = \frac{3}{4}

  8. Convert the fraction to a percentage.

    Percentage unshaded=34×100%=0.75×100%=75%\text{Percentage unshaded} = \frac{3}{4} \times 100\% = 0.75 \times 100\% = 75\% 75%\boxed{75\%}

    12. Express 50 as a product of its prime factors.

  9. Divide 50 by the smallest prime number, 2.

    50÷2=2550 \div 2 = 25

  10. Divide 25 by the next smallest prime number that divides it, which is 5.

    25÷5=525 \div 5 = 5

  11. Divide 5 by 5.

    5÷5=15 \div 5 = 1

  12. Write 50 as the product of these prime factors.

    50=2×5×5=2×5250 = 2 \times 5 \times 5 = 2 \times 5^2 2×52\boxed{2 \times 5^2}

    13. Given that a US dollar cost Ush.3560, find the amount in Uganda shillings one can pay for a TV set which costs US dollars 150.

  13. Identify the exchange rate and the cost in US dollars.

    1 US dollar = Ush. 3560
    Cost of TV = US dollars 150

  14. Multiply the cost in US dollars by the exchange rate to find the amount in Uganda shillings.

    Amount in Ush.=Cost in USD×Exchange rate\text{Amount in Ush.} = \text{Cost in USD} \times \text{Exchange rate} Amount in Ush.=150×3560\text{Amount in Ush.} = 150 \times 3560

  15. Calculate the product.

    150×3560=534000150 \times 3560 = 534000

    The amount in Uganda shillings is Ush. 534,000.

    Ush. 534,000\boxed{\text{Ush. } 534,000}
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