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Convert 21 from base 10 to base 2. Calculate 15% discount on N5,000. List 3 cylindrical and 3 rectangular prism household objects. Simplify 5x + 10 - 2x + 4.

Mathematics

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MATHEMATICS

1. Number Bases: Convert 21 from Base 10 to Base 2

  1. Divide 21 by 2.

    21÷2=10 remainder 121 \div 2 = 10 \text{ remainder } 1
  2. Divide 10 by 2.

    10÷2=5 remainder 010 \div 2 = 5 \text{ remainder } 0
  3. Divide 5 by 2.

    5÷2=2 remainder 15 \div 2 = 2 \text{ remainder } 1
  4. Divide 2 by 2.

    2÷2=1 remainder 02 \div 2 = 1 \text{ remainder } 0
  5. Divide 1 by 2.

    1÷2=0 remainder 11 \div 2 = 0 \text{ remainder } 1
  6. Read the remainders from bottom to top.

    The base 2 representation of 21 is:

    101012\boxed{10101_2}

    2. Percentages: Calculate the discount on an Easter hamper

  7. Calculate 15% of N5,000.

    Discount=15%×N5,000\text{Discount} = 15\% \times \text{N}5,000 Discount=15100×5000\text{Discount} = \frac{15}{100} \times 5000
  8. Perform the multiplication.

    Discount=15×50\text{Discount} = 15 \times 50 Discount=750\text{Discount} = 750

    The discount is:

    N750\boxed{\text{N}750}

    3. Geometry: List 3 cylindrical and 3 rectangular prism household objects

    • Cylindrical Objects:
      • Tin can (e.g., for food)
      • Toilet paper roll
      • Drinking glass
    • Rectangular Prism Objects:
      • Book
      • Shoebox
      • Brick

    4. Algebra: Simplify the expression 5x+10−2x+45x + 10 - 2x + 4

  9. Group like terms.

    (5x−2x)+(10+4)(5x - 2x) + (10 + 4)
  10. Combine the xx terms.

    (5−2)x=3x(5 - 2)x = 3x
  11. Combine the constant terms.

    10+4=1410 + 4 = 14

    The simplified expression is:

    3x+14\boxed{3x + 14}

    5. Fractions: Calculate the fraction of cake left

  12. Find the total fraction of cake eaten.

    Total eaten=25+14\text{Total eaten} = \frac{2}{5} + \frac{1}{4}
  13. Find a common denominator, which is 20.

    Total eaten=2×45×4+1×54×5\text{Total eaten} = \frac{2 \times 4}{5 \times 4} + \frac{1 \times 5}{4 \times 5} Total eaten=820+520\text{Total eaten} = \frac{8}{20} + \frac{5}{20} Total eaten=8+520=1320\text{Total eaten} = \frac{8 + 5}{20} = \frac{13}{20}
  14. Subtract the eaten fraction from the whole cake (1).

    Fraction left=1−1320\text{Fraction left} = 1 - \frac{13}{20} Fraction left=2020−1320\text{Fraction left} = \frac{20}{20} - \frac{13}{20} Fraction left=20−1320=720\text{Fraction left} = \frac{20 - 13}{20} = \frac{7}{20}

    The fraction of the whole cake left is:

    720\boxed{\frac{7}{20}}

    6. Decimals: Solve 12.5×0.412.5 \times 0.4 without using a calculator

  15. Multiply the numbers as if they were whole numbers.

    125×4=500125 \times 4 = 500
  16. Count the total number of decimal places in the original numbers.

    12.5 has 1 decimal place.

    0.4 has 1 decimal place.
    Total decimal places = 1+1=21 + 1 = 2.

  17. Place the decimal point in the product (500) two places from the right.

    5.005.00

    The product is:

    5\boxed{5}

    7. LCM: Find the Lowest Common Multiple (LCM) of 12, 18, and 24

  18. List the prime factorization of each number.

    12=22×3112 = 2^2 \times 3^1 18=21×3218 = 2^1 \times 3^2 24=23×3124 = 2^3 \times 3^1
  19. For each prime factor, take the highest power that appears in any of the factorizations.

    For 2: The highest power is 232^3 (from 24).
    For 3: The highest power is 323^2 (from 18).

  20. Multiply these highest powers together.

    LCM=23×32\text{LCM} = 2^3 \times 3^2 LCM=8×9\text{LCM} = 8 \times 9 LCM=72\text{LCM} = 72

    The Lowest Common Multiple is:

    72\boxed{72}

    8. Angles: Draw an angle of 120∘120^\circ and label it correctly as "Obtuse"

    An angle of 120∘120^\circ is an obtuse angle because it is greater than 90∘90^\circ but less than 180∘180^\circ.
    To draw it:

    • Draw a straight line segment. This will be one arm of the angle.
    • Place the protractor's center on one endpoint of the line segment (the vertex). Align the baseline of the protractor with the line segment.
    • Find the 120∘120^\circ mark on the protractor and make a small dot.
    • Draw a second line segment from the vertex to the dot.
    • Label the angle as 120∘120^\circ and indicate that it is an obtuse angle.

    9. Word Problem: Calculate cloth needed for 6 outfits

  21. Multiply the cloth needed for one outfit by the number of outfits.

    Total cloth=2.5 meters/outfit×6 outfits\text{Total cloth} = 2.5 \text{ meters/outfit} \times 6 \text{ outfits}
  22. Perform the multiplication.

    Total cloth=15 meters\text{Total cloth} = 15 \text{ meters}

    The total meters of cloth needed is:

    15 meters\boxed{15 \text{ meters}}

    10. Symmetry: Draw a square and a rectangle and their lines of symmetry

    • Square: A square has 4 lines of symmetry.
      • Two lines pass through the midpoints of opposite sides (horizontal and vertical).
      • Two lines pass through opposite vertices (diagonals).
    • Rectangle: A rectangle has 2 lines of symmetry.
      • Two lines pass through the midpoints of opposite sides (one horizontal, one vertical).
      • (A rectangle does not have diagonal lines of symmetry unless it is also a square).

    DIGITAL TECHNOLOGIES

    Shortcut Challenge:

    • a) Highlight your name and press Ctrl + B. What happened to the text?
      • The text became bold.
    • b) Press Ctrl + E. Where did your text move to on the page?
      • The text moved to the center of the page.
    • c) Press Ctrl + J three times. Did the text get smaller or larger?
      • Ctrl + J is the shortcut for Justify alignment in Microsoft Word. It aligns text to both the left and right margins. It does not make the text smaller or larger.
    • d) Observation: In the "Insert" tab, click "Shapes". Draw a star. Which menu tab appears at the very top (usually in a different color) once the star is selected?
      • The Format tab (specifically "Shape Format" or "Drawing Tools Format") appears.
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