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Convert "sawa sau lah" to a decimal fraction, and express "8.5 rupees" and "50 meters 4 cm" in their respective units.

Mathematics

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Question 7 (continued from previous page):

b) 8.5 روپے مطلب (8.5 rupees means)

  1. Separate the whole number and the decimal part.

    8.5 rupees=8 rupees+0.5 rupees8.5 \text{ rupees} = 8 \text{ rupees} + 0.5 \text{ rupees}

  2. Convert the decimal part of rupees to paisa.

    Since 1 rupee=100 paisa1 \text{ rupee} = 100 \text{ paisa},
    0.5 rupees=0.5×100 paisa=50 paisa0.5 \text{ rupees} = 0.5 \times 100 \text{ paisa} = 50 \text{ paisa}
    So, 8.5 rupees8.5 \text{ rupees} means 8 روپے 50 پیسے\boxed{\text{8 روپے 50 پیسے}}.

    c) 50 میٹر 4 سم یعنی (50 meters 4 cm means)

  3. Convert centimeters to meters.

    Since 1 meter=100 cm1 \text{ meter} = 100 \text{ cm},
    4 cm=4100 meters=0.04 meters4 \text{ cm} = \frac{4}{100} \text{ meters} = 0.04 \text{ meters}

  4. Add the meters together.

    50 meters+0.04 meters=50.04 meters50 \text{ meters} + 0.04 \text{ meters} = 50.04 \text{ meters}
    So, 50 meters 4 cm50 \text{ meters } 4 \text{ cm} means 50.04 میٹر\boxed{\text{50.04 میٹر}}.

    d) سوا سو لہ اس کسر کو عشری علامت کا استعمال کر کے لکھیے۔ (Write "sawa sau lah" as a decimal fraction.)
    The term "سوا" (sawa) means "one and a quarter" or 1141 \frac{1}{4}. The instruction asks to write this as a decimal fraction.

  5. Convert the mixed fraction to an improper fraction.

    114=1×4+14=541 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}

  6. Convert the fraction to a decimal.

    54=1.25\frac{5}{4} = 1.25
    (The terms "سو لہ" appear to be extraneous or a typo in this context, as "سوا" directly translates to the required decimal fraction.)
    The decimal fraction is 1.25\boxed{\text{1.25}}.

    Question 8:

    a) ذیل کے اعداد میں مثلثی عدد کے گرد دائرہ بنائیے۔ (Circle the triangular number among the following numbers.)
    The given numbers are: 4, 5, 6, 8, 9, 10, 12.
    Triangular numbers are numbers obtained by summing consecutive positive integers starting from 1.
    The sequence of triangular numbers is:
    T1=1T_1 = 1
    T2=1+2=3T_2 = 1+2 = 3
    T3=1+2+3=6T_3 = 1+2+3 = 6
    T4=1+2+3+4=10T_4 = 1+2+3+4 = 10
    T5=1+2+3+4+5=15T_5 = 1+2+3+4+5 = 15
    From the given list, the triangular numbers are 6 and 10. Since the question asks for "the" triangular number (singular), we will identify the first one in the list.
    The triangular number is 6\boxed{\text{6}}.

    b) ذیل کے تواتر کو مکمل کیجیے۔ (Complete the following sequence.)
    The sequence is: 10, 15, 21, .........

  7. Find the difference between consecutive terms.

    15−10=515 - 10 = 5
    21−15=621 - 15 = 6

  8. Observe the pattern in the differences.

    The differences are increasing by 1 (5, then 6). So, the next difference should be 7.

  9. Add the next difference to the last term to find the next number in the sequence.

    Next term = 21+7=2821 + 7 = 28
    The completed sequence is 10, 15, 21, 28\boxed{\text{28}}.

    c) ذیل کے تواتر کو مکمل کیجیے۔ (Complete the following sequence.)
    The sequence shows patterns of dots:

    • First image: 5 rows of 5 dots, total 5×5=255 \times 5 = 25 dots.
    • Second image: 4 rows of 4 dots, total 4×4=164 \times 4 = 16 dots.
    • Third image: 3 rows of 3 dots, total 3×3=93 \times 3 = 9 dots. The pattern is a sequence of decreasing perfect squares: 52,42,325^2, 4^2, 3^2.
  10. Determine the next terms in the sequence.

    The next term should be 22=42^2 = 4 dots.
    The term after that should be

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