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A school has 960 pupils. If 3/5 are boys, how many girls are there? (2 marks) (b) A number is divisible by both 3 and 4. Give the smallest 3-digit number that meets this condition (2 marks) 23. Round off 78.456 to: (a) The nearest whole number (1 mark) (b) One decimal place (1 mark)

Mathematics

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Answers

4 parts
21

108\text{108}

22

384 wasichana\text{384 wasichana}

a

78\text{78}

b

78.5\text{78.5}

Step-by-step solution

6 steps

Sawa Safron, twende na maswali haya ya hesabu.

Part 21· 2 steps

(b)

Nambari inayogawanyika na 3 na 4 ni nambari inayogawanyika na Kigawo Kidogo Zaidi cha Pamoja (LCM) cha 3 na 4.

  1. Tafuta LCM ya 3 na 4.

    LCM(3,4)=12\text{LCM}(3, 4) = 12
  2. Tafuta nambari ndogo zaidi ya tarakimu 3 ambayo ni zao la 12.

    Nambari ndogo zaidi ya tarakimu 3 ni 100.
    Gawanya 100 kwa 12:

    10012=8 na baki ya 4\frac{100}{12} = 8 \text{ na baki ya } 4

    Hii inamaanisha 12×8=9612 \times 8 = 96 (nambari ya tarakimu 2).
    Nambari inayofuata ya tarakimu 3 ambayo ni zao la 12 ni:

    12×9=10812 \times 9 = 108

    Nambari hii ni ya tarakimu 3 na inagawanyika na 3 na 4.

    Jibu: 108\boxed{\text{108}}

Part 22

384 wasichana\text{384 wasichana}

Shule ina jumla ya wanafunzi 960. Ikiwa 35\frac{3}{5} ni wavulana, tunahitaji kujua idadi ya wasichana.

  1. Tafuta sehemu ya wasichana.

    Jumla ya sehemu ni 1.

    Sehemu ya wasichana=1−35=55−35=25\text{Sehemu ya wasichana} = 1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{2}{5}
  2. Kokotoa idadi ya wasichana.

    Idadi ya wasichana=25×960\text{Idadi ya wasichana} = \frac{2}{5} \times 960 Idadi ya wasichana=2×9605\text{Idadi ya wasichana} = 2 \times \frac{960}{5} Idadi ya wasichana=2×192\text{Idadi ya wasichana} = 2 \times 192 Idadi ya wasichana=384\text{Idadi ya wasichana} = 384

    Jibu: 384 wasichana\boxed{\text{384 wasichana}}

Part 23

Zungusha 78.456 kwa:

Part a

78\text{78}

Nambari kamili iliyo karibu zaidi

  1. Angalia tarakimu ya kwanza baada ya desimali, ambayo ni 4.

    Kwa kuwa 4 ni chini ya 5, tunazungusha chini (tunaacha nambari kamili kama ilivyo).

    78.456≈7878.456 \approx 78

    Jibu: 78\boxed{\text{78}}

Part b

78.5\text{78.5}

Sehemu moja ya desimali

  1. Angalia tarakimu ya pili baada ya desimali, ambayo ni 5.

    Kwa kuwa 5 ni 5 au zaidi, tunazungusha juu tarakimu ya kwanza baada ya desimali.
    Tarakimu ya kwanza baada ya desimali ni 4, kwa hivyo inakuwa 5.

    78.456≈78.578.456 \approx 78.5

    Jibu: 78.5\boxed{\text{78.5}}

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