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A road which is 300 km long is represented on a map by 6cm. What scale is used to represent this length.

Mathematics

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Answer

1:5,000,000\text{1:5,000,000}

Step-by-step solution

4 steps

  1. Andika urefu halisi wa barabara na urefu wake kwenye ramani.

    Urefu wa barabara halisi = 300 km300 \text{ km}
    Urefu wa barabara kwenye ramani = 6 cm6 \text{ cm}

  2. Badilisha urefu halisi wa barabara kuwa sentimita ili kuendana na kitengo cha urefu kwenye ramani.

    Tunajua kuwa 1 km=1000 m1 \text{ km} = 1000 \text{ m} na 1 m=100 cm1 \text{ m} = 100 \text{ cm}.
    Hivyo, 1 km=1000×100 cm=100,000 cm1 \text{ km} = 1000 \times 100 \text{ cm} = 100,000 \text{ cm}.
    Urefu wa barabara halisi katika sentimita:

    300 km=300×100,000 cm=30,000,000 cm300 \text{ km} = 300 \times 100,000 \text{ cm} = 30,000,000 \text{ cm}

  3. Kokotoa kipimo (scale) kwa kugawa urefu kwenye ramani kwa urefu halisi.

    Kipimo = Urefu kwenye ramaniUrefu halisi\frac{\text{Urefu kwenye ramani}}{\text{Urefu halisi}}
    Kipimo = 6 cm30,000,000 cm\frac{6 \text{ cm}}{30,000,000 \text{ cm}}

  4. Rahisisha uwiano ili upate fomu ya $1:n$.

    Gawanya namba zote mbili kwa 6:

    66:30,000,0006\frac{6}{6} : \frac{30,000,000}{6} 1:5,000,0001 : 5,000,000
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