The scale of the map is 1: 1,000,000. How many kilometers are there between objects if the distance between them on the map is 3 centimeters?
1. Let’s make the proportion:
1/1000000 = 3 / x.
We use the main property of the “cross to cross” proportion: to find the unknown denominator of the second fraction (x), it is necessary to multiply the denominator of the first fraction (1,000,000) by the numerator of the second fraction (3) and divide this product by the numerator of the first fraction (1). Thus:
x = 1,000,000 * 3/1 = 1,000,000 * 3 = 3,000,000 (cm).
2. Since we need to calculate what the distance between objects will be in kilometers, we will translate 3,000,000 cm into km.
1 m contains 100 cm, then:
1 m = 100 cm;
x = 3,000,000 cm.
x = 3,000,000 / 100 = 30,000 (m).
1 km contains 1000 m, then:
1 km = 1000 m;
x = 30,000 m.
x = 30000/1000 = 30 (km).
Thus, 3,000,000 cm is equal to 30 km.
Answer: 30 km.
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