In a forest meadow

The students planted 280 spruces and 60 pines on forest plots. Express the ratio of the number of planted pines to the number of planted spruces as the smallest possible natural numbers.

Final Answer:

r =  3:14

Step-by-step explanation:

$$\begin{gathered} a=280 \\ b=60 \\ 280=2^3\cdot 5\cdot 7 \\ 60=2^2\cdot 3\cdot 5 \\ \text{GCD}(280,60)=2^2\cdot 5=20 \\ x=GCD(a,b)=GCD(280,60)=20 \\ a=280=14\cdot 20=14x \\ b=60=3\cdot 20=3x \\ r=\frac{b}{a}=\frac{60}{280}=\frac{3}{14}\approx 0.2143=3:14 \end{gathered}$$

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