# Ratio

Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order.

Result

r = (Correct answer is: 6/2:3)

#### Solution:

$a=78 \ \\ b=26 \ \\ c=39 \ \\ \ \\ 78=2 \cdot 3 \cdot 13 \ \\ 26=2 \cdot 13 \ \\ 39=3 \cdot 13 \ \\ \text{GCD}(78, 26, 39)=13 \ \\ \ \\ x=GCD(a,b,c)=GCD(78,26,39)=13 \ \\ \ \\ r_{0}=a/x=78/13=6 \ \\ r_{1}=b/x=26/13=2 \ \\ r_{2}=c/x=39/13=3 \ \\ r=6:2:3$

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