Question

Jacob used 1/7 of a liter of water to fill 1/9 of the fish aquarium. How many liters r needed to fill the aquarium?

Answer 1

we know that 1/7 of a liter filled up 1/9 of the aquarium, well, a "whole" will be 9/9.

how many liters will it be to fill up the 9/9 of the aquarium?


`\bf \begin{array}{ccll} \stackrel{liters}{water}&\stackrel{fish}{aquarium}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ (1)/(7)&(1)/(9)\\\\ w&(9)/(9) \end{array}\implies \cfrac{(1)/(7)}{w}=\cfrac{(1)/(9)}{(9)/(9)}\implies \cfrac{(1)/(7)}{(w)/(1)}=\cfrac{(1)/(9)}{(9)/(9)}\implies \cfrac{1}{7}\cdot \cfrac{1}{w}=\cfrac{1}{9}\cdot \cfrac{9}{9} \\\\\\ \cfrac{1}{7w}=\cfrac{1}{9}\implies 9=7w\implies \cfrac{9}{7}=w`

Answer 2

Since 1/7 L of water fills 1/9 of the aquarium, 9 times 1/7 will fill the aquarium:

9(1/7) = 9/7 = 1 2/7 L of water will fill the aquarium.